A storm dumps 1.0 cm of rain on a city 6 km wide and 8 km long in a 2-h period. How many metric tons (1 metric ton = 103 kg) of water fell on the city? (1 cm3 of water has a mass of 1 g = 10−3 kg.) How many gallons of water was this?

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

B is the answer

Answer:

the answer will be d.PLATO users

Answer:

Step-by-step explanation:

The shorter the term, the lower the amount of interest.

The lower the interest rate, the lower the amount of interest.

The loan that has both a shorter term and a lower interest rate will cost less in interest.

___

The total of payments for the 30-year loan is 396,232.87.

The total of payments for the 20-year loan is 290,013.55.

The amount saved by taking the shorter loan is the difference of these amounts: $106,219.32.

_____

You can use an amortization formula, spreadsheet, or a financial calculator to compute the payments for each loan. The total repayment amount is the product of the monthly payment and the number of them, 360 for the 30-year loan; 240 for the 20-year loan.

Answer:

42 and 44

Step-by-step explanation:

The even numbers are numbers which can be written as 2n where n is any integer number.

Therefore, two consecutive numbers would be "2n" and "2n + 2"

We then have that

2n + (2n+2) = 86

4n + 2 = 86

4n = 84

n = 21

And the even number 2n is 2(21) = 42.

(We can verify this answer by doing 42 + 44 = 86)

Explanation:

3. ∠2 and ∠3 are a linear pair → definition of a linear pair

4. ∠3 and ∠4 are a linear pair → definition of a linear pair

5. m∠2 +m∠3 = 180° → definition of a linear pair (or angle addition postulate)

6. m∠3 +m∠4 = 180° → definition of a linear pair (or angle addition postulate)

7. m∠2 +m∠3 = m∠3 +m∠4 → substitution property

8. m∠2 = m∠4 → subtraction property

9. ∠2 ≅ ∠4 → definition of congruent angles

_____

A pair of angles is a "linear pair" if they are adjacent and supplementary. ∠2 and ∠3 are adjacent and the non-common legs form a straight line. It isn't clear what your definition of linear pair is and what you need to do to claim that the angles sum to 180°. Above, we have assumed a definition of "linear pair" that includes the facts that → they sum to 180°; → non-adjacent sides form a straight line.

Final answer:

When Mike increased the size of his truck tires from the original P215/60R16 to the larger P235/70R16 without recalibrating his speedometer, the actual speed he was going on the new tires when his speedometer showed 60 mph was approximately 54.2 mph.

Explanation:

When Mike increased the size of his truck tires without recalibrating his speedometer, his speedometer reading would be inaccurate. To determine how fast he is going on the new tires when his speedometer shows 60 mph, we can use the concept of tire revolutions per mile.

The original tire size, P215/60R16, has a diameter of approximately 25.7 inches, while the larger tire size, P235/70R16, has a diameter of approximately 29.0 inches. The new tires cover a greater distance in one revolution compared to the original tires.

To calculate the actual speed, we can use the equation:

Actual Speed = Speedometer Reading * (Original Tire Diameter / New Tire Diameter)

Substituting the given values:

60 mph * (25.7 inches / 29.0 inches)

By simplifying this calculation, the actual speed is approximately 54.2 mph. Therefore, the correct answer is A. 54.2 mph.

Mike is actually traveling approximately 64.4 mph. Hence the correct option is c.

Calculate the difference in tire circumference:

Original circumference: 2 * π * radius = 2 * π * (215 mm / 25.4 mm/inch) * (60 + 30%) = 79.3 inches (assuming 30% aspect ratio)

New circumference: 2 * π * (235 mm / 25.4 mm/inch) * (70 + 30%) = 85.1 inches

Difference: 85.1 inches - 79.3 inches = 5.8 inches

Calculate the percentage increase in circumference:

(5.8 inches / 79.3 inches) * 100% = 7.3%

Apply the percentage increase to the speedometer reading:

Actual speed = Speedometer reading * (1 + % increase)

Actual speed = 60 mph * (1 + 7.3%) = 60 mph * 1.073

Actual speed ≈ 64.4 mph

Therefore, when the speedometer shows 60 mph, Mike is actually traveling approximately 64.4 mph. Hence the correct option is c.

Answer:

Step-by-step explanation:

z = a + bi

the complex conjugate is : Z = a-bi

so : Z-z =  (a-bi) - ( a + bi ) = a-bi -a -bi

Z-z = -2bi ...is a pure imaginary number (the statement is true)

The statement is true, Z-z is a pure imaginary number = -2bi.

What is conjugate complex?

A conjugate of a complex number is another complex number which has the same real part as the original complex number and the imaginary part has the same magnitude but opposite sign.

Here, given that, z = a+ib,

Let, Z be the complex conjugate of z, then, Z=a-ib

Now, Z-z = (a-ib)-(a+ib)

               =a-ib-a-ib

               =-i2b  (which is purely imaginary)

Hence, proved. The given statement is true.

To learn more on Complex conjugate click:

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Answer:

  60

Step-by-step explanation:

For each 3 blocks Colton placed, Gage place 1, so Colton placed 3/4 of the total number blocks.

  3/4 × 80 = 60

Colton placed 60 blocks on the castle.

Answer:

60

Step-by-step explanation:

Answer:

57/4

Step-by-step explanation:

Answer:

11 + 4 = 15

Rewrite the problem:

15-3/4= ?

15-3= 12

the divide it by 4:

12 / 4 = 3

ANSWER: 3

Step-by-step explanation:

Answer:

The answer to your question is: 387.5 times distance from earth to the sun than distance from the earth to the moon

Step-by-step explanation:

Data

distance from earth to the sun = 9.3 x 10⁷ miles

distance from the earth to the moon = 2.4 x 10⁵ miles

distance ES to EM

Then we need to divide

 distance from earth to the sun / distance from the earth to the moon

9.3 x 10⁷ miles / 2.4 x 10⁵ miles

= 387.5 times is greater.

The distance from Earth to the Sun is about 387.5 times greater than the distance from Earth to the Moon. This is calculated by dividing the distance from Earth to the Sun by the distance from Earth to the Moon.

To determine how many times greater the distance from Earth to the Sun is than the distance from Earth to the Moon, we need to divide the distance from Earth to the Sun by the distance from Earth to the Moon. So, we have 9.3 × 107 miles (distance to the Sun) divided by 2.4 × 105 miles (distance to the Moon).

When you perform this calculation, you get a value of approximately 387.5. Therefore, the distance from Earth to the Sun is about 387.5 times greater than the distance from Earth to the Moon.

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Answer:

y = - 9

Step-by-step explanation:

x = 7 is the equation of a vertical line parallel to the y- axis and passing through all points with an x- coordinate of 7

A line perpendicular to it is a horizontal line parallel to the x- axis with equation y = c

Where c is the value of the y- coordinates the line passes through.

The line passes through (5, - 9) with y- coordinate - 9, thus

equation of line is y = - 9

Answer:

2 papers

Step-by-step explanation:

shark stickers : 15

whale stickers : 21

dolphin stickers : 47

papers:40

papers with dolphin stickers: 47

papers with shark stickers: 4, 8 , 12, 16, 20,24,28,32,36, 40 (every fourth paper, multiples of 4 till 40)

40/4 = 10  papers with shark stickers

papers with whale stickers: 5, 10,15, 15, 20, 25,30,35,40 (multiples of 5 till 40)

Papers with the three kinds of stickers : 2 (paper 20 and 40 )

Answer:

2 papers

Step-by-step explanation:

Answer:

a) 0.4

Step-by-step explanation:

Got it right on quiz

The multiplicative rate of change for the exponential function is 5/2, indicating that the function increases by a factor of 5/2 for each unit increase in x.

The multiplicative rate of change for an exponential function

[tex]\( f(x) = a \times b^x \)[/tex]

is given by the base of the exponential term, b .

In the function

[tex]\( f(x) = 2 \left(\frac{5}{2}\right)^{-x} \),[/tex]

the base of the exponential term is 5/2.

So, the multiplicative rate of change is 5/2

Answer:$18.00

Step-by-step explanation:5×3=15

$3+$15=$18

Answer:

Step-by-step explanation:

To

Answer:

Step-by-step explanWe can easily calculate for the height of the prism since all needed measurements are given. Volume of a rectangular prism is expressed by the equation:

V = lwh

where l is the length, w is the width and h is the height of the prism.

655 = 9 (5.2) hation:

h=14ft

Answer:

The domain is (all possible values of x) [tex]\{0,1,2,3,4,5\}[/tex]

The range is (all possible values of f(x)) [tex]\{250,200,150,100,50,0\}[/tex]

Step-by-step explanation:

A contestant on a game show is given $250.  He is asked five questions and loses $50 for every wrong answer.

Let x be the number of wrong answers. Then you get a relationship

[tex]\begin{array}{cc}x&f(x)\\ 0&250\\1&200\\2&150\\3&100\\4&50\\5&0\end{array}[/tex]

The domain is (all possible values of x) [tex]\{0,1,2,3,4,5\}[/tex]

The range is (all possible values of f(x)) [tex]\{250,200,150,100,50,0\}[/tex]

Answer:

down below(hope this helps

Step-by-step explanation:

Answer:

$12.5 per week

Step-by-step explanation:

(300)+12.5 +12.5+12.5+12.5=350

The rate of change in Michael's savings account per week is $12.50.

To find the rate of change in Michael's savings account per week, we need to determine how much the account balance increased per week. We can subtract the initial balance from the final balance and divide that by the number of weeks:

Rate of change per week = (Final balance - Initial balance) / Number of weeks

Using the given information, the rate of change per week is:

(350 - 300) / 4 = 50 / 4 = 12.5

Therefore, the rate of change in Michael's savings account per week is $12.50.

Answer:

The C-intercept, 15, means that if Janelle drove 0 miles on a particular day it would cost her 15 dollars to rent the car for that day.

Step-by-step explanation:

The slope, 0.32, means that the cost for renting the car on a particular day increases by 0.32 of a dollar for each mile she drives on that day.

The slope of the equation C=0.32m+15 is 0.32. The slope represents the rate of change in the cost per day for each unit increase in the number of miles Janelle drives. In this case, for every additional mile Janelle drives, the cost of renting the car increases by 0.32 dollars.

Answer:

The correct answer is the second option.

Step-by-step explanation:

If X + R = S, then X = S - R. You need to subtract each pair:

-2 - 0 = -2

-8 - 3 = -11

0 - (-4) = 4

2 - 5 = -3

Answer:

B

Step-by-step explanation:

Edge2020

Answer:

Each share lost $20 in value over 4 days time

Step-by-step explanation:

$5 loss for 4 days

5 x 4 = 20

$20 loss in 4 days.

Answer:

85.25

Step-by-step explanation:

155 x (11/20) =85.25 feet

Answer:

The answer to your question is letter C

Step-by-step explanation:

A. [9-4x2) + (-4x2y) + 10x2y] + 2xy2  : in this polynomial the first term is not a like term, then this is incorrect.

B. 10x2y + 2xy2 + [(-4x2) + (-4x2y)]  : in this polynomial, the terms that are grouped, are not like terms, then is incorrect.

C. (-4x2) + 2xy2 + [10x2y + (-4x2y)]  ; This polynomial is the right answer because the like terms are grouped.

D. [10x2y + 2xy2 + (-4x2y)] + (-4x2): This polynomial is incorrect because one of the terms that are grouped is not a like term.

Answer:

-2

Step-by-step explanation:

he wants to get -7 because -4 + -3 = -7

he has -5 currently, so to get to -7 I added -2 which is the amount he needs.

I hope this helps you :)

Stuart requires a score of atleast - 2 on his last hole in other to beat his best score.

Best score = - 4

Required score < Best score + (-2)

Required score < - 4 + (-2)

Current score = - 5

Therefore, the least score required to beat his best score is - 7

Therefore, the required score on last hole will be :

Therefore, a score of - 2 is required on last hole in other to beat his best score.

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Answer:

Length = 128.3

Step-by-step explanation:

The 3 sides of a regular triangle are the same, the 2 sides that are in terms of x are equal:

5x + 40 = 8x - 13

40 + 13 = 8x - 5x

53 = 3x

17.7 = x

The length of a side = 5(17.7) + 40 = 128.3

Answer:

20 months

Step-by-step explanation:

Let the number of months be denoted by x.

Then, we shall form two equations to represent the total cost from each dealer. Thus,

2500 + 150x is the cost of the motorcycle from the first dealer.

3000 + 125x is the cost of the motorcycle from the second dealer.

If the costs from the dealers are equal, then

2500 + 150x =3000 +125x

150x- 125x = 3000-2500

        25x = 500

          x = 500/ 25

           x =20 months

Answer:

The expected value is 5.

Step-by-step explanation:

As we can see, X=Y+Z. Then, by the linearity of the expected value operator, we have that

[tex]E(X)=E(Y)+E(Z).[/tex]

Observe that Y and Z have countable sets of outcomes (1,2,3,....) then,

[tex]E(X)=\sum^\infty_{n=1}nP(Y=n)[/tex],

[tex]E(Z)=\sum^\infty_{n=1}nP(Z=n)[/tex],

Then:

[tex]E(Y)=\sum^\infty_{n=1}nP(Y=n)=\sum^\infty_{n=1}n(\frac{1}{2} )^n=\\\\\sum^\infty_{m=1}\sum^\infty_{n=m}(\frac{1}{2} )^n=\sum^\infty_{m=1}(\frac{1}{2} )^{m-1}=\sum^\infty_{m=0}(\frac{1}{2} )^{m}=2.[/tex]

[tex]E(Z)=\sum^\infty_{n=1}nP(Z=n)=\frac{1}{3}\sum^\infty_{n=1}n(\frac{2}{3} )^{n-1}=\frac{1}{3}\sum^\infty_{m=1}\sum^\infty_{n=m}(\frac{2}{3} )^{n-1}[/tex]

Observe that, by the geometric series formula:

[tex]\sum^\infty_{n=m}(\frac{2}{3} )^{n-1}=\sum^\infty_{n=1}(\frac{2}{3} )^{n-1}-\sum^{m-1}_{n=1}(\frac{2}{3} )^{n-1}=3-\sum^{m-1}_{n=1}(\frac{2}{3} )^{n-1}=\\\\3-\sum^{m-2}_{n=0}(\frac{2}{3} )^{n}=3-\frac{1-(\frac{2}{3})^{m-1} }{1-\frac{2}{3}}=3(\frac{2}{3})^{m-1}[/tex]

Therefore

[tex]E(Z)=\frac{1}{3}\sum^\infty_{m=1}\sum^\infty_{n=m}(\frac{2}{3} )^{n-1}=\frac{1}{3}\sum^\infty_{m=1}3(\frac{2}{3})^{m-1} =\\\\ \sum^\infty_{m=1}(\frac{2}{3})^{m-1} = \sum^\infty_{m=0}(\frac{2}{3})^{m} =3.[/tex]

Finally, E(X)=E(Y)+E(Z)=2+3=5.

Using the binomial distribution, it is found that the expected value of the total number of tosses is of 5.

For each coin, there are only two possible outcomes, either it is heads, or it is tails. The outcome of a coin is independent of any other coin, hence the binomial distribution is used to solve this question.

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The expected number of trials until q successes is:

[tex]E_s(X) = \frac{q}{p}[/tex]

For coin A, we obtain Heads with probability 1/2, hence:

[tex]E_{sA}(X) = \frac{1}{\frac{1}{2}} = 2[/tex]

For coin B, we obtain Heads with probability 1/3, hence:

[tex]E_{sB}(X) = \frac{1}{\frac{1}{3}} = 3[/tex]

2 + 3 = 5, hence, the expected value of the total number of tosses is of 5.

More can be learned about the binomial distribution at https://brainly.com/question/14424710

Answer:

The last graph, where the functions intersect at only one point.

Step-by-step explanation:

A system of equations with only one solution is the one that in some point the solutions of each ecuation is exactly the same. In the graphs 1 and 3, where the equations does not intersect each other, the system of equations have no solution. In the second graph, the equations intersect 2 times, so the system of equations have 2 solutions.

Answer:

The last graph:/ D

Step-by-step explanation:

i got it right on the test

Answer:

[tex] - \frac{2[1 - x]}{3} = g[f(x)] \\ \\ \frac{3x}{2 - x} = f[g(x)][/tex]

Step-by-step explanation:

They are not.

For the g[f(x)] function, you substitute ³/ₓ ₋ ₁ from the f(x) function in for x in the g(x) function to get this:

[tex] \frac{2}{ \frac{3}{x - 1}} [/tex]

Then, you bring x - 1 to the top while changing the expression to its conjugate [same expressions with opposite symbols]:

[tex] - \frac{2[1 - x]}{3}[/tex]

You could also do this [attaching another negative would make that positive].

For the f[g(x)] function, ²/ₓ from the g(x) function for x in the f(x) function to get this:

[tex] \frac{3}{ \frac{2}{x} - 1}[/tex]

Now, if you look closely, ²/ₓ is written as 2x⁻¹, and according to the Negative Exponential Rule, you bring the denominator to the numerator while ALTERING THE INTEGER SYMBOL FROM NEGATIVE TO POSITIVE:

[tex] \frac{3x}{2 - x} [/tex]

When this happens, x leaves the two and gets attached to the three, and 1 gets an x attached to it.

I am joyous to assist you anytime.