An 8-cylinder Crown Victoria gives 18 miles per gallon in city driving and 21 miles per gallon in highway driving. A 300-mile trip required 15.5 gallons of gasoline. How many whole miles were driven in the city?

The only statement that holds for the given operation is Statement II

Given the following operartions

a [] b = a+b - ab/2

We need to check the true statement

For the expression x [] (y+z) =  x [] y +  x [] z

x [] (y+z) = x+y+z - x(y+z)/2

x [] (y+z) = x+y+z - (xy+xz)/2

x [] y +x [] z =  x+y - xy/2 +[x+z - xz/2 ]

x [] y +x [] z = x+y+x+z -xy/2 - xz/2

x [] y +x [] z = 2x+y+z - (xy+xz)/2

This shows that the statement I is incorrect

For the second statement

y [] z =  y+z - yz/2

x [] (y [] z) = x + (y+z - yz/2) - x(y+z-yz/2)/2

x [] (y [] z) = x+y+z-yz/2 -xy/2 - xz/2+xyz/4

For the other expression

x [] y =  x+y - xy/2

(x [] y) [] z = x+y - xy/2 + z - z(x+y - xy/2)/2

(x [] y) [] z = x+y+z- xy/2 -zx/2 - zy/2 + xyz/4

This shows that x [] (y [] z) = (x [] y) [] z is correct (Statement II)

For the third statement

x [] z =  x+z - xz/2

y [] z =  y+z - yz/2

z [] 0 = z+0 - z(0)/2

z [] 0 = z

x[]z + y[]z - z[]0 = x+z - xz/2 + y+z - yz/2 - z

x[]z + y[]z - z[]0 = x+y+z - xz/2 - yz/2

For the expression (x+y)[] z

(x+y)[] z = (x+y)+z - (xyz)/2

Hence the statement III is not valid

Based on the explanations above, the only statement that holds for the given operation is Statement II

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Each number in the sum is even, so we can remove a factor of 2.

2 + 4 + 6 + 8 + ... + 78 + 80 = 2 (1 + 2 + 3 + 4 + ... + 39 + 40)

Use whatever technique you used in (a) and (b) to compute the sum

1 + 2 + 3 + 4 + ... + 39 + 40

With Gauss's method, for instance, we have

S = 1 + 2 + 3 + ... + 38 + 39 + 40

S = 40 + 39 + 38 + ... + 3 + 2 + 1

2S = (1 + 40) + (2 + 39) + ... + (39 + 2) + (40 + 1) = 40×41

S = 20×21 = 420

Then the sum you want is 2×420 = 840.

Answer:

down there

Step-by-step explanation:

we can see that angel rso and esk are congruent because they are verticle angels.

we also know that angel tse plus esk is equal to tsk, so angel tse+rso=tsk by algebra

Answer:

5621 years

Step-by-step explanation:

Plug everything in first.

[tex]N=N_0e^{-kt}\\\\\implies 0.57 = e^{-0.0001t}\\\\\implies\ln \left(0.57\right)=-0.0001t\\\\t=-\frac{\ln \left(0.57\right)}{0.0001}[/tex]

Round to closest amount of years = 5621 years

Answer:

The correct answer is -14

Step-by-step explanation:

Answer:

just hey effect me II rieirjttjhg shewtha

The lower limit of the interval is 0.712 if the survey of 504 citizens found that 378 of them favor a new bill introduced by the city.

It is defined as the sampling distribution following an approximately normal distribution for known standard deviation.

We have:

A survey of 504 citizens found that 378 of them favor a new bill introduced by the city.

Sample proportion = p = 378/504 = 0.75

q = 1 - p = 1 - 0.75 = 0.25

[tex]\rm SD = \sqrt{\dfrac{pq}{n}}[/tex]

[tex]\rm SD = \sqrt{\dfrac{0.75\times0.25}{504}}[/tex]

SD = 0.01928

For 95% confidence interval Z value = 1.96

Lower limit = 0.75 - 1.96(0.01928)

= 0.712

Thus, the lower limit of the interval is 0.712 if the survey of 504 citizens found that 378 of them favor a new bill introduced by the city.

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[tex]z=\dfrac{kx^3}{y^3}\\\\\\59=\dfrac{k\cdot 8^3}{8^3}\\k=59\\\\\\z=\dfrac{59x^3}{y^3}\\\\\\z=\dfrac{59\cdot 3^3}{4^3}=\dfrac{1593}{64}[/tex]

Answer:

29 ft

Step-by-step explanation:

The distance along the ground from one stake to the tree, 21 ft, and the distance up the trunk from the ground, 20 ft, are the legs of a right triangle. The length of the wire is the hypotenuse of the right triangle. We can use the Pythagorean theorem to solve this problem.

a² + b² = c²

(21 ft)² + (20 ft)² = c²

c² = 841 ft²

c = √(841 ft²)

c = 29 ft

Answer: 29 ft

Answer: {-3, -2, 1, 5}

Step-by-step explanation:

The domain is the set of x-values.

Answer:

[tex]-\frac15[/tex]

Step-by-step explanation:

Hello!

We can utilize the slope formula to find the slope.

Slope Formula: [tex]S = \frac{y_2-y_1}{x_2-x_1}[/tex]

Remember that a coordinate is written in the form (x,y)

The slope of the line is [tex]-\frac15[/tex].

Answer:

-1/5

Step-by-step explanation:

To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(-4 - (-2)) / (5 - (-5))

Simplify the parentheses.

= (-4 + 2) / (5 + 5)

= -2 / 10

Simplify the fraction.

-2/10

= -1/5

This is your slope.

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the school purchased 742 items in total.

Just add 256+332+154

which equals...742. :)

Answer:

742 items

Step-by-step explanation:

Add up all the items that the cafeteria purchased. 256+332+154=742!

The number of red tiles in the box given the chance ratio of red to blue tiles is 18

= 12 + 2x

Number of red tiles = 3 / 8 × 12+2x

x = 3(12 + 2x) / 8

x = (36 + 6x) / 8

8x = 36 + 6x

8x - 6x = 36

2x = 36

x = 36/2

x = 18 tiles

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Answer: 28

Step-by-step explanation:

The required value for the sum is 9580.

[tex]\frac{10000}{(1+\frac{0.115}{4})^2}+68\frac{1-\frac{1}{(1+\frac{0.115}{4})^2}}{\frac{0.115}{4}}[/tex]

Simplification in mathematics to solve the given condition on its operators.

[tex]\frac{10000}{(1+\frac{0.115}{4})^2}+68\frac{1-\frac{1}{(1+\frac{0.115}{4})^2}}{\frac{0.115}{4}}[/tex]

= [tex]\frac{10000}{1.028^2} +68*\frac{1-\frac{1}{1.028^2} }{\frac{0.115}{4} } \\9451+68*\frac{1-0.94}{\frac{0.115}{4} } \\\\9451+68*\frac{0.054}{\frac{0.115}{4} } \\\\\\9451+3.72{\frac{4}{0.115} } \\\\\\9451+129\\[/tex]

= 9580

The required solution is given as 9580.

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The amount of stockholders’ equity as of August 31 of the current year is $26400.

The owner's equity will be:

= Cash + Supplies + Equipment - Account payable

= 27900 + 900 + 8500 - 7300

= 26400

Therefore, the amount of stockholders’ equity as of August 31 of the current year is

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sinA+sinB+sinC

=2sin(A+B)/2cos(A-B)/2+sin C

=2sin(pi-C)/2cos(A-B)/2+2sin C/2cosC/2

=2cosC/2(cos(A-B)/2+cos(A+B)/2)

=4 cos A/2 cos B/2 cos C/2

= RHS

Answer:

b.) 2

Explanation:

Given:

rewrite knowing 2⁵ = 32, (-2)⁵  = -32

simplify, ⁿ√xⁿ = x

distribute inside parenthesis

[tex]\large\displaystyle\text{$\begin{gathered}\sf Apply \ the \ laws \ of \ exponents:\sqrt[n]{-a}=-\sqrt[n]{a}, if \ n \ is \ odd \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \sqrt[5]{-32}=-\sqrt[5]{32} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{=-\left(-\sqrt[5]{32}\right)} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf Decompose \ the \ number \ into \ prime \ factors: 32=2^{5}. \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{=-\left(-\sqrt[5]{2^5}\right)} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf Apply \ the \ laws \ of \ exponents:\sqrt[n]{a^n}=a,\:\quad \:a\ge 0 \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \sqrt[5]{2^5}=2 \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf Remove \ parentheses:\quad \:-\left(-2\right)=2 \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{=2 \ \ \to \ \ \ Answer} \end{gathered}$}[/tex]

Answer:

[tex]y=-\frac{3}{2}x+\frac{7}{2}[/tex]

Step-by-step explanation:

So when two lines are parallel there slopes are the same, but there y-intercepts are different, since if they had the same y-intercept, then they would be the same exact line. To convert an equation into slope-intercept form you simple isolate y by moving everything else to the other side, and then divide by the coefficient of y so the coefficient of y becomes 1. This will give you the equation in the form: y=mx+b where m is the slope and b is the y-intercept (because when the linear equation crosses the y-axis, the x is 0, thus mx will be 0, leaving only b, so the y-intercept is b).

Original Equation:

3x + 2y = 4

Subtract 3x from both sides

2y = -3x + 4

Divide both sides by 2

y = -3/2x + 2

Generally any parallel line will be in the form:

[tex]y=-\frac{3}{2}x + b\ \ \ \ \ b\ne2[/tex]. Since as stated before if two lines have the same slope and y-intercept, they're the same line, which is not the same as parallel, since parallel lines never intersect.

So since we're given a point in the parallel line (-1, 5) we can plug those values into the equation to find the value of b

[tex]5=-\frac{3}{2}(-1) + b[/tex]

Multiply and

[tex]5=\frac{3}{2}+ b[/tex]

Convert 5 into a fraction with a denominator of 2

[tex]\frac{5}{1} * \frac{2}{2} = \frac{10}{2}[/tex]

Write equation using this form of 5:

[tex]\frac{10}{2}=\frac{3}{2}+b[/tex]

Subtract 3/2 from both sides

[tex]\frac{7}{2}=b[/tex]

Now take this value and input it into the slope-intercept form to finish the equation: [tex]y=-\frac{3}{2}x+\frac{7}{2}[/tex]

The liquid that will be the least dense liquid in the density column is; The  liquid floating on the top.

The formula for density is;

Density = Mass/Volume

Thus, the greater the mass, the more the density. Thus, it means that heavier objects will sink while lighter ones will float.

Thus, this means that the liquid that is most dense will be at the bottom of the liquid.

The liquid that is least dense will be at the top of the liquid.

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49^2m-m : Not equivalent

7^2m-2m : Not equivalent

7^2m-m : Not equivalent

This is actually a trick question. All of the following are actually false statements. Want to know why? Let me show you.

For exponents, if you are dividing a number to some power (i.e 5^3) by the SAME number to a different power (i.e 5^2), then the expression is 5^3-2 or 5^1 = 5. This is true for any number a such that a^b ÷ a^c = a^b-c.

Since 7 and 49 are not the same number, this rule does not apply and thus cannot be simplified any further.

Let me prove why. 5^3 = 125, and 5^2 = 25, and 125 ÷ 25 = 5. This is also the same as 5^3-2 = 5^1 = 5. We just proved this as so.

But, what about 7 and 49, or 2 different numbers. Well it doesn't apply. 7^3 = 343, and 49^2 = 2401, and 343 ÷ 2401 ≈ 0.14. Thus, this is NOT equal to 7^3-2 which is 7. We just proved that a^y ÷ b^z ≠ a^y-z. Congratulations!

Hope this helped!

$17500 was invested in the first account at a rate of return of 10% (after a year) while $11000 was invested in the second account at a rate of 4% loss over the same period.

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

Let x represent the amount of money invested at 10% and y represent the amount of money invested at a loss of 4%, hence:

x + y = 28500    (1)

Also:

(x * 1 year * 0.1) + (y * 1 year * -0.04) = 1310

0.1x - 0.04y = 1310   (2)

From equation 1 and 2:

x = 17500, y = 11000

$17500 was invested in the first account at a rate of return of 10% (after a year) while $11000 was invested in the second account at a rate of 4% loss over the same period.

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The determination of the money multiplier and the money supply for each reserve requirement listed in the following table are as follows:

Reserve Requirement    Simple Money     Money Supply

(percent)                             Multiplier             (Dollars)

  5                                          20                      $8,000

10                                           10                      $4,000

The money multiplier is the ratio of the reserve to the money supply.

The formula for determining the money multiplier is 1/r where r is the reserve ratio.

The money supply is the total amount of money circulating in the commercial banking system.

The quantity of the money supply is determined by multiplying the money multiplier by the total reserves.

Reserve Requirement    Simple Money     Money Supply

(percent)                             Multiplier             (Dollars)

  5                                    20 (1/0.05)               $8,000 ($400 x 20)

10                                     10 (1/0.1)                  $4,000 ($400 x 10)

Reserve Requirement    Simple Money     Money Supply

(percent)                             Multiplier             (Dollars)

  5

10

Thus, the money multiplier and money supply for the 5% reserve requirement are higher than for the 10% reserve requirement.

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The correct statement regarding when the events will be independent is given as follows:

B. The probability of getting a red convertible is 0.06.

Two events, A and B are independent, if:

[tex]P(A \cap B) = P(A)P(B)[/tex]

In this problem, the probabilities are given as follows:

The events will be independent if:

[tex]P(A \cap B) = 0.2 \times 0.3 = 0.06[/tex]

The intersection of events A and B is a red convertible car, hence the correct option is:

B. The probability of getting a red convertible is 0.06.

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Answer:

c

Step-by-step explanation:

absolute values are positive and abs value of 0 = 0

Answer:

1.25 is the median for the first 12 days in January

Answer:

117 degrees

Step-by-step explanation:

Answer:

11/15 < 4/5

Step-by-step explanation:

1.  5/6 = 10/12, so the first answer is not correct

2. 1/4 = 4/16, so the second answer is not correct

3. 3/4 = 9/12 and 4/6 = 8/12, so the third answer is not correct

4. 4/5 = 12/15 > 11/15, so this answer is correct

The expression a/b ÷ c/d = ad/bc is A. true.

Given to show that if a/b and c/d are rational expressions, then a/b ÷ c/d = ad/bc.

The ratio of two polynomials is an example of a rational expression. If an expression f is rational, it can be expressed in the form p/q, where p and q are polynomials.

Here we have a ,b ,c and d in the form of p/q form.

We take the reciprocal of the expression on the right side of the division sign when the rational expression a/b is to be divided by the rational expression c/d.

so, L.H.S = a/b ÷ c/d

= a/b × 1/(c/d)

= a/b × d/c

= ad/bc

= R.H.S

since L.H.S = R.H.S

a/b ÷c/d = ad/bc

Hence the expression a/b ÷ c/d = ad/bc is A.true.

Your question was incomplete. Please find the missing content here.

If A/B and C/D are rational expressions, then: A/B ÷C/D

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Answer:

A. sin θ = 5/8

Step-by-step explanation:

csc θ = 1/sin θ

csc θ = 8/5

1/sin θ = 8/5

sin θ = 5/8

Answer:

y = -19x + 14

Step-by-step explanation:

For each increase of x by 1, y decreases by 19, giving us -19x. When x = 0, y = 14, therefore, y = -19x + 14