Lena drove 355 miles using 17 gallons of gas. At this rate, how many gallons of gas would she need to drive 284 miles.​

The selection sequence for the facility departments is I, O, B, C, A, D, E, F, T.

The relationship chart for the facility departments is given below: A|BEIOTB|CEFOC|DOD|ETOE|FTE|ITX

From the relationship chart, the following TCR values can be calculated as follows:

T(A, B) = 2T(B, C) = 1T(C, D) = -1T(D, E) = -1T(E, F) = -1T(I, O) = 0T(O, T) = -4T(E, T) = -3

And the selection sequence can be found as follows:

Step 1: Select I and O. As T(I, O) = 0, there is no conflict between these departments.

Step 2: Select B and C. As T(B, C) = 1 and T(I, O) = 0, the TCR for B and C is 1.

Step 3: Select A and D. As T(A, B) = 2 and T(B, C) = 1, the TCR for A and D is 3.

Step 4: Select E and F. As T(D, E) = -1 and T(E, F) = -1, the TCR for E and F is -2.

Step 5: Select T. As T(E, T) = -3 and T(O, T) = -4, the TCR for T is -7.

The selection sequence for the facility departments is I, O, B, C, A, D, E, F, T.

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Use spherical coordinates to evaluate the triple integral, the value of the triple integral is 16π/3.

To evaluate the triple integral using spherical coordinates, first, convert the given limits to spherical coordinates. The limits of integration are: ρ (rho) ranges from 0 to 2, θ (theta) ranges from 0 to 2π, and φ (phi) ranges from 0 to π/2. The conversion of the integrand from Cartesian to spherical coordinates gives ρ² sin(φ). The triple integral in spherical coordinates is:
∫(0 to 2) ∫(0 to 2π) ∫(0 to π/2) ρ² sin(φ) dφ dθ dρ
Now, evaluate the integral with respect to φ, θ, and ρ in that order:
∫(0 to 2) ∫(0 to 2π) [-ρ² cos(φ)](0 to π/2) dθ dρ = ∫(0 to 2) ∫(0 to 2π) ρ² dθ dρ
∫(0 to 2) [θρ²](0 to 2π) dρ = ∫(0 to 2) 4πρ² dρ
[(4/3)πρ³](0 to 2) = 16π/3
Thus, the value of the triple integral is 16π/3.

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The simple interest for a deposit of $ 5,000 at 3 % rate of interest for 1 year would be $ 150

What is Simple Interest?

Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.

Simple Interest = ( Principal Amount x Rate x Time Period ) / 100

Given data ,

Let the simple interest be represented as S

Now , the value of S is

The principal amount = $ 5,000

The rate of interest R = 3 %

The time period T = 1 year

So , the Simple Interest is given by the equation

Simple Interest = ( Principal Amount x Rate x Time Period ) / 100

Substituting the values in the equation , we get

Simple Interest S = ( 5000 x 3 x 1 ) / 100

On simplifying the equation , we get

Simple Interest S = 150000 / 100

Simple Interest S = $ 150

Therefore , the value of S is $ 150

Hence , the simple interest for the deposit is $ 150

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Answer:

7+2x=3x

Step-by-step explanation:

7 more than twice a number is 3 times the same number.

solution,

Let the number be x, the

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

Step-by-step explanation:

let the number be x ,

so,

twice of number = 2x

3 times the number = 3x

and 7 more than 2x = 3x

so, the equation is,

7 + 2x = 3x

x = 7

verifying,

7 + 2(7) = 3(7)

→ 7 + 14 = 21

→ 21 = 21

hope this answer helps you dear!

Answer: the speed of the elevator is 4.6 miles per hour.

Step-by-step explanation:

Given, The elevator in the Washington Monument takes 75 seconds to travel 506 feet to the top floor.

Since 1 hour = 3600 seconds

⇒ 1 second = \(\dfrac{1}{3600}\) hour

⇒ 75 seconds = \(\dfrac{75}{3600}\) hour \(=\dfrac{1}{48}\) hour

1 mile = 5280 feet

1 feet = \(\dfrac{1}{5280}\) mile

506 feet = \(\dfrac{506}{5280}\) miles \(=\dfrac{23}{240}\) miles

Speed = \(\dfrac{Distance}{Time}\)

\(=\dfrac{\dfrac{23}{240}}{\dfrac{1}{48}}\\\\=\dfrac{23\times48}{240}\\\\=\dfrac{23}{5}\\\\=4.6\text{ miles per hour}\)

Hence, the speed of the elevator is 4.6 miles per hour.

Answer:

1 hour and 8 minutes

Step-by-step explanation:

After travelling 1 hour you’ve reached 60 miles. So you go 1 mile/ minute.

You have then 8 miles left. You get: 8 minutes. Which gives us the answer:

1 hour and 8 minutes.

Answer:Its 315

Step-by-step explanation:

Hope this helps!

Answer:

\(g\circ f=\{(1,3),(3,6),(5,8)\}\).

\(f\circ g\) does not exist.  

Step-by-step explanation:

It is given that,

\(f=\{(1,2),(3,4),(5,6)\}\)

\(g=\{(2,3),(4,6),(6,8)\}\)

We need to find the composition gof.

\((g\circ f)(x)=g(f(x))\)

Now,

\((g\circ f)(1)=g(f(1))=g(2)=3\)

\((g\circ f)(3)=g(f(3))=g(4)=6\)

\((g\circ f)(5)=g(f(5))=g(6)=8\)

So, \(g\circ f=\{(1,3),(3,6),(5,8)\}\).

We need to check whether \(f\circ g\) exist of not.

If range of g(x) is subset of domain of f(x), then we can say composition function \(f\circ g\) exists.  

Now,

Range of g(x) = {3,6,8}

Domain of f(x) = {1,3,5}

Since range of g(x) is not a subset of domain of f(x), then we can say composition function \(f\circ g\) does not exist.  

The probability that the flight would be delayed when it is raining = 0.79

Given that

the probability that it will rain is 0. 15

the probability that the flight will be delayed is 0. 11.

the probability that it will not rain and the flight will leave on time is 0. 75.

from the above

we can say that

the probability that the flight would be delayed when it is raining = 0.15 + 0.75 - 0.11

= 0.9- 0.11

= 0.79

The probability that the flight would be delayed when it is raining = 0.79

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By solving the systems of equations we can say there were 373 children and 235 adults who swam at the public pool that day.

To determine the number of children and adults who swam at the public pool, we can set up a system of equations based on the given information.

Let's assume the number of children is represented by 'C' and the number of adults by 'A'.

From the problem, we have the following information:

1. The total number of people who used the pool is 608:

C + A = 608

2. The total receipts from admission were $1029.50:

1.50C + 2.00A = 1029.50

To solve this system of equations, we can use various methods, such as substitution or elimination.

Using the substitution method, we can solve the first equation for C:

C = 608 - A

Substituting this value into the second equation:

1.50(608 - A) + 2.00A = 1029.50

912 - 1.50A + 2.00A = 1029.50

0.50A = 117.50

A = 235

Substituting the value of A back into the first equation:

C + 235 = 608

C = 373

Therefore, there were 373 children and 235 adults who swam at the public pool that day.

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Answer:

4. y=-5x+2

Step-by-step explanation:

Subtract the 5x from both sides

Answer:

we can look at a graph

Step-by-step explanation:

Step-by-step explanation:

Using the unit circle, the answer is

135 degrees

Answer:figure it out yourself

Step-by-step explanation:

Step-by-step explanation:

Let x and y be the present ages of the father and his son respectively.

x + y = 80

2y = 40

y = 20

x + 20 = 80

x = 60

Answer:

n+5>11

Step-by-step explanation:

> is greater than

< is less than

> with the line under it is greater than or equal to

<with the line under it is less than or equal to

Answer:

8 in

Step-by-step explanation:

Area of a square = l×w

Since it is a square then l and w are equal to each other.

So we can instead just say l^2 = A

l^2 = 68.2

l = square root of 68.2

l = 8.26

Answer:

For 4x - 5y = 14 I got (0, - 14/5) (that is 14 over 5 as a fraction)

For y = x - 3 I got (0, -3)

I hope this helps!

Answer:

The probability of P(Aç) = 27/35

The linear expression that is not equivalent to the other three is D) (-5x-1)+(6x + 7).

A linear expression is an algebraic expression which is composed of constants, variables, and coefficients that are related by only addition and multiplication operations. It usually takes the form of ax + b, where 'a' and 'b' are constants and 'x' is a variable. Linear expressions can be used to describe various mathematical and physical phenomena, such as the slope of a line or the volume of a cylinder.

This linear expression is not equivalent to the other three because it does not have the same coefficient for the x terms and the constant terms. The other three expressions all have the same coefficients for the x terms and the constant terms, making them equivalent.

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Hi!

\(|15x+2|=8\\\\\\15x+2=8\\15x=8-2\\15x=6 \ \ |:15\\\boxed{x_1=0,4}\\\\\\15x+2=-8\\15x=-8-2\\15x=-10 \ \ |:15\\\boxed{x_2=-\frac{2}{3}}\)

Answer:

x = 2/5      x = -2/3

Step-by-step explanation:

|15x + 2 |= 8

There are two solutions, one positive and one negative

15x + 2 = 8  and 15x + 2 = -8

Subtract 2 from each side

15x + 2-2 = 8-2  and 15x + 2-2 = -8-2

15x = 6                             15x = -10

Divide by 15

15x/15 = 6/15                   15x /15 = -10/15

x = 2/5                               x = -2/3

Answer:

a) 1

b) n² - n

c) 2n - 1

d) B, always odd

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Log x+y = logbx − logbyGiven log630 ≈ 1.898 and log62 ≈ 0.387, log615 ≈ 2.086.

Given log 630 ≈ 1.898 and log 62 ≈ 0.387,

We have log 630 = log (6 * 62 * 10) = log 6 + log 62 + log 10 = 1 + 0.387 + 1 = 2.387

And log 615 = log (6 * 62 * 5) = log 6 + log 62 + log 5 = 1 + 0.387 + 0.699 = 2.086

So, log 615 ≈ 2.086

In the example given, log 630 ≈ 1.898 and log 62 ≈ 0.387. These logarithmic values are used to simplify other logarithmic expressions and, the logarithm of 615 was found to be approximately 2.086.

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Answer:

She needs 168 more cels to draw to complete the film sequence

Step-by-step explanation:

120 Cells in 5 seconds

You want 12 seconds.

Ratio (Proportion)

120:5

Lets find the "unit rate" of the proportion.

120/5 = 24

So the unit ratio is 24:1

Now, we can deduce to it being:

120:5

240:10

264:11

288:12

She has 120 done.

So, 288-120 = 168.

She needs 168 more cels to draw to complete the film sequence

The linear equation that describe the relationship between the book collection by Cameron, c and Kenji, c each month is represented as c = k - 11.

Linear equations are defined as the equations of degree one. It is represents equation for the straight line. The standard form of linear equation is written as, ax + by + c = 0, where a ≠ 0 and b ≠ 0. We have specify that Cameron collects and his friend Kenji start collecting the old books. The above table figure which contains data of books collected by both in different months. We have to determine the equation many books Cameron will have (c) when Kenji has k books. Let c and k denotes the books collected by Cameron and Kenji respectively. We see there is always increase in old book collection by one in case of both of them (Cameron and Kenji) each month. So, there exits a linear equation. Also, from the table, the Kenji's book collection is always 11 units less from Cameron's book collection. So, the required equation is written by c = k - 11 for each month. Hence, the required equation is equal to c = k - 11.

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Complete question:

The above figure complete the question.

Cameron collects old books, and they convinced their friend Kenji to start collecting as well. Every month, they go to the store together, and they each buy a book. This table shows how many books they each have: They both want an equation they can use to find how many books Cameron will have (c) when Kenji has k books. Complete their equation.

Answer:

c=k+11

Step-by-step explanation:

The sum of (8a + 2b - 4) and (3b - 5) is (8a + 5b - 9). We can find it in the following manner.

To find the sum of (8a + 2b - 4) and (3b - 5), we can simply add the corresponding coefficients of the variables a and b, as well as any constant terms.

So we have:

(8a + 2b - 4) + (3b - 5)

= 8a + 2b + 3b - 4 - 5 (grouping like terms)

= 8a + 5b - 9

Therefore, the sum of (8a + 2b - 4) and (3b - 5) is (8a + 5b - 9).

We can also explain this process by using the distributive property of addition over subtraction. This property states that the sum of two numbers with the same sign (positive or negative) can be found by adding their absolute values and keeping the common sign.

In this case, we can think of the expression (8a + 2b - 4) as the sum of three terms: 8a, 2b, and -4. Similarly, we can think of the expression (3b - 5) as the sum of two terms: 3b and -5.

Using the distributive property, we can add the terms with the same variable together:

(8a + 2b - 4) + (3b - 5)

= 8a + (2b + 3b) - (4 + 5)

= 8a + 5b - 9

Thus, we obtain the same result.

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Step-by-step explanation:

in an arithmetic sequence any new term is created by adding a defined constant to the previous term.

a1 = 2

the defined constant to be added = common difference = a2 - a1 = 11

so,

a2 = 2 + 11 = 13

a3 = a2 + 11 = a1 + 2×11 = 2 + 22 = 24

a4 = a3 + 11 = a1 + 3×11 = 2 + 33 = 35

Answer:

Juanita and Esperanza run 400 meters and 8400 meters respectively and Evelyn make 4.125 laps.

Step-by-step explanation:

The complete question is: A telesecundaria school has a race track that measures one kilometer .

Three students ran the following distances Juanita: 1 laps, Esperanza  21 laps and Evelyn: 1650 m. How many meters did Juanita and Esperanza run?  And how many laps did Evelyn make?

As we know that 1 meter = 0.0025 laps

So, the number of laps Evelyn make = 1650 \(\times\) 0.0025

                                                             = 4.125 laps

Also, 1 lap = \(\frac{1}{0.0025}\) meters

        1 lap = 400 meters

So, the meters that Juanita run = 1 \(\times\) 400 = 400 meters

Similarly, the meters that Esperanza run = 21 \(\times\) 400

                                                                   = 8400 meters

Hence, Juanita and Esperanza run 400 meters and 8400 meters respectively and Evelyn make 4.125 laps.