William’s car uses 1 litre of fuel to travel 12km. How much fuel will be needed to travel
420km?

The volume of the triangular prism is 3x³ + 16x² + 3x - 10. And the volume of the triangular prism when height is 50% reduced will be 1.5x³ + 8x² + 1.5x - 5.

Volume is a measurement of three-dimensional space that is utilized. The concept of length is linked to the notion of capacity.

The dimensions of the triangular prism are (2x + 2), (x + 5), and (3x - 2). Then the volume is given as,

V = (1/2) · (2x + 2) · (x + 5) · (3x - 2)

V = (x + 1) · (x + 5) · (3x - 2)

V = (x² + 6x + 5) · (3x - 2)

V = 3x³ + 16x² + 3x - 10

If the height is reduced by 50%, then the volume is given as,

V = (1/2) · [0.50 × (2x + 2)] · (x + 5) · (3x - 2)

V = (1/2) · (x + 1) · (x + 5) · (3x - 2)

V = (1/2) · (x² + 6x + 5) · (3x - 2)

V = (1/2) · (3x³ + 16x² + 3x - 10)

V = 1.5x³ + 8x² + 1.5x - 5

The volume of the triangular prism is 3x³ + 16x² + 3x - 10. And the volume of the triangular prism when height is 50% reduced will be 1.5x³ + 8x² + 1.5x - 5.

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we can graph the solution on the number line. The solution will be the intersection of the two inequalities, which is u >= 5. The solution to the compound inequality is u >= 5.

To solve the compound inequality, we need to isolate the variable on one side of the inequality.

For the first inequality, 4u + 5 > 13, we can subtract 5 from both sides to get:
4u > 8

Then, we can divide both sides by 4 to get:
u > 2

For the second inequality, 2u + 6 >= 16, we can subtract 6 from both sides to get:
2u >= 10

Then, we can divide both sides by 2 to get:
u >= 5

Now, we can graph the solution on the number line. The solution will be the intersection of the two inequalities, which is u >= 5.

On the number line, we can draw a closed circle at 5 and shade to the right to indicate that the solution includes 5 and all numbers greater than 5.

The solution to the compound inequality is u >= 5.

Here is the graph of the solution on the number line:

    0  1  2  3  4  5  6  7  8  9  10

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It will take Sean 3.75 hours to plant seeds in 0.5 square yards of the garden. Answer: 3.75 hours.

Multiplication is a basic arithmetic operation that involves combining two or more numbers to get a product. It is often represented using the multiplication symbol "*", and the numbers involved are referred to as factors. The result of a multiplication operation is called the product.

We can start by using the ratio of square yards to time as a proportion:

0.2 sq yd / 1.5 hrs = 0.5 sq yd / x hrs

Cross-multiplying, we get:

0.2 sq yd * x hrs = 1.5 hrs * 0.5 sq yd

Simplifying, we get:

x = (1.5 hrs * 0.5 sq yd) / 0.2 sq yd

x = 3.75 hrs

Therefore, it will take Sean 3.75 hours to plant seeds in 0.5 square yards of the garden. Answer: 3.75 hours.

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We can conclude that the equation of the line of best fit is -

ŷ = 713.70516X + 1077.04596. Also, the slope {m} is 713.70516 and {y} -

intercept is 1077.04596.

Given is a table as shown in the image.

-6.6

-5.6

-3.6

-1.6

-0.6

0.4

2.4

3.4

5.4

6.4

-4887.5

-3887.5

-2587.5

-1287.5

-637.5

962.5

1762.5

2312.5

3737.5

4512.5

43.56

31.36

12.96

2.56

0.36

0.16

5.76

11.56

29.16

40.96

{SS} : 178.4

32257.5

21770

9315

2060

382.5

385

4230

7862.5

20182.5

28880

{SP} : 127325

Sum of {X} = 66

Sum of {Y} = 57875

Mean {X} = 6.6

Mean {Y} = 5787.5

Sum of squares {SSₓ} = 178.4

Sum of products {SP} = 127325

Regression Equation -

ŷ = bX + a

b = SP/SSₓ = 127325/178.4 = 713.70516

a = MY - bMₓ = 5787.5 - (713.71*6.6) = 1077.04596

ŷ = 713.70516X + 1077.04596

Slope -

{m} = 713.70516

{y} - intercept = 1077.04596

Therefore, we can conclude that the equation of the line of best fit is -

ŷ = 713.70516X + 1077.04596. Also, the slope {m} is 713.70516 and {y} -

intercept is 1077.04596.

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Answer:

4p + 5 + 4p

Answer:

8p+5

Step-by-step explanation:

4p+4p+5

8p+5

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Step-by-step explanation:

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Thank You!

Answer:

ok divide is easy

Step-by-step explanation:

dividing is not adding or subtracting

Answer:

The percent decrease is 36%.

Step-by-step explanation:

The sets of points that have a distance of 4 units between them are:

Point X and Point W

Point T and Point S

To find the distance between two points, we use the distance formula:

distance = √ (x₂ – x₁)² + (y₂ – y₁) ²

We can calculate the distances between each pair of points and check if any of them are equal to 4.

The distances between the following pairs of points are 4 units:

Point X (3,9) and Point W (5,0): distance = √((5 - 3)² + (0 - 9)²) = √52 = 4.12

Point T (5,0) and Point S (-1,0): distance = √((-1 - 5)² + (0 - 0)²) = √36 = 6

Point T (5,0) and Point S (-3,0): distance = √((-3 - 5)² + (0 - 0)²) = √64 = 8

Point R (1,6) and Point Q (-1,2): distance = √((-1 - 1)² + (2 - 6)²) = √20 = 4.47

Point P (-1,0) and Point O (0,9): distance = √((0 - (-1))² + (9 - 0)²) = √82 = 9.06

Therefore, the only sets of points that have a distance of exactly 4 units between them are Point X and Point W, and Point T and Point S.

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Answer:

12

Step-by-step explanation:

9.63 years are required for $390 to become $660. A charge for borrowing money or other assets is called an interest.

Compound interest simply indicates that the interest paid on a savings account, loan, or investment grows exponentially over time rather than linearly.

[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]

Here, A = Amount,

P = Principal Amount

r = Rate of interest

n = Number of times interest is charged in a year

t = number of years

Given ,Here Principal Amount is $390, the rate of interest is 5.5%(0.055),

the number of times the interest is charged in a year (n=4),

and the final amount is $660,

therefore, number of years will be equal to,

[tex]660 = 390(1 + \frac{0.055}{4} )^{4*t}[/tex]

[tex]\frac{660}{390} = (1.01375)^{4*t}[/tex]

[tex]1.6923 = (1.01375)^{4*t}[/tex]

[tex]log_{1.01375}1.6923 = 4t[/tex]

[tex]4t = 38.5234[/tex]

[tex]t = 9.63[/tex]

Hence, number of years it will take for $390 to become $660 is 9.63 years.

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The graphs of y = 1/2x - 10 - 3 and y = 1/x are different in shape and behavior, and their only similarity is that they are both continuous functions.

What is a graph ?

Graph can be defined as visual representation of data using ordered pairs.

The graphs of y = 1/2x - 10 - 3 and y = 1/x have different shapes and behaviors.

The graph of y = 1/2x - 10 - 3 is a linear function with a slope of 1/2 and a y-intercept of -13. This means that the graph will have a constant slope of 1/2, and will be downward sloping from left to right. As x increases, y decreases at a steady rate.

On the other hand, the graph of y = 1/x is a non-linear function that is a hyperbola. This means that the graph will be curved and will have two branches, one in the first quadrant and the other in the third quadrant. The graph will approach the x and y-axes but will never touch them. The curve will be symmetric about the line y = x, which means that for every point (x, y) on the graph, there will be a corresponding point (y, x) on the graph.

Therefore, the graphs of y = 1/2x - 10 - 3 and y = 1/x are different in shape and behavior, and their only similarity is that they are both continuous functions.

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The multiplication sentence will be: Volume = Length × Width × Height.

Each of these measurements should be in centimeters (cm) in order to calculate the volume in cubic centimeters (cm^3).

To calculate the volume of a rectangular prism, you can use the multiplication sentence: Volume = Length × Width × Height. Each of these measurements should be in centimeters (cm) in order to calculate the volume in cubic centimeters (cm^3).

For example, if the length of the rectangular prism is 5 cm, the width is 3 cm, and the height is 2 cm, the multiplication sentence would be:

Volume = 5 cm × 3 cm × 2 cm

The volume of this rectangular prism would be 30 cm^3.

In general, the multiplication sentence to calculate the volume of a rectangular prism is:

Volume = Length × Width × Height

Make sure to include the units (cm) in your multiplication sentence in order to get the correct answer in cubic centimeters (cm^3).

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The solution to the equation tan²(x) = sec(x) − 1 in the interval [0, 2π) is x = 0

Consider equation tan²(x) = sec(x) − 1

We know that tan(x) = sin(x)/cos(x) and sec(x) = 1/cos(x)

so the equation becomes,

[tex]\frac{sin^2(x)}{cos^2(x)}-\frac{1}{cos(x)}+1=0[/tex]

sin²(x) - cos(x) + cos²(x) = 0

We know that the trignometric identity sin²(x) + cos²(x) = 1

(1 - cos²(x)) - cos(x) + cos²(x) = 0

1 - cos²(x) - cos(x) + cos²(x) = 0

1 - cos(x) = 0

cos(x) = 1

We know that for x = 0 and 2π, the value of cos(x) is 1

In the interval [0, 2π), the solution for equation would be x = 0

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The complete question is:

Find all solutions of the equation in the interval [0, 2π). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) tan²(x) = sec(x) − 1

The given equation is a second order differential equation, which can be solved using the method of undetermined coefficients. The homogenous solution of the equation is:
yh = c1e2t + c2e-t

By applying the initial conditions, we get: c1 = 0, c2 = 0.
Therefore, the homogenous solution is: yh = 0.
The particular solution of the equation is:
yp = At2 + Bt + C
Substituting yp and its derivatives in the given equation and equating the coefficients of each term on both sides, we get:
A = 1/2, B = 0, C = 0
Therefore, the particular solution is: yp = 1/2t2
Thus, the solution of the given equation is:
y(t) = yh + yp = 1/2t2

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The area of the arrow shaped polygon in square units is: 80 square units

For triangle BCD:

b = Base = 4 - 2 = 2 units

h = Height = 4 units

Area = [tex]\frac{1}{2}[/tex]bh

Area = [tex]\frac{1}{2}[/tex] × 2 × 4

Area = 8 square units

For triangle DEF

b = Base = 2 - (-1) = 3 units

h = Height = 4 units

Area = [tex]\frac{1}{2}[/tex] × 3 ×  4

Area = 6 square units

For trapezoid ABFG:

a = 4 - (-1) = 5.5 units

b = 4 - (-8) = 12 units

h = 8 units

Area =  [tex]\frac{1}{2}[/tex](a + b)h

Area =  [tex]\frac{1}{2}[/tex](5.5 + 12)8

Area = 70 square units

Total area = 8 + 6 + 70

Total Area = 84 square units

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Answer:

B. 14 +(-6)

Step-by-step explanation:

Adding the term negative 6 to 14 is equivalent to subtracting 6 from 14

Answer:

Step-by-step explanation:

ifdk

Answer:

2x-12y

Step-by-step explanation:

This is equivalent to the original fraction--4(1/2x - 3y)

If we were to solve 4(1/2x - 3y), we'd get: 2x-12y.

Meaning, 2x-12y is equivalent to 4(1/2x - 3y).

The vast majority of the Sun's energy radiates out into space and does not reach Earth.

Why does so little of the Sun's energy reach Earth?

The reason is that space is vast, and the Sun's energy radiates out in all directions, spreading out over enormous distances. By the time it reaches Earth, it has become highly diluted, with only a tiny fraction of the original energy remaining.

Factors that reduce the amount of the Sun's energy reaching Earth-

The Sun's energy is produced through nuclear fusion in its core, where hydrogen atoms are fused together to form helium, releasing vast amounts of energy in the process. This energy then radiates outwards from the core, passing through various layers of the Sun's atmosphere before eventually reaching the surface and being emitted into space.

As the Sun's energy travels through space, it encounters various obstacles, such as interstellar dust and gas, as well as the solar wind, which is a stream of charged particles that constantly flows out from the Sun. These obstacles can scatter and absorb some of the Sun's energy, further reducing the amount that reaches Earth.

Only a small fraction of the Sun's energy is intercepted by Earth, where it is absorbed by the atmosphere, oceans, and land. The energy that is absorbed by Earth drives the planet's weather and climate systems, powering phenomena such as wind, rain, and the water cycle. The rest of the Sun's energy continues to radiate out into space, where it can influence the temperature and behavior of other planets and celestial objects.

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Therefore , the solution of the given problem of plotting data comes out to be  75 represents the top quartile (Q3)  outside the whiskers are also depicted on the plot as individual points.

The most popular method for displaying data in a geographical format is to demonstrate the correlation between two additional factors. Digital or hand-drawn sketches are both acceptable. Starting at the starting the spot, move three separate parts upward and then two or more components in the right. The display of the reference system must show the numerals for positions 2, 3, and 4.

Here,

The following details are displayed by the box-and-whisker plot:

The cutoff is somewhere around 35.

=> Around 55 constitutes the bottom quartile (Q1).

=> At around 65, the median (Q2) is.

=> Around 75 represents the top quartile (Q3).

The top number is somewhere around 95.

The whiskers stretch to the minimum and maximum scores, while the box represents the middle 50% of the scores (between Q1 and Q3).

A few outliers that lay outside the whiskers are also depicted on the plot as individual points.

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The runner's average rate of change from 60 to 120 minutes is 0.093 miles per minute based on the given information.

Given that,

In the table, it shows the distance a runner has traveled.

The time (in minutes) and distance (in miles) values are as follows:

0 minutes: 0 miles

30 minutes: 3.48 miles

60 minutes: 6.42 miles

90 minutes: 9.18 miles

120 minutes: 12.0 miles

To find the runner's average rate of change from 60 to 120 minutes,

Use the formula:

The average rate of change = (Change in the distance) / (Change in time)

From the table,

At 60 minutes:

The runner has traveled 6.42 miles,

And at 120 minutes:

The runner has traveled 12.0 miles.

So, the change in distance is 12.0 miles - 6.42 miles = 5.58 miles.

The change in time is 120 minutes - 60 minutes = 60 minutes.

Now, we can calculate the average rate of change:

The average rate of change = 5.58 miles / 60 minutes

The average rate of change = 0.093 miles per minute.

Hence,

The runner's average rate of change from 60 to 120 minutes is 0.093 miles per minute.

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Therefore , the solution of the given problem of unitary method comes out to be t there are 1000 squirrels in the conservation area.

To finish a job using the unitary method, divide the lengths of just this minute subset by two. In a nutshell, the unit method eliminates a desired item from both the characterized by a set and colour subsets. 40 pens, for instance, variable will cost Rupees ($1.01). It's conceivable that one nation will have complete control over the strategy used to achieve this. Almost all living things have a unique trait.

Here,

The Lincoln-Petersen index can be used to calculate an approximate squirrel population estimate for the protected area:

There were n1 squirrels in the first group.

Second sample's fox count is equal to n2.

Second sample's total number of labelled squirrels is m2.

The following provides the Lincoln-Petersen index:

=> n1 * n2 / m2

Assume that the first sample consisted of 100 squirrels that were captured and tagged by the researcher. 20 of the 200 squirrels the researcher caught for the second group had tags on them. the following algorithm is used.

=> n1 * n2 / m2 = 100 * 200 / 20 = 1000

Therefore, it is believed that there are 1000 squirrels in the conservation area. It is crucial to keep in mind that this is only an approximation and might not be correct.

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The permutation [[1,2,3,4,5,6],[6,5,4,3,2,1]] can be written as a product of disjoint cycles as (1,6)(2,5)(3,4).



A permutation can be represented as a product of disjoint cycles. A cycle is a sequence of numbers that are permuted in a circular fashion. For example, the cycle (1,2,3) means that 1 is permuted to 2, 2 is permuted to 3, and 3 is permuted to 1.

To write the given permutation as a product of disjoint cycles, we can start with the first number in the first row, 1, and see where it is permuted to in the second row. In this case, 1 is permuted to 6. Then we look at where 6 is permuted to, which is 1, completing the cycle (1,6).

Next, we move on to the next number in the first row that has not been included in a cycle, which is 2. We see that 2 is permuted to 5, and 5 is permuted to 2, completing the cycle (2,5).

Finally, we move on to the next number in the first row that has not been included in a cycle, which is 3. We see that 3 is permuted to 4, and 4 is permuted to 3, completing the cycle (3,4).

Therefore, the given permutation can be written as a product of disjoint cycles as (1,6)(2,5)(3,4).

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To solve this problem, we need to first find the common denominator of the two fractions and then subtract the numerators. The common denominator is (x^(2)+4x-21)*(6x-18).

So, we can rewrite the problem as:
[(x^(2)+11x+28)*(6x-18) - (x^(2)+2x-8)*(x^(2)+4x-21)]/[(x^(2)+4x-21)*(6x-18)]
Next, we need to simplify the numerators by distributing and combining like terms:
[(6x^(3)-18x^(2)+66x^(2)-198x+168x-504) - (x^(4)+4x^(3)-21x^(2)+2x^(3)+8x^(2)-16x-8x^(2)-32x+168)]/[(x^(2)+4x-21)*(6x-18)]
[(6x^(3)-18x^(2)+66x^(2)-198x+168x-504) - (x^(4)+6x^(3)-21x^(2)+8x^(2)-48x+168)]/[(x^(2)+4x-21)*(6x-18)]
[(6x^(3)-18x^(2)+66x^(2)-198x+168x-504) - x^(4)-6x^(3)+21x^(2)-8x^(2)+48x-168]/[(x^(2)+4x-21)*(6x-18)]
Next, we can combine like terms in the numerator:
[-x^(4)+12x^(2)-30x-336]/[(x^(2)+4x-21)*(6x-18)]

Finally, we can simplify the denominator by factoring:
[-x^(4)+12x^(2)-30x-336]/[(x+7)(x-3)*(6x-18)]

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It will take 13 years for the account value to reach $10,800.

Compound interest means addition of interest to the principal sum of a loan or deposit which means interest on principal plus interest.

We will use the formula for compound interest [tex]A = P(1 + r/n)^{nt}[/tex]

Given that

A = Final account value ($10,800)

P = Principal amount ($4,500)

r = Annual interest rate (7% or 0.07)

n = 1

t = ?

$10,800 = $4,500(1 + 0.07/1)^(1*t)

Dividing by $4,500:

2.4 = (1.07)^t

Taking the logarithm of sides:

log(2.4) = log((1.07)^t)

Using logarithmic identity log(a^b) = b*log(a):

log(2.4) = t*log(1.07)

Dividing by log(1.07):

t = log(2.4) / log(1.07)

t = 12.9394949072

t = 13.

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The coordinates of R′ for the dilation centered at P with scale factor 0.5 are R' (-1, -0.5).

In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape.

Next, we would have to dilate the coordinates of the preimage by using a scale factor of 0.5 centered at the point P (-3, -3) by using this mathematical expression:

(x, y)  →  (k(x - a) + a, k(y - b) + b)

For coordinate R, we have;

Coordinate R = (1, 2)  →  (0.5(1 - (-3)) + (-3), 0.5(2 - (-3)) + (-3))

Coordinate R = (1, 2)  →  (0.5(1 + 3) - 3, 0.5(2 + 3) - 3)

Coordinate R = (1, 2)  →  (0.5(4) - 3, 0.5(5) - 3)

Coordinate R' = (1, 2)  →  (-1, -0.5)

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The indicated trigonometric values in the specified quadrant are sec(O) = 1/3, sin(O) = sqrt(-8), and csc(O) = 1/sqrt(-8).

To find the indicated trigonometric value in the specified quadrant using the function value, we need to use the relationships between the different trigonometric functions. The given function value is cosich (C) = 3 in quadrant 2.

First, we can use the relationship between cosine and secant to find the value of secant. The relationship is:
sec(O) = 1/cos(O)

Since cosich (C) = 3, we can substitute this value into the equation and solve for sec(O):
sec(O) = 1/3

Next, we can use the relationship between cosine and sine to find the value of sine. The relationship is:
sin^2(O) + cos^2(O) = 1

Substituting the value of cosich (C) = 3 into the equation, we get:
sin^2(O) + 3^2 = 1

Solving for sin^2(O), we get:
sin^2(O) = 1 - 9 = -8

Taking the square root of both sides, we get:
sin(O) = sqrt(-8)

Since we are in quadrant 2, the value of sine will be positive. Therefore, the value of sin(O) is sqrt(-8).

Finally, we can use the relationship between sine and cosecant to find the value of cosecant. The relationship is:
csc(O) = 1/sin(O)

Substituting the value of sin(O) = sqrt(-8) into the equation, we get:
csc(O) = 1/sqrt(-8)

Therefore, the value of csc(O) is 1/sqrt(-8).

In conclusion, the indicated trigonometric values in the specified quadrant are sec(O) = 1/3, sin(O) = sqrt(-8), and csc(O) = 1/sqrt(-8).

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Answer:

Step-by-step explanation:

open the icon

The triangles are similar thus option A. Yes, SSS

When the corresponding properties of two or more triangles have common relations, then the triangles are said to be similar. Thus the similarity property can be expressed as either Side-Side-Side, Side-Angle-Side, Side-Angle-Angle, Angle-Side-Side etc.

Though two or more triangles are said to be similar but not congruent.

Considering the properties of the triangles ABX and YZX, it can be concluded that the triangles are similar by Side-Side-Side similarity property. Therefore the appropriate option is A. Yes, SSS.

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