calculate the cost of 4 liters of gasoline if 10 Liters of gasoline cost $8.20 (using proportional relationship).

A . $3.28
B. $4.20
C. $8.20
D.$10

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Answer:

  Tn = -4n² +40n +36

Step-by-step explanation:

A graphing calculator readily performs the quadratic regression, yielding the formula ...

  Tn = -4n² +40n +36

__

The first and second differences of the given sequence terms are ...

  28, 20, 12 and -8, -8

The coefficient of the squared term is half the second difference, so is -4. Then the sequence of squared terms is -4n²:

  -4, -16, -36, -64

Subtracting these values from the original sequence gives the linear sequence ...

  76, 116, 156, 196

which has first term 76 and common difference 40. The equation for the n-th term of this is ...

  an = 76 +40(n -1) = 36 +40n

Adding this linear sequence to the sequence of squared terms, we get ...

  Tn = -4n² +40n +36

Answer:

-(x+6) (x-8)

Step-by-step explanation:

-(x^2-2x-48)

two values the multiply to get 48 and the difference of those two numbers gives you -2.

6,-8

6 x -8 =-48

6-8=-2

In this case we factored out the negative so leave it outside

-(x+6) (x-8)

Answer:

-1(x-8)(x+6) is the answer just took the test

Step-by-step explanation:

Answer:draw a triangle

Step-by-step explanation:

Answer: (300 + 45x) / x

Step-by-step explanation:

Based on the information given in the question, the total cost will be the addition of the fixed cost and the variable cost which will be:

= 300 + (45 × x)

= 300 + 45x

The amount that needs to be charge for each attendee in order to cover the cost of hosting the event will be:

= (300 + 45x) / x

Answer:

So, remember that:

cos(x) > 0   for  -pi/2 < x < pi/2

cos(x) < 0 for  pi/2 < x < (3/2)*pi

and

sin(x) > 0 for 0 < x < pi

sin(x) < 0 for -pi < x <0  or  pi < x < 2pi

Also, we have the periodicty of the sine and cocine equations, such that:

sin(x) = sin(x + 2pi)

cos(x) = cos(x + 2pi)

Now let's solve the problem:

[tex]sin(\frac{13*\pi}{36} )[/tex]

here we have:

x = (13/36)π

This is larger than zero and smaller than π:

0 < (13/36)π < π

then:

[tex]sin(\frac{13*\pi}{36} )[/tex]

Is positive.

The next one is:

[tex]cos(\frac{7*\pi}{12} )[/tex]

Here we have x = (7/12)*pi

notice that:

7/12 > 1/2

Then:

(7/12)*π > (1/2)*π

Then:

[tex]cos(\frac{7*\pi}{12} )[/tex]

is negative.

next one:

[tex]sin(\frac{47*\pi}{36} )[/tex]

here:

x = (47/36)*π

here we have (47/36) > 1

then:

(47/36)*π > π

then:

[tex]sin(\frac{47*\pi}{36} )[/tex]

is negative.

the next one is:

[tex]cos(\frac{17*\pi}{10} )[/tex]

Here we have x = (17/10)*π

if we subtract 2*π (because of the periodicity) we get:

(17/10)*π - 2*π

(17/10)*π - (20/10)*π

(-3/10)*π

this is in the range where the cosine function is positive, thus:

[tex]cos(\frac{17*\pi}{10} )[/tex]

is positive.

the next one is:

[tex]tan(\frac{41*\pi}{36} ) = \frac{sin(\frac{41*\pi}{36} )}{cos(\frac{41*\pi}{36} )}[/tex]

here we have:

x = (41/36)*π

Notice that both functions, sine and cosine are negatives for that value, then we have the quotient of two negative values, so:

[tex]tan(\frac{41*\pi}{36} ) = \frac{sin(\frac{41*\pi}{36} )}{cos(\frac{41*\pi}{36} )}[/tex]

is positive.

The final one is:

[tex]tan(\frac{5*\pi}{9} ) = \frac{sin(\frac{5*\pi}{9} )}{cos(\frac{5*\pi}{9} )}[/tex]

Here:

x = (5/9)*π

The sin function is positive with this x value, while the cosine function is negative, thus:

[tex]tan(\frac{5*\pi}{9} ) = \frac{sin(\frac{5*\pi}{9} )}{cos(\frac{5*\pi}{9} )}[/tex]

Is negative.

9514 1404 393

Answer:

  $19.36

Step-by-step explanation:

Any average is the sum of numbers, divided by the number of them.

Here, the numbers are grouped, but the computation of the average works the same way.

The total value of donations received is ...

  $100×10 +$50×20 +$20×30 +$10×100 +$5×35

  = $1000 +1000 +600 +1000 +175 = $3775

The total number of donations received is ...

  10 +20 +30 +100 +35 = 195

Then the average (mean) donation is the total value divided by the total number ...

  $3775/195 ≈ $19.35897 ≈ $19.36 . . . mean donation

Answer:

quadratic

y=mx+c

Step-by-step explanation:

Answer:

y = 11/20

Step-by-step explanation:

-4/5 + y = -1/4

Add 4/5 to each side

-4/5  +4/5 + y = -1/4+4/5

y = -1/4 + 4/5

Get a common denominator

y = -1/4 *5/5   + 4/5 *4/4

y = -5/20 + 16/20

y = 11/20

Check

-4/5 +11/20 = -1/4

Get a common denominator

-4/5*4/4 + 11/20 = -1/4*5/5

-16/20 +11/20 = -5/20

-5/20 = - 5/20

Check

Step-by-step explanation:

[tex] - \frac{4}{5} + y = - \frac{1}{4} \\ y = \frac{ - 1}{4} + \frac{4}{5} \\ y = \frac{ - 5 + 16}{20} \\ y = \frac{11}{20} [/tex]

[tex]y = \frac{11}{20} [/tex]

The distance between Balloon B and Balloon A is 999 feet (correct to the nearest whole number); that is, Balloon B is 999 feet from balloon A

The diagram for the question is shown as described in the question in the attachment below.

From the diagram,

Let the height from balloon A to the ground be /AG/ and the height from balloon B to the ground be /BD/ and the point where Charlie is be C

/AG/ = 1200 feet

/AG/ = /BD/ = 1200 feet ( as shown in the diagram)

The distance between the two balloons is equal to /GD/

Also, from the diagram, /GD/ = /GC/ + /CD/

To find /GC/,

Consider ΔAGC

/AG/ = 1200 feet

/GC/ = ?

From the question, "Balloon A has risen at a 56° angle"

∴ x° = 56°

Using the formula

[tex]tan(x^{o} ) = \frac{/AG/}{/GC/}[/tex]

[tex]tan(56^{o}) = \frac{1200}{/GC/}[/tex]

[tex]/GC/ = \frac{1200}{tan(56^{o}) }[/tex]

/GC/ = 809.41 feet

To find /CD/

Consider ΔBCD

/BD/ = 1200 feet

/CD/ = ?

From the question, "Balloon B has risen at a 81° angle"

∴ y° = 81°

Using the formula

[tex]tan(y^{o} ) = \frac{/BD/}{/CD/}[/tex]

[tex]tan(81^{o}) = \frac{1200}{/CD/}[/tex]

[tex]/CD/ = \frac{1200}{tan(81^{o}) }[/tex]

/CD/ = 190.06 feet

Now, recall that /GD/ = /GC/ + /CD/

∴ /GD/ = 809.41 feet + 190.06 feet

/GD/  = 999.47 feet

/GD/ ≅ 999 feet (to  the nearest whole number)

Hence, the distance between the two balloons is 999 feet

Balloon B is 999 feet from balloon A.

Learn more here: https://brainly.com/question/15979174

Answer:

999 Units

Step-by-step explanation:

Answer:

The correct answer is the letter C.

Step-by-step explanation:

We can use the following trigonometric identity:

[tex]cos(60)=\frac{6}{b}[/tex] (1)

[tex]cos(45)=\frac{c}{b}[/tex] (2)

Solving each equation by b and equaling we have:

[tex]\frac{6}{cos(60)}=\frac{c}{cos(45)}[/tex]

[tex]\frac{6}{cos(60)}=\frac{c}{cos(45)}[/tex]

Let's recall that:

[tex]cos(45)=\frac{1}{\sqrt{2}}[/tex]

[tex]cos(60)=\frac{1}{2}[/tex]

Then we have:

[tex]c=\frac{cos(45)*6}{cos(60)}[/tex]

[tex]c=\frac{2*6}{\sqrt{2}}[/tex]

[tex]c=\frac{12}{\sqrt{2}}[/tex]

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

Using equation (1) we can find b.

[tex]cos(60)=\frac{6}{b}[/tex]  

[tex]b=12[/tex]      

Finally, we can find a using the next equation:

[tex]tan(60)=\frac{a}{6}[/tex]

[tex]a=6*tan(60)[/tex]

[tex]a=6\sqrt{3}[/tex]

Therefore, the correct answer is the letter C.

I hope it helps you!

Answer:

[tex]-32^\frac{3}{5} = -8[/tex]

Step-by-step explanation:

Given

[tex]-32^\frac{3}{5}[/tex]

Required

The equivalent expression

We have:

[tex]-32^\frac{3}{5}[/tex]

Rewrite as:

[tex]-32^\frac{3}{5} = (-32)^\frac{3}{5}[/tex]

Expand

[tex]-32^\frac{3}{5} = (-2^5)^\frac{3}{5}[/tex]

Remove bracket

[tex]-32^\frac{3}{5} = -2^\frac{5*3}{5}[/tex]

[tex]-32^\frac{3}{5} = -2^3[/tex]

[tex]-32^\frac{3}{5} = -8[/tex]

These are variables on your graph

Answer:

24cm

Step-by-step explanation:

Question: Find the length of side OR.

Answer + explanation:

24cm

Since PQ = 24 cm, OR = 24 cm because they're paralleled and congruent!

Answer:

<O = 125

OR = 24

Step-by-step explanation:

consecutive angles are supplementary in a parallelogram

<R + <O = 180

55 + <O =180

<O = 180-55

< O = 125

opposite sides are congruent in a parallelogram

PQ = OR = 24

Answer:

2 significant figures  

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

2

Only the 7 and the 6 are significant. The zeros are place holders and not significant figures.

Step-by-step explanation:

I hope this works for ya.

Answer:

this is the answer

Step-by-step explanation:

thank you

Answer:

-196/4 = -49

Step-by-step explanation:

Mental math. If you can't do that then use a calculator. It's faster to type it in on g oogle

Step-by-step explanation:

The graph clearly has a positive slope. So Answer D couldn't be correct. Next: the y-intercept of this line is (0, -2), so b in the formula y = mx÷ b must be -2.

Therefore the correct equation of this line is

y = x - 2 (choice a)

9514 1404 393

Answer:

  a. Definition of bisector.

Step-by-step explanation:

Line l is a line through the midpoint M. We can conclude it is a bisector, because, by definition, a bisector is a line through the midpoint.

The conclusion is justified by the definition of a bisector.

Answer:

Im pretty sure its 1,000 miles (dont forget the unit)

Step-by-step explanation:

Determine if this problem is a inverse variation or direct variation problem! This means that:

equation would be:

1=40

25=x

cross multiply*

x=25*40

x=1,000 miles apart! (dont forget the unit)

If this doesnt work then try this equation!

1=40

25=x

Multiply 1*40 and 25 *x

40=25x......    

40/25= 1.6

x=1.6! (Extra step)

Cheers!

Answer: 100 Miles

Step-by-step explanation: took the miles and got it correct.

(Also it's 2.5 inches apart, not 25.)

Answer:

H0 : σ²=10²

H1 : σ²>10²

χ² = 45.796

Pvalue = 0.2442

Do not reject H0 because Pvalue is greater Than significance level

There is insufficient evidence to warrant rejection of the claim that the standard deviation of​ men's pulse rates is equal to 10 beats per minute.

Step-by-step explanation:

Given that :

Sample size, n = 41

Sample standard deviation, s = 10.7

Population standard deviation, σ = 10

Significance level, α = 0.10

The Hypothesis :

H0 : σ²=10²

H1 : σ²>10²

Using the χ² test for population variance :

The test statistic, χ² = (n-1)*s²/σ²

χ² = (41 - 1) * 10.7²/ 10²

χ² = (40 * 114.49) / 100

χ² = 4579.6 / 100

χ² = 45.796

The Pvalue ;

df = n - 1 ; 41 - 1 = 40

Pvalue(45.796, 40) = 0.2442

Since Pvalue > α ; WE fail to reject H0

Do not reject H0 because Pvalue is greater Than significance level

There is insufficient evidence to warrant rejection of the claim that the standard deviation of​ men's pulse rates is equal to 10 beats per minute.

Answer:

C

Step-by-step explanation:

The equation that described the graph is x<-5

Answer:

x = 8

Step-by-step explanation:

Set 2x + 3 = 3x - 5

Solve for x

x = 8

Answer:

6.5%

Step-by-step explanation:

sales price x sales tax rate = sales tax

156.50 x sales tax rate = 10.17

sales tax rate = 10.17/156.50

sales tax rate = .065 or 6.5%

Answer:

4

Step-by-step explanation:

count up from -5 to -1

so -5,-4,-3,-2,-1 and there are four numbers excluding-5

9514 1404 393

Answer:

  a) quadrant III

  b) 4π/3, -2π/3

  c) (1/2, (√3)/2)

  d) ((√3)/2, -1/2

Step-by-step explanation:

a) The attachment shows the point P and the numbering of the quadrants (in Roman numerals). Point P lies in quadrant III.

__

b) Measured counterclockwise, the angle to point P is 240° or 4π/3 radians. Measured clockwise, the angle is -120° or -2π/3 radians. In the diagram, these are shown in green and purple, respectively.

__

c) Adding π/2 to the angle 4π/3 or -2π/3 brings it to 11π/6, or -π/6. This point is marked as P' (blue) on the diagram. The coordinate transformation for π/2 radians CCW rotation is ...

  (x, y) ⇒ (-y, x)

  P(-1/2, -√3/2) ⇒ P'(√3/2, -1/2)

In terms of trig functions, the coordinates of the rotated point are ...

  P'(cos(-π/6), sin(-π/6)) = P'(√3/2, -1/2)

__

d) Adding or subtracting π radians to/from the angle moves it directly opposite the origin. Both coordinates change sign. This point is P'' (red) on the diagram.

Answer:

true

Step-by-step explanation:

because some of x if x=3 then 3<6 is true

Answer:

15.56

Step-by-step explanation:

Given the vectors ||u|| = 5√2 units, and ||v|| = 6√2 units.

||u + v|| ≈  5√2 +  6√2

||u + v|| ≈  (5+6)√2

Since √2≈ 1.4142

||u + v|| ≈   11(1.4142)

||u + v|| ≈  15.56

Hence the correct option is D

Answer: 11.05

Step-by-step explanation: got it right

Answer:

340 cars at $ 34 should be rented to produce the maximum income of $ 11,560.

Step-by-step explanation:

Given that a car rental agency rents 480 cars per day at a rate of $ 20 per day, and for each $ 1 increase in rate, 10 fewer cars are rented, to determine at what rate should the cars be rented to produce the maximum income and what is the maximum income, the following calculations must be performed:

480 x 20 = 9600

400 x 28 = 11200

350 x 33 = 11550

300 x 38 = 11400

310 x 37 = 11470

320 x 36 = 11520

330 x 35 = 11550

340 x 34 = 11560

Therefore, 340 cars at $ 34 should be rented to produce the maximum income of $ 11,560.