The weight of an object on the Moon is about 0.167 of its weight on Earth. How much does a 180-pound astronaut weigh on the Moon?

2a) The equation used to answer the question is (1/Time to fill the pool) = (1/Time taken by hose) - (1/Time taken by leak).

2b) It would take 40 minutes to fill the pool with water when there is a small hole causing a leak.

To solve this, we can use the concept of rates of work.

2a) The equation we would use to answer the question is:

(1/Time to fill the pool) = (1/Time taken by hose) - (1/Time taken by leak)

2b) Let's plug in the values given in the question:

(1/Time to fill the pool) = (1/30 minutes) - (1/120 minutes)

To find the time to fill the pool, we first need to find a common denominator for the fractions. The common denominator is 120, so we can rewrite the fractions as:

(1/Time to fill the pool) = (4/120) - (1/120)

Now, add the fractions on the right side:

(1/Time to fill the pool) = (3/120)

Next, take the reciprocal of both sides to solve for the time to fill the pool:

Time to fill the pool = 120/3

Time to fill the pool = 40 minutes

So, it would take 40 minutes to fill the pool.

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Step-by-step explanation:

the answer is 14

3/7 • 2 1/14

=14

Answer:

y = \(\frac{7}{6}\) x - 3

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 )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (9, 2 ) and (x₂, y₂ ) = (3, - 5 )

m = \(\frac{-5-2}{3-9}\) = \(\frac{-7}{-6}\) = \(\frac{7}{6}\)

• Parallel lines have equal slopes , so

m = \(\frac{7}{6}\) is the slope of the parallel line

the line crosses the y- axis at (0, - 3 ) ⇒ c = - 3

y = \(\frac{7}{6}\) x - 3 ← equation of parallel line

Hey there!

\( \\ \)

\( \green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}}\)

\( \\ \)

To find the equation of a line, we first have to determine its slope knowing that parallel lines have the same slope.

Let the line that we are trying to determine its equation be \( \: \sf{d_1} \: \) and the line that is parallel to \( \: \sf{d_1} \: \) be \( \: \sf{d_2} \: \) .

\( \sf{d_2} \:\) passes through the points (9 , 2) and (3 , -5) which means that we can find its slope using the slope formula:

\( \sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{y_2} - \orange{y_1}}{\red{x_2} - \blue{x_1 }}} \)

\( \\ \)

⇒Subtitute the values :

\( \sf{(\overbrace{\blue{9}}^{\blue{x_1}}\: , \: \overbrace{\orange{2}}^{\orange{y_1}}) \: \: and \: \: (\overbrace{\red{3}}^{\red{x_2}} \: , \: \overbrace{\green{-5}}^{\green{y_2}} )} \)

\( \implies \sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{-5} - \orange{2}}{\red{ \: \: 3} - \blue{9 }} = \dfrac{ - 7}{ - 6} = \boxed{ \bold{\dfrac{7}{6} }}}\)

\( \sf{\bold{The \: slope \: of \: both \: lines \: is \: \dfrac{7}{6}}} \).

Assuming that we want to get the equation in Slope-Intercept Form, let's substitute m = 7/6:

Slope-Intercept Form:

\( \sf{y = mx + b} \\ \sf{Where \: m \: is \: the \: slope \: of \: the \: line \: and \: b \: is \: the \: y-intercept.} \)

\( \implies \sf{y = \bold{\dfrac{7}{6}}x + b} \) \( \\ \)

We know that the coordinates of the point (0 , -3) verify the equation since it is on the line \( \: \sf{d_1} \: \). Now, replace y with -3 and x with 0:

\( \implies \sf{\overbrace{-3}^{y} = \dfrac{7}{8} \times \overbrace{0}^{x} + b} \\ \\ \implies \sf{-3 = 0 + b} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \sf{\boxed{\bold{b = -3}} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \)

Therefore, the equation of the line \( \: \bold{d_1} \: \) is \( \green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}} \)

\( \\ \)

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Answer:

times 1 by 80 and 5 by 80

Step-by-step explanation:

then you can determine from there

Answer:

6m+ 4

Step-by-step explanation:

2(2m-1) + 2(m+3)

4m - 2 + 2m + 6

6m + 4

The solution to the literal equation is y = x - 2.

To solve inequality in y, we need a number such that the assertion holds if we replace y with that number. Isolating the variable on one side of the inequality and leaving the other terms constant is the first step in resolving the inequality.

From the given information:

4x + 1 = 9 + 4y

To solve for y, we have to switch the sides:

9 + 4y = 4x + 1

Subtract 9 from both sides

9 - 9 + 4y = 4x + 1 - 9

4y = 4x - 8

Divide both sides by 4

\(\dfrac{4y}{4}= \dfrac{4x}{4}-\dfrac{8}{4}\)

y = x - 2

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Answer:

A

Step-by-step explanation:

diameter

The another name for the chord that passes through the center of the circle is the diameter.

The correct option is (A).

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point.

As per the given data:

We have to find out the alternate name for a chord that passes through the center of a circle out of the given options.

Diameter:

It's a chord that passes through the center and touches the ends of the circumference of the circle.

Hence, this is correct.

Circumference:

It's the length of the boundary of a circle, hence this cannot be a chord.

This is incorrect.

Center:

It's a point and a chord is a line, hence this cannot be true.

Radius:

A radius is not a chord, as it does not touch the endpoints on the circumference of the circle.

The another name for the chord that passes through the center of the circle is the diameter.

Hence, The another name for the chord that passes through the center of the circle is the diameter.

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Answer:

3.1 sec.

Step-by-step explanation:

The system of linear differential equations is homogeneous and the largest interval such that a unique solution of the initial value problem is guaranteed to exist is (-∞, ∞).

Given the system of linear differential equations can be put in the form (A - λI)X = 0, where λ and X are the eigenvalue and eigenvector of the matrix A, respectively. Determine λ and X and determine whether the system is homogeneous or non-homogeneous. Choose the largest interval such that a unique solution of the initial value problem is guaranteed to exist.For the given system of linear differential equations:

dx/dt = 4x + 6y

dy/dt = -2x - 4y

the matrix A is given by:

 [4   6 ][-2 -4 ]

The eigenvalue λ can be found from the characteristic equation det(A - λI) = 0 as follows:

[4 - λ   6    ][-2    -4 - λ] = 0λ² - λ - 8 = 0

Solving the above equation, we get, λ = -1 and λ = 8.

Therefore, λ1 = -1 and λ2 = 8 are the eigenvalues of matrix A.

To find the eigenvectors, we solve the equation (A - λI)X = 0 for each λ separately.

For λ1 = -1, we get[A - (-1)I]X = 0

⇒[5   6 ][x    ] = 0[-2   -3][y    ]      [x    ][-2y  ]

Therefore, the eigenvector corresponding to

λ1 = -1 is

X1 = [x y]T = [2 -1]T.

For λ2 = 8, we get

[A - 8I]X = 0⇒[-4   6 ][x    ]

= 0[-2  -12][y    ]  [x    ][3y   ]

Therefore, the eigenvector corresponding to

λ2 = 8 is

X2 = [x y]T = [3 1/2]T.

The given system of linear differential equations can be written in the matrix form as

dX/dt = AX,

where A is the matrix [4 6][-2 -4] and X is the column vector [x y]T.

The general solution of this system is given by

X(t) = c1 e^(λ1t)X1 + c2 e^(λ2t)X2,

where c1 and c2 are constants of integration and X1 and X2 are the eigenvectors corresponding to the eigenvalues λ1 and λ2, respectively. Therefore, the general solution of the given system is given by

x(t) = 2c1 e^(-t) + 3/2 c2 e^(8t)y(t)

= -c1 e^(-t) + 1/2 c2 e^(8t)

where c1 and c2 are constants of integration to be determined from the initial conditions. Since the system of differential equations is homogeneous, the trivial solution x(t) = y(t) = 0 is a solution of the system. Hence, the system is homogeneous.

The given initial value problem has initial conditions x(0) = 1 and y(0) = 0.

Therefore, we have

c1 + 3/2 c2 = 1 and

-c1 + 1/2 c2 = 0

Solving these two equations, we get c1 = 1/5 and c2 = 2/5.

Therefore, the particular solution of the given initial value problem is given by

x(t) = (2/5) e^(-t) + (6/5) e^(8t)y(t)

= -(1/5) e^(-t) + (1/5) e^(8t)

Hence, the largest interval such that a unique solution of the initial value problem is guaranteed to exist is (-∞, ∞).

The system of linear differential equations is homogeneous and the largest interval such that a unique solution of the initial value problem is guaranteed to exist is (-∞, ∞).

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In total Victoria worked for \(8 \frac{1}{4}\) hours. Therefore, option D is the correct answer.

Given that, Victoria logged in to work at 8:15 am and logged out at 4:25 pm.

A clock or a timepiece is a device used to measure and indicate time. The clock is one of the oldest human inventions, meeting the need to measure intervals of time shorter than the natural units such as the day, the lunar month and the year.

Victoria logged in to work at 8:15 am

8:15 am →9:15 am →10:15 am→11:15 am→12:15 pm→1:15 pm→2:15 pm→3:15 pm→4:15 pm

8:15 am →9:15 am = 1 hour

9:15 am →10:15 am = 1 hour

10:15 am→11:15 am = 1 hour

11:15 am→12:15 pm = 1 hour

12:15 pm→1:15 pm = 1 hour

1:15 pm→2:15 pm = 1 hour

2:15 pm→3:15 pm = 1 hour

3:15 pm→4:15 pm = 1 hour

So, in total Victoria logged in for 8 hours 10 mins

Its nearest quarter is \(8 \frac{1}{4}\) hours

In total Victoria worked for \(8 \frac{1}{4}\) hours. Therefore, option D is the correct answer.

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Answer:

cost of bag is Rs.1500 and umbrella is Rs.500

Step-by-step explanation:

let cost of umbrella be x

so cost of bag = 5x - 1000

total cost = Rs 2000

Now,

5x - 1000 + x = 2000

6x = 3000

x = Rs.500 (cost of umbrella)

5x - 1000 = 5×500-1000 = Rs.1500 (cost of bag)

Answer:

The substitution method can be used for any set of equations.

I'll proceed assuming you meant to ask how the substitution method can be used to solve for x and y in the 2 equations you entered.

------------------------

y=2x-1 and y=-3x+4

Since both expressions on the right sides of the eqns = y, they equal each other.

2x-1 = -3x+4

This is substitution, the right sides were substituted for y.

Add 3x

5x-1 = 4

Add 1

5x = 4

x = 1 x

Now substitute 1 for x into either eqn to find y.

y = 2*1-1

y = 1 y

we're done.

Step-by-step explanation:

Answer:

x=7

y=22

Step-by-step explanation:

So how you do these problems is to basically solve this as an algebraic equation since we know that both of your problems are the same due to the transitive property of equality.

\(2x+8=3x+1\\2x=3x-7\\-x=-7\\x=7\)

Now that we know that x is 7, substitute it into the equations:

\(y=2*7+8\\y=14+8\\y=22\)

In conclusion, by substitution, x=7 and y=22. Hope this answered your question :D

Answer:

A

Step-by-step explanation:

the other options have a common difference

Answer:

A is not arithmetic series

Step-by-step explanation:

In B,C and D there is arithmetic series as a2-a1=a3-a2

In A. there is no such series.....

If you want the probability of randomly drawing a red marble to be 3/5, you need to add 13 red marbles.

The probability of drawing a red marble is equal to the quotient between the number of red marbles and the total number of marbles in the bag.

Initially, there are 12 red marbles and 32 in total, so if we add another x red marbles, we will have:

Then the probability will be:

p = (12 + x)/(32 + x)

And we want this to be 3/5, then we need to solve:

(12 + x)/(32 + x) = 3/5

(12 + x)*5 = 3*(32 + x)

60 + 5x = 96 + 3x

5x - 3x = 96 - 60

2x = 36

x = 36/2 = 13

x = 13

You need to add 13 red marbles.

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Answer:

D

Step-by-step explanation:

Solve through logic and brain rather than lengthy calculations

Trick to be used

See

Only option D contains y≤4

Option D is correct

Answer:

4g + 4

Step-by-step explanation:

Perimeter of a rectangle = 2(length + width)

Length = 0.7g + 2

Width = 1.3g

Plug in the values into the equation

Perimeter = 2(0.7g + 2 + 1.3g)

Perimeter = 2(0.7g + 1.3g + 2)

Perimeter = 2(2g + 2)

= 2*2g + 2*2

Perimeter = 4g + 4

Answer:

12x =102-6

x=96/12

x=8 is the correct answer

Answer:

Answer is x=8.

Step-by-step explanation:

12x+6=102

12x+6-6=102-6

12x=96

12x/12=96/12

x=8

I hope it's helpful!

Answer:

the answer is -6

Step-by-step explanation:

if you have -5 and you take away another number, you end up with -6

Answer:

-6

Step-by-step explanation:

-5 - 1 ISNT -4

-5 + 1 IS -4

The expression (-2 - 4i) + (8 - 7i) evaluates to 6 - 11i.

To evaluate the expression (-2 - 4i) + (8 - 7i), we'll combine the real parts and the imaginary parts separately.

Starting with the real parts: -2 + 8 = 6.

Now let's combine the imaginary parts: -4i + (-7i) = -4i - 7i = -11i.

Putting the real part and the imaginary part together, we have:

6 - 11i.

Thus, the expression (-2 - 4i) + (8 - 7i) evaluates to 6 - 11i.

In the final form a+bi, where "a" represents the real part and "bi" represents the imaginary part, the result is:

6 - 11i.

This means that the real part of the sum is 6, and the imaginary part is -11i.

It's also worth mentioning that the expression (-2 - 4i) + (8 - 7i) represents the addition of two complex numbers. The complex number (-2 - 4i) has a real part of -2 and an imaginary part of -4i. The complex number (8 - 7i) has a real part of 8 and an imaginary part of -7i. When these two complex numbers are added together, we obtain the resulting complex number 6 - 11i, which represents a combination of a real part and an imaginary part.

Complex numbers are often represented in the form a+bi, where "a" is the real part and "bi" is the imaginary part. This notation helps distinguish between the real and imaginary components and allows for easy arithmetic operations on complex numbers. In this case, the sum of (-2 - 4i) and (8 - 7i) simplifies to 6 - 11i when written in the standard form a+bi.

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Answer:

It's 19. Glad to help lol

Answer:

19

Step-by-step explanation:

Answer: 7e-5 millimeters, and the nanometer scale is more appropriate

Step-by-step explanation: PLEASE MARK ME BRAINLIEST!!!!!!

-divide the length value by 1e+6

-The millimeter scale and the centimeter scale are two huge, while the nanometer scale is too small. The nanometer scale is often used to measure atoms and viruses.

Answer:

a) The length of the virus in millimetres is 0.000 07 mm.

b) Viruses are microscopic and so nanometres are the more appropriate unit for writing the length of the virus since the nanometre is a smaller unit of measurement than the millimetre.

Step-by-step explanation:

SI is the abbreviation for The International System of Units.

The SI base unit for length is metres (m).

Milli and nano are SI prefixes used to form decimal multiples or submultiples of SI units.

Therefore, to convert nanometres to millimetres, multiply the nanometres by 10⁻⁶:

So 70 nanometres is:

Viruses are microscopic and so nanometres are the more appropriate unit for writing the length of the virus since the nanometre is a smaller unit of measurement than the millimetre.

Answer:

-3x - 2

Step-by-step explanation:

-6x-4/2

-3x - 2 (divided 2 to everything)

Best of Luck!

The country is 3250 miles in distance from east to west, and 3400 miles from north to south.

Given Information

It is given that,

The distance of the country on map from east to west, l = 65 inches

The distance of the country on map from north to south, b = 68 inches

As per the given scaling of map, 1 inch = 50 miles

How large is the actual country?

Thus, the actual distance from east to west, L = l × 50 miles

L = 65 × 50 miles

L = 3250 miles

The actual distance from north to south, B = b × 50 miles

B = 68 × 50 miles

B = 3400 miles

Therefore, the actual size of the country is 3250 miles in distance from east to west, and 3400 miles in distance from north to south.

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Answer:

I think it will c because I have some eggs at home

To form TIC as quickly as possible at a process temperature of 927°C, we should use V (vanadium) in the metallurgical process.

In order to determine the element that should be used to form TIC (titanium carbide) as soon as possible, we need to compare the values of the Gibbs free energy (ΔG) for the reactions involving each element.

Given the reaction equations and the corresponding values of ΔG for each reaction, we can calculate the values of ΔG at the process temperature of 927°C. By comparing these values, we can determine which reaction is most favorable for the formation of TIC.

From the given data:

ΔG for the reaction V + C = VC is given as -83600 + 6.6T.

ΔG for the reaction Si + C = SiC is given as -53400 + 24.2T.

ΔG for the reaction 3Cr + 2C = Cr3C2 is given as -87020 - 16.5T.

By substituting the process temperature of 927°C (which is equivalent to 1200 K) into the corresponding equations, we can calculate the values of ΔG for each reaction.

After comparing the calculated values, we find that the reaction V + C = VC has the lowest value of ΔG at 927°C. This indicates that the formation of TIC using vanadium is the most favorable and spontaneous reaction at this temperature.

Therefore, to form TIC as quickly as possible at a process temperature of 927°C, we should use vanadium (V) in the metallurgical process.

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The probability you expect the spinner to not land on B is 0.4.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes

Given that, a spinner is divided into three equal parts A, B, and C.

The repeated experiment of spinning the spinner twice is simulated 125 times.

The total number of outcomes = 125

The number of favorable outcomes = 12+18+15+17+13= 75

Probability of landing on B = 75/125

= 0.6

Probability of not landing on B

= 1-0.6

= 0.4

Therefore, the probability you expect the spinner to not land on B is 0.4.

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"Your question is incomplete, probably the complete question/missing part is:"

A spinner is divided into three equal parts A, B, and C. The repeated experiment of spinning the spinner twice is simulated 125 times. A table of outcomes is shown.

Based on the table, for what probability can you expect the spinner to not land on B?

(A) 0.10

(B) 0.33

(C) 0.40

(D 0.66

The number of calories that Darrell will burn in 1 minute while kayaking is given as follows:

4 calories.

The number of calories that Darrell will burn in 1 minute while kayaking is obtained applying the proportions in the context of the problem.

For each input-output pair in the table, the constant of proportionality is of 4, hence the number of calories that Darrell will burn in 1 minute while kayaking is given as follows:

4 calories.

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Answer:

x = 39

Step-by-step explanation:

Its an isosceles triangle, so,

angle A = angle C = 2x

Sum of angles in a triangle = 180, which is why when you add x - 15 , 2x and 2x its equal to 180.

Now you have a linear equation. Solve it to find the value of x.