If it cost ​$6 to fill a gas tank in 1970​, how much would it have cost to fill the same tank in 2010​?

Answer:

  $83,802

Step-by-step explanation:

The description is of an annuity due. Payments at the beginning of the period earn interest for the period, unlike those made at the end of the period.

The future value of an annuity due is given by the formula ...

  FV = P(1 +r)((1 +r)^t -1)/r

where P is the annual payment, r is the annual interest rate, and t is the number of years.

This is essentially the sum of t terms of a geometric series with first term P(1+r) and common ratio (1+r).

For P=$1000, r = 0.06, and t = 30, the future value is ...

  FV = $1000(1.06)(1.06^30 -1)/0.06 ≈ $83,801.68

To the nearest dollar, the account value will be $83,802.

__

Additional comment

Spreadsheets and many graphing calculators have time-value-of-money (TVM) formulas built in. You need to make sure to choose the option that gives an annuity due, rather than an ordinary annuity. In the attached TVM picture, this setting is accomplished by PmtMode=1.

Answer:

shorter side: 5 km

longer side: 27 km

Step-by-step explanation:

So you're already given the formula for the area of a rectangle, the next thing to do is assign length and width in terms of some unknown variable, which for convenience, I'll just say is x. So let's say one of the sides is x, the one that's the shorter side, since the longer side can be related to the shorted side, which is x. The longer side is 12km longer than 3 times the other side, so since the other side is x, it's length is (3x+12). So we simply multiply this by x, to get the area which is 135

"Known" Values: one side=x, other side=3x+12, area=135 km^2

[tex]135=x(3x+12)[/tex]

Distribute the x

[tex]135=3x^2+12x[/tex]

Subtract 135 from both sides

[tex]0=3x^2+12x-135[/tex]

Now since the equation is equal to zero, we can use the quadratic equation. In this case a=3, b=12, and c=-135

[tex]x=\frac{-12\pm\sqrt{12^2-4(3)(-135)}}{2(3)}[/tex]

Simplify denominator and multiply inside of the radical

[tex]x=\frac{-12\pm\sqrt{144+1,620}}{6}[/tex]

If you're confused where the negative went in the radical, it canceled out when multiply -4 by -135. Now add the stuff in the radical

[tex]x=\frac{-12\pm\sqrt{1,764}}{6}[/tex]

Simplify the radical

[tex]x=\frac{-12\pm 42}{6}[/tex]

Now you might think there are two solutions to this equation, but the thing is that one of the sides simply cannot have a "negative length", because in this context, x must be positive. So it's easy to see you have to use the positive sign, since using the negative sign would result in -12-42 over 6 which is certainly negative. So we can ignore that solution as it doesn't mean anything in this context. We only need the positive solution

[tex]x=\frac{-12+42}{6}[/tex]

Add values

[tex]x=\frac{30}{6}[/tex]

Divide

[tex]x=5[/tex]

Since the shorter side was 5, that's the solution to the shorter side, now to find the longer side we plug in 5 into the equation: [tex]3x+12[/tex] which becomes 3(5) + 12 = 15+12 = 27. This means the two lengths are 5 and 27

Step-by-step explanation:

let x = length of shorter side

[tex](3x + 12)(x)= 135[/tex]    This is the equation

[tex]3x^2+12x=135[/tex]        use distributive property to multiply out

[tex]3x^2+12x-135=0[/tex]   subtract 135 from both sides to get in position to factor

[tex]3(x^2+4x-45)[/tex]           factor out a 3

[tex]3(x-5)(x-9)[/tex]           factor the resulting expression

[tex]x=5,9[/tex]                       two answers (we want one so see which one works)

Check both values of x

[tex]5*3+12=27[/tex]

[tex]27*5=135[/tex]

Therefore, we know the shorter side is 5 km and the longer side is 27 km.

At this point, we do not even need to check x=9

The correct expansion is the one in option b:

[tex]Log_9(\frac{6}{11}) = Log_9(6) - Log_9(11)[/tex]

Here we must use the logarithmic property:

[tex]Log(a) -Log(b) = Log(\frac{a}{b})[/tex]

Our expression in this case is:

[tex]Log_9(\frac{6}{11})[/tex]

Using the above property, we can rewrite the expression as:

[tex]Log_9(\frac{6}{11}) = Log_9(6) - Log_9(11)[/tex]

From this, we conclude that the correct option is B.

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[tex]2x - 7x + 2 + 1 - 2[/tex]

[tex]2x - 7x + 3 - 2[/tex]

[tex] - 5x + 1[/tex]

Answer:

Not going to give answer, but let you solve

Step-by-step explanation:

You first have to start by drawing a number line and mark two integers between the fraction lines. Then you have to divide the section between the two integers in an equal number of parts which is equal to the denominator.

Hope I helped

The point P could be located in quadrant I, quadrant IV and the x-axis

The coordinate of point P is given as:

P = (a, b)

Where a is positive

When a is positive, then the likely locations of P are:

Hence, point P could be located in quadrant I, quadrant IV and the x-axis

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Answer:

(1,5)

Step-by-step explanation:

The solution to the system of equations is where the two graphs intersect.

The two lines intersect at x=1 and y =5

The point of intersection is (1,5)

Answer: (1, 5)

Step-by-step explanation: Over to the right one, up five; I hope this helps!

Key: (xGraph, yGraph) If a number is positive on the x axis, go right, if negative, go left. The same applies to the y graph, if the number is positve, go up, if negative go down. Your solution is where the two lines meet.

Answer:

slope = - 32 , y- intercept = 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 32x + 5 ← is in slope- intercept form

with slope m = - 32 and y- intercept c = 5

[tex]\frak{Hi!}[/tex]

[tex]\orange\hspace{300pt}\above2[/tex]

                          We have the equation [tex]\boldsymbol{\sf y=-32x+5}[/tex].

                          We need to know its slope and y-intercept.

                         If an equation has the y=mx+c form,  the slope is always

                         multiplied by x, the x co-ordinate. Such is the case here,

                          thereupon we note that the slope is [tex]\boldsymbol{\sf{-32}}[/tex].

                         As for the y-intercept, that's a constant. Do you remember

                         that constants have no variables attached to them?

                         Since the only number that has no variables attached to it is

                         5, we note that this is the desired value, the y-intercept.

done!!

[tex]\orange\hspace{300pt}\above3[/tex]

                        [tex]\large\boldsymbol{\sf{calligraphy}}[/tex]

Answer:

Is there a graph related to this question?

Answer:

120 Vials

Step-by-step explanation:

160/1and1/3

160/4over3

Multiply top by 3

480/4

120

The number of vials in the case is given by the equation A = 120 vials

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of vials in the case be represented as A

Now , the equation will be

The total amount of med = 160 ounces

The amount of med in each vial = 1 1/3 ounces

The amount of med in each vial = 4/3 ounces

So , the number of vials in the case A = total amount of med / amount of med in each vial

Substituting the values in the equation , we get

The number of vials in the case A = 160 / ( 4/3 )

The number of vials in the case A = ( 160 x 3 ) / 4

The number of vials in the case A = 40 x 3

The number of vials in the case A = 120 vials

Therefore , the value of A is 120

Hence , the number of vials is 120

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The height of the flagpole with an angle of elevation to the top of the pole of 31° is 60.086 feet

An equation is an expression that shows the relationship between two or more numbers and variables.

Trigonometric ratio is used to show the relationship between the sides and angles of a triangle.

Let h represent the height of the flagpole, hence:

tan(31) = h/100

h = 60.086 feet

The height of the flagpole with an angle of elevation to the top of the pole of 31° is 60.086 feet

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The equation of the line going through (-6, 0) and (0, -3) is y = -(1/2)x - 3

The equation of the line going through (0, 3) and (-4, -5) is y = 2x + 3

An equation is an expression that shows the relationship between two or more variables and numbers.

The equation of the line going through (-6, 0) and (0, -3) is:

y - 0 = [(-3 - 0) / (0- (-6)](x - (-6))

y = -(1/2)x - 3

The equation of the line going through (0, 3) and (-4, -5) is:

y - 3 = [(-5 - 3) / (-4 - 0)](x - 0)

y = 2x + 3

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Answer:

2

-1/2

Step-by-step explanation:

The equations of the transformed graphs are [tex]f(x) = \frac 23\sqrt{x - 3}[/tex], [tex]f(x) = 8\sqrt{x }-3[/tex], [tex]f(x) = \sqrt{\frac x7} + 5[/tex] and [tex]f(x) = \sqrt{-x} - 10[/tex]

The function #1

The function is given as::

[tex]f(x) = \sqrt{x}[/tex]

It is shifted right by 3 units.

So, we have:

[tex]f(x) = \sqrt{x - 3}[/tex]

It is shrunk vertically by a factor of 2/3

[tex]f(x) = \frac 23\sqrt{x - 3}[/tex]

Hence, the equation of the transformed graph is [tex]f(x) = \frac 23\sqrt{x - 3}[/tex]

The function #2

The function is given as::

[tex]f(x) = \sqrt{x}[/tex]

It is stretched vertically by a factor of 8

[tex]f(x) = 8\sqrt{x }[/tex]

It is shifted down by 3 units.

So, we have:

[tex]f(x) = 8\sqrt{x }-3[/tex]

Hence, the equation of the transformed graph is [tex]f(x) = 8\sqrt{x }-3[/tex]

The function #3

The function is given as::

[tex]f(x) = \sqrt{x}[/tex]

It is stretched horizontally by a factor of 7

[tex]f(x) = \sqrt{\frac x7}[/tex]

It is shifted up by 5 units.

So, we have:

[tex]f(x) = \sqrt{\frac x7} + 5[/tex]

Hence, the equation of the transformed graph is [tex]f(x) = \sqrt{\frac x7} + 5[/tex]

The function #4

The function is given as::

[tex]f(x) = \sqrt{x}[/tex]

It is reflected across the y-axis

[tex]f(x) = \sqrt{-x}[/tex]

It is shifted down by 10 units.

So, we have:

[tex]f(x) = \sqrt{-x} - 10[/tex]

Hence, the equation of the transformed graph is [tex]f(x) = \sqrt{-x} - 10[/tex]

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The expression that is equivalent to the given expression is 16⁴

From the question, we are to determine the expression that is equivalent to the given expression

The given expression is

[tex](\frac{1}{16} )^{-4}[/tex]

Evaluating

[tex](\frac{1}{16} )^{-4}[/tex]

[tex]= (16^{-1} )^{-4}[/tex]

[tex]= 16^{-1 \times -4}[/tex]

[tex]= 16^{4}[/tex]

Hence, the expression that is equivalent to the given expression is 16⁴

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Answer: AB = 90.7 meter

Given following:

Find angle A :

⇒ 180° - (104.6° + 14.4°)

⇒ 61°

Now, use sine rule:

[tex]\sf \dfrac{AB}{BC} = \dfrac{sin(C^{\circ })}{sin(A^{\circ \:})}[/tex]

[tex]\sf \dfrac{AB}{319} = \dfrac{sin(14.4) } {sin(61)}[/tex]

[tex]\sf AB = \dfrac{319 \ sin(14.4) } {sin(61)}[/tex]

[tex]\sf AB = 90.70464953 \quad \approx \quad 90.7 \ m \ (rounded \: to \: nearest \ tenth)[/tex]

Answer: 2

Step-by-step explanation:

     This system has 2 solutions because there are two points of intersection. See attached for where I pointed them out.

Solve by elimination.

[tex](\vec A + 3\, \vec B) - (\vec A - \vec B) = (-3\,\vec\imath + \vec\jmath) - (\vec\imath - 2\,\vec\jmath)[/tex]

[tex]\implies 4\,\vec B = -4\,\vec\imath + 3\,\vec\jmath \implies \boxed{\vec B = -\vec\imath + \dfrac34\,\vec\jmath}[/tex]

[tex]\implies \vec A = \vec\imath - 2\,\vec\jmath + \vec B[/tex]

[tex]\implies \boxed{\vec A = -\dfrac54 \,\vec\jmath}[/tex]

Step-by-step explanation:

Multiply the factors

[tex](x - 1)(x + 1)(x + 3)[/tex]

[tex]( {x}^{2} - 1)(x + 3)[/tex]

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

The highest exponent is 3, so the degree is 3

The probability that all men will be interviewed first is; 1/55

To solve this question we will make use of the probability combination formula which is;

nCr = n!/(r! * (n - r)!)

Thus, since we want to find the probability that all men will be interviewed first, then we will use the formula;

3(3!)/((11C1) * (10C1) * (9C1)) = 18/990

Simplifying that fraction  gives us; 1/55

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Answer:

#of advanced tickets (x) = 30

#of same-day tickets (y) = 20

Step-by-step explanation:

x-#of advanced tickets

y-#of same-day tickets

[tex]x+y=50,\\35x+30y=1650[/tex]

5x+30(x+y)=1650

5x+30(50)=1650

5x=150

x=30

y=20

Answer:

The last option

Step-by-step explanation:

When you plug in 1 for the x and 2 for y, the answer is -5 for the first equation and is 12 for the second equation. I hope that helps!

The percentage composition of salt in the solution is; 84.2%.

Since, it follows that there are 16 ounces in 1 pound. Then the 3 lb of salt is equivalent to; 3×16 = 48ounces.

Consequently, the percentage of salt in the solution as described is;

{48/57} × 100%

Percentage composition of salt is therefore;

= 84.2%.

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Answer:

(30+30) +(7+1) = 68

Step-by-step explanation:

hope this helps you (ʘᴗʘ✿)

Answer:

2304 inches

Step-by-step explanation:

please mark brainiest

Answer:

2304

Step-by-step explanation:

If you would like a step-by-step explanation, please just let me know. I sincerely hope this helps.

Answer:

$1.26

Step-by-step explanation:

A 20% off means multiplying by 1-0.2=0.8

4.39*0.8=3.512

3.512-1=2.512

2.512-1.25=1.262

1.262 rounded to the nearest cent is $1.26

Answer:

Pints

Step-by-step explanation:

Answer:

Sanjay has more milk (12 pints)

Step-by-step explanation:

A quarter equals two pints

3 quarts = 3(2) = 6 pints

Lisa has 6 pints

Sanjay has 12 pints

Hope this helps