Lamonte's car used 5 gallons to travel 125 miles. How many gallons of gas would he need to travel 400 miles?

The solution to the differential equation is \(y = 23(x^2/2 + ((24/23)/2)x - 1/46)^(1/23)\).

Differential equations are mathematical expressions that describe the relationship between a function and its derivatives. Solving differential equations involves finding the function that satisfies the equation.

For the first problem, we can use separation of variables to solve the equation. This involves isolating the variables on opposite sides of the equation and integrating. We start by rearranging the equation to \(y' = -2ty\) and then dividing both sides by y to get\(y'/y = -2t\).

Integrating both sides gives us\(ln|y| = -t^2 + C\), where C is a constant of integration. To solve for C, we can use the initial condition y(1) = -3 - e. Plugging in t=1 and y=-3-e gives us \(-ln|3+e| = -1 + C, so C = ln|3+e| - 1\). Therefore, the solution to the differential equation is \(y = -3 - e^(t^2 - ln|3+e| + 1)\).

For the second problem, we again use separation of variables by rearranging the equation to \(2y'/x^2 = 1+23/y\) and integrating both sides. This gives us \(y = 23(x^2/2 + Cx)^(1/23)\), where C is a constant of integration. To solve for C, we use the initial condition y(1) = 1+23, which gives us 1+23 = 23(1/2 + C), so C = (1+23)/23 - 1/2.

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Answer:

A ratio of 3:1 means that there are 4 parts altogether. The fractions from the ratio can therefore be deduced as. 43 and 41. These represent the percentages: 75%:25%

Answer:

Step-by-step explanation:

The ratio can be converted into a fraction

therefore we can divide by the denominator in order to convert 30 Euros to a 3:1 ratio.

The fraction =3/4 and 1/4

so we have to divide 30 by 4

= 7.5 Euros

so;

3:1

(22.5):(7.5)

(45/2):(15/2)

45:15

divide by 15

3:1

Applying the distributive property of the product:

Answer:

4x³ - 13x + 6

Step-by-step explanation:

(2x - 1)(2x² + x - 6)

each term in the second factor is multiplied by each term in the first factor , that is

2x(2x² + x - 6) - 1 (2x² + x - 6) ← distribute both parenthesis

= 4x³ + 2x² - 12x - 2x² - x + 6 ← collect like terms

= 4x³ - 13x + 6

EXPLANATION

The greatest common of pairs is:

6 and 3:

Prime factorization of 6: 2*3

Prime factorization of 3: 3

The prime factors common to 6,3 are

=3 [Not a valid option]

30 and 36:

Prime factorization of 30: 2*3*5

Prime factorization of 36: 2*2*3*3

The prime factors common to 30,36 are

=2*3=6 [Valid option]

24 and 48:

Prime factorization of 24: 2*2*2*3

Prime factorization of 48: 2*2*2*2*3*3

The prime factors common to 24,48 are

=2*2*2*3=24 [Not a valid option]

60 and 88:

The prime factors common to 60,88 are

=2*2=4 [Not a valid option]

18 and 66:

The prime factors common to 18,66 are

=2*3=6 [Valid option]

72 and 84:

The prime factors common to 72,84 are

=2*2*3=12 [Valid option]

The right options are 2. 30 and 36 and 5. 18 and 66

(a) Therefore, the relation between redshift and distance for a photon in the tired-light hypothesis is\(z = e^{kr} - 1\)

(b)  The redshift is approximately given byz\(\approx kr\)

(a) Deriving the relation between redshift and distance for a photon in the tired-light hypothesis

As mentioned in the problem, the relationship between energy and distance is given as:

\(\frac{dE}{dr} = -kE\)

Therefore, we can write the above equation as\(\frac{dE}{E} = -kdr\)

Integrating both sides we get,

\(\int\limits_{{E_0}}^{E}\frac{dE}{E} = -\int\limits_0^r kdr  \\\ln \left(\frac{E}{E_0}\right) = -kr  \\\frac{E}{E_0} = e^{-kr}\)

As we know that photon energy is inversely proportional to the wavelength of the light.

Hence we can write the relation between wavelength and distance as,

\(\frac{\lambda}{\lambda_0} = \frac{E_0}{E} = e^{kr}\)

Now, we can write the relation between redshift and distance as,

\(\frac{\lambda}{\lambda_0} - 1 = z = e^{kr} - 1\)

Therefore, the relation between redshift and distance for a photon in the tired-light hypothesis is

\(z = e^{kr} - 1\)

(b) Showing that the relation is linear at low redshift We can show that the relation is linear at low redshift by using a Taylor expansion. The exponential function can be expanded as

\(e^{kr} \approx 1 + kr\)

Hence, the redshift is approximately given byz\(\approx kr\)

Therefore, we can see that at low redshifts the relation between redshift and distance is linear.

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The equation which represents the situation and how old is Tina is "The equation that represents this situation is t − 3 = 18. Tina is 21".

Equate Cole's age

t - 3 = 18

t = 18 + 3

t = 21

Therefore, the equation which represents the situation and how old is Tina is "The equation that represents this situation is t − 3 = 18. Tina is 21".

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The probability that the top face has an odd number of dots is 1/2. A die is a small cube that is used in gambling, games, and fortune-telling. A die is a polyhedral object that has six faces, twelve edges, and eight vertices. On the die, each face is numbered with a certain number of dots or digits.

The problem of the probability of the top face having an odd number of dots is being asked. The problem says that one of the dots is removed from the standard die at random with each dot equally likely to be chosen, then the die is rolled. Therefore, the dots will not be the same as in the standard die. An odd number is a number that, when divided by two, gives a remainder of one. 1, 3, and 5 are examples of odd numbers on a standard die. There are three possibilities: one, three, and five. Each face of the die has an equal chance of being chosen. There are only five possible results because one of the dots is removed from the standard die at random. There is a 1 in 5 chance that the missing dot will be an odd number. Hence, the probability that the top face has an odd number of dots is 1/2.

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Answer:

31.9

Step-by-step explanation:

15 + 3.6 + 18.6

To find the limit of (x + x²)/(9 − 4x²) as x approaches infinity, we can first try to apply l'Hospital's Rule, which states that if the limit of the ratio of the derivatives exists, then it is equal to the original limit.

However, in this case, a more elementary method is available: dividing both the numerator and denominator by the highest power of x.

1. Divide both the numerator and denominator by x²: lim (x/x² + x²/x²) / (9/x² - 4x²/x²) x→[infinity]

2. Simplify the expressions: lim (1/x + 1) / (9/x² - 4) x→[infinity]

3. As x approaches infinity, the terms with x in the denominator will approach 0: lim (0 + 1) / (0 - 4) x→[infinity]

4. Simplify the expression: (1) / (-4) The limit of (x + x²)/(9 − 4x²) as x approaches infinity is -1/4.

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Answer:

Table 4 represents a function.

Step-by-step explanation:

Functions require that each x-value has a unique y-value. In the other tables you see a value repeated in the x column, with a different value in the y column.

A graph of the inequality w ≤ 200 is shown in the image attached below.

In this scenario, we would solve the given inequality by making "w" the subject of formula as follows;

w/-10 ≤ -20

By multiplying both sides of the inequality by -10, we have the following:

-10 × w/-10 ≤ -20 × -10

w ≤ 200

Next, we would use an online graphing calculator to plot the inequality as shown in the graph attached below. Additionally, the circle is closed because of the less than or equal to (≤) symbol.

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The set is linearly dependent because at least one of the vectors is a multiple of another vector. So, the correct answer is C.

The given vectors are:

v1 = 2v2 = 4v3 = 78 -2 3

To determine whether the vectors V1, V2, and V3 are linearly independent or linearly dependent, we'll use the following method:

We'll create a linear combination of the vectors that has a non-zero answer.

v1 * a + v2 * b + v3 * c = 0

Where a, b and c are scalars that are not all equal to zero.

If the answer is zero, the set of vectors is linearly independent; otherwise, it is linearly dependent.

Therefore, we'll substitute the given values in the above equation.

2a + 4b + 7c = 0

8a - 2b + 3c = 0

If we multiply the first equation by -4 and add it to the second equation, we obtain:-

34c = 0c = 0

This implies that 2a + 4b = 0.

If we divide the first equation by 2, we get: a + 2b = 0

If we multiply the first equation by 3 and subtract it from the third equation, we obtain:

-5a + 5b = 0a = b

Thus, v1 = 2v2.

Since one of the vectors is a multiple of the other, the given set of vectors is linearly dependent.

Therefore, the correct answer is C.

The set is linearly dependent because at least one of the vectors is a multiple of another vector.

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Answer:

It's B

Step-by-step explanation:

B

Answer:

B-----

Step-by-step explanation:

The sample of rock if it has 15.625 grams of uranium -235 to decay will be 3.52 billion years. Then the correct option is B.

A radioactive material's half-life is the amount of time needed for half of the nucleus of an atom to decompose.

The half-life of uranium -235 is 703.8 million years.

A sample of rock started with 500 grams of uranium -235.

500 grams - 250 grams ⇒ 703.8 million years

250 grams - 125 grams ⇒ 703.8 million years

125 grams - 62.5 grams ⇒ 703.8 million years

62.5 grams - 31.25 grams ⇒ 703.8 million years

31.25 grams - 15.625 grams ⇒ 703.8 million years

Then the total number of years will be

Total years = 703.8 + 703.8 + 703.8 + 703.8 + 703.8

Total years = 3519 million years

Total years = 3.519 billion years

Total years = 3.52 billion years

The sample of rock if it has 15.625 grams of uranium -235 to decay will be 3.52 billion years.

Then the correct option is B.

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The area of the floor in the scale drawing will be equal to 150 in².

An object's area is how much space it takes up in two dimensions. It is the measurement of the number of unit squares that completely encompass the surface of a compact figure. The squared unit, which is frequently expressed as inches, square feet, etc., is the accepted unit of area.

As per the given information in the question,

Length of the classroom, l = 30 feet and,

The width of the classroom, w = 20 feet.

As per the scale drawing, the length of the classroom, l' = 15 feet

Let the scale width, w' = x feet

As we can see that the original length is twice the scale drawing.

Then, the original width also is twice the scale drawing.

So, w' = 20/2 = 10 feet.

Now, the area of the floor in the scale drawing will be,

A = wl

A = (15)(10)

A = 150 in².  

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Answer:

$182

Step-by-step explanation:

he made $154 in 11 hours

so it means that in 1 hour he makes 154/11

and then in 13 hours he makes 154/11*13=182

Answer:

$182

Step-by-step explanation:

U will divide 154 by 11 to get for one hour then ur result will be multiplyed by 13 to give u the answer.

154/11=44

44×13=182

Please the image attached below to find the image by pure translation of the figure seen in the picture set aside.

In this problem we find a figure formed by eight vertices: (1, 3), (1, 4), (4, 4), (4, 3), (2, 3), (3, 3), (2, 1), (3, 1), each of which has to be modified by applying the translation vector (4, 5). Now we proceed to find the resulting coordinates:

(1, 3) + (4, 5) = (5, 8)

(1, 4) + (4, 5) = (5, 9)

(4, 4) + (4, 5) = (8, 9)

(4, 3) + (4, 5) = (8, 8)

(2, 3) + (4, 5) = (6, 8)

(3, 3) + (4, 5) = (7, 8)

(2, 1) + (4, 5) = (6, 6)

(3, 1) + (4, 5) = (7, 6)

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The probability of low sales for the next three days, given that sales were low today, is 1.0 or 100%.

To find the transition matrix for the Markov chain, we can represent it as follows:

     |  P(1 → 1)  P(1 → 2)  P(1 → 3) |

     |  P(2 → 1)  P(2 → 2)  P(2 → 3) |

     |  P(3 → 1)  P(3 → 2)  P(3 → 3) |

From the given information, we can determine the transition probabilities as follows:

P(1 → 1) = 1 (since if sales are low one day, they are always low the next day)

P(1 → 2) = 0 (since if sales are low one day, they can never be average the next day)

P(1 → 3) = 0 (since if sales are low one day, they can never be high the next day)

P(2 → 1) = 0.1 (10% chance of going from average to low)

P(2 → 2) = 0.4 (40% chance of staying average)

P(2 → 3) = 0.5 (50% chance of going from average to high)

P(3 → 1) = 0.7 (70% chance of going from high to low)

P(3 → 2) = 0 (since if sales are high one day, they can never be average the next day)

P(3 → 3) = 0.3 (30% chance of staying high)

The transition matrix is:

     |  1.0  0.0  0.0 |

     |  0.1  0.4  0.5 |

     |  0.7  0.0  0.3 |

To find the probability of low sales for the next three days, we can calculate the product of the transition matrix raised to the power of 3:

     |  1.0  0.0  0.0 |³

     |  0.1  0.4  0.5 |

     |  0.7  0.0  0.3 |

Performing the matrix multiplication, we get:

     |  1.0  0.0  0.0 |

     |  0.1  0.4  0.5 |

     |  0.7  0.0  0.3 |

So, the probability of low sales for the next three days, given that sales were low today, is 1.0 or 100%.

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The complete question :

The Creamlest Cone, a local ice cream shop, classifies sales each day as "Tow." average,"or "high. "if sales are low one day, then they are always low the next day if sales are average one day, then there is a 10% chance they will be low the next day, a 4090 chance they wal be average the next day and a 50% chance they will be high the next day. If sales are high one day, then there is a 70% chance they wil be low the next day and a 30% chance they will be high the next day if state 1 = ow sales, state 2 average sales, and state 3 high sales, find the transition matnx for the Markov chain write entries as integers or decimals. If sales were low today, what is the probability that they will be low for the next three days? Write answer as an integer or decimal

Answer:

0.79 or 0.80

Step-by-step explanation:

= 2^1/5 ÷ 3^1/3

= 0.796462955

To assist you in filling in the missing part of the equation, it is crucial to have the full equation provided by the student. Without it, it is not possible to accurately determine the missing part or provide a precise answer.

However, I can provide some general guidance on how to approach measurement conversions. Typically, conversion equations involve multiplying the given measurement by a conversion factor. The conversion factor relates the given unit to the desired unit of measurement. By multiplying the given measurement by the appropriate conversion factor, the student can obtain the equivalent value in the desired unit.

For example, if the equation is related to converting distance from miles to kilometers, the missing part might involve the conversion factor representing the number of kilometers in one mile. The student would need to fill in the missing part with the appropriate value. To ensure accuracy, it is essential to identify the specific units involved in the measurement conversion and find the corresponding conversion factor. Common conversion factors can be found in reference materials or online resources.

Please provide the complete equation or any additional information you have so that I can provide a more specific and accurate answer. With the complete equation, I will be able to guide you step-by-step in filling in the missing part correctly.

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Answer:

Yes, they do

Step-by-step explanation:

The more you focus on a concept, the more you get an understanding of it without being taught by another person.

Hard math concepts are hard cause you haven't found an easier way to get an understanding of it.

Answer:

The answer is 6

Step-by-step explanation:

60-36-18=6

The cost of one yard of green fabric is $10.

Let's assume that the cost of one yard of green fabric is represented by the variable x. Since the blue fabric costs $3 more per yard, the cost of one yard of blue fabric can be expressed as (x + $3).

La Tanya buys 4 yards of blue fabric, so the total cost of the blue fabric is 4(x + $3). She also buys 7 yards of green fabric, so the total cost of the green fabric is 7x.

The total cost of the fabrics is given as $122, so we can set up the equation:

4(x + $3) + 7x = $122

Simplifying the equation:

4x + $12 + 7x = $122

11x + $12 = $122

11x = $122 - $12

11x = $110

Dividing both sides by 11:

x = $110 / 11

x = $10

Therefore, the cost of one yard of green fabric is $10.

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Answer:

the answer is 180cm for the rectangle

the answer is 126cm for the triangle.

the answer is 880ml for the rectangle.

Step-by-step explanation:

first diagram (rectangle)

area=l×b

15×12

180cm

second diagram(triangle)

area =

\( \frac{1}{2} \times l \times b \\ \frac{1}{2} \times 14 \times 18 \\ = 7 \times 18 \\ 126cm\)

third diagram( rectangle)

area=

\(l \times b \\ \\ 44 \times 20 \\ 880ml\)

The correct statement is;

⇒ AB is parallel to CD

Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.

Given that;

Figure of parallel lines and transversal is show.

Now, By figure,

⇒ AB is parallel to CD

Hence, The correct statement is;

⇒ AB is parallel to CD

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Answer:

34 square feet

Step-by-step explanation:

First, you need to find the other side of the garden in order to find the area a=l*w

The formula to find the length is, p-w*2=x x÷2=l

because, perimeter is l+l+w+w and area is just l*w

4.25*2=8.50

24.50-8.50=16

16÷2=8

l=8

So now we need to multiply the length and width to get the area.

8*4.25=34 sq. ft.

I hope that helps!

The side lengths of the triangle ABC are 6 cm, 8 cm and 12 cm

From the question, we have the following parameters that can be used in our computation:

Ratio of the lengths of the sides of △ABC = 3:4:6.

Also, we have the following parameter:

Perimeter of the triangle whose vertices are the midpoints of the sides △ABC is 13cm.

This means that the perimeter of the triangle ABC is twice the perimeter of the triangle whose vertices are the midpoints of the sides △ABC

Mathematically, this can be represented as

P = 2p

Where

P = perimeter of ABC

p = perimeter of the other triangle

Substitute the known values in the above equation, so, we have the following representation

P = 2 * 13

Evaluate

P = 26

This means that the side lengths must add up to 26

Recall that

Ratio = 3 : 4 : 6

Multiply by 2

Ratio = 6 : 8 : 12

When these are added, we have

Total = 26

Hence, the side lengths are 6, 8 and 12

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