Julie bought g gallons of gasoline for ​$2.75 per gallon and c cans of oil for ​$3.35 per can. If she bought 8.4 gallons of gasoline and 7 cans of​ oil, how much did she spend in​ all?What expression can be used to determine the total amount julie spent on gasoline and​ oil?

Answer:2

Step-by-step explanation:

4*(4+2)=2*(2x+5+3)

4*6=2*(2x+8)

24=4x+16

4x=8

x=2

The required volume of the composite figure is given as 18,300 cm³.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

Here,
The volume of the composed figure is given as,
Split the figure into two,
So,
Volume = Volume of 1 + Volume of 2

Volume = 15 × 15 × 30 + 35 × 22 × 15
Volume = 6750 + 11550
Volume = 18,300 cm³

Thus, the required volume of the composite figure is given as 18,300 cm³.

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Answer:

56.52mm

Step-by-step explanation:

first we need to find the circumference of the wheel, which equals 2*pi*r

then we divide the circumference by 25 since the wheel is split into 25 arcs by the 25 spokes, so our answer is:

2(3.14)(225)/(25) = 56.52mm

Step-by-step explanation:

3.

30 + 60+ x=l 180°( being sum of angle of triangle is 180°)

90+ x= 180°

x= 180 - 90

=90

Height of a cuboid is three-fourths of its length,breadth is 4 cm and total surface area is 608.

the length of the cuboid is 24 cm and its height is 18 cm.

Let us denote the length of the cuboid as "l" and the height of the cuboid as "h".

Based on the facts provided, we may conclude:

h = (3/4)l

Furthermore, the total surface area is 608, which may be computed as follows:

608 = 2(lb + bh + lh)

Extending the formula and changing the value of h:

608 = 2(lb + bh + l(3/4)l)

2(lb + 4h + (3/4)l^2) = 608

Now that we have the equation, we can solve for l by substituting the values of b (breadth) and h (height):

2(4l + 4h + (3/4)l^2) = 608

8l + 8h + (3/2)l^2 = 304

(3/2)l^2 + 8l + 8h = 304

We can now solve for l using the quadratic formula:

l = (-8 ± √(8^2 - 4 * (3/2) * (304 - 8h))) / (2 * (3/2))

Because h = (3/4)l, we may simplify by substituting this formula for h:

l = (-8 ± √(8^2 - 4 * (3/2) * (304 - 3l))) / (2 * (3/2))

Expanding the square root:

l = (-8 ± √(64 + 12l)) / 3

When we solve for l, we get:

l = 24

Finally, for h, substitute the value of l into the equation:

h = (3/4) * 24 = 18

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Answer: Let's call the length of one side of the equilateral triangle x.

Then, the height of the triangle can be represented as √3/2.

By the Pythagorean theorem, we have:

(x/2)^2 + (√3/2)^2 = (x/2)^2 + 3/4 = x^2/4 + 3/4 = x^2/4 + 3/4 = x^2/4

So:

x^2 = 4 * (x^2/4 + 3/4) = 4x^2/4 + 4 * 3/4 = 4x^2/4 + 3

Solving for x:

3x^2/4 = 3

x^2 = 4

x = 2

So the length of one side of the equilateral triangle is 2 feet.

Step-by-step explanation:

92.161 is one thousanth less than 92.162

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

____is one thousanth less than 92.162

Complete the blank with a variable

So, we have

x is one thousanth less than 92.162

Express as an equation

x = 92.162 - 0.001

Evaluate

x = 92.161

Hence, the expression in the blank is 92.161

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The doubling time for the number of Wikipedia articles during this period is 346.56 days.

So, based on the question, we need to find t. And the condition required to find t will be -

N(t) = 2 [tex] N_{0} [/tex]

So, keeping the value of N (t) in the equation mentioned in question.

[tex] N_{0} [/tex] [tex] {e}^{t/500} [/tex] = 2 [tex] N_{0} [/tex]

Cancel [tex] N_{0} [/tex] on both sides of the equation

[tex] {e}^{t/500} [/tex] = 2

Taking log in both sides of the equation and generating equation according to the rule

t/500 = ln 2

t = 500 × ln 2

Performing multiplication on Right Hand Side of the equation

t = 346.57

Thus, the time period is 346.57 days

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The complete question is attached in the figure.

Answer:

a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g. 4 in 4x y).

Answer:

A coefficient is a numerical or constant quantity placed before and multiplying variable.

Step-by-step explanation:

For example, 4x+8=12. 4 is the coefficient.

-108 is the depth of the submarine after 9 ​minutes.

An expression is combination of variables, numbers and operators.

The given expression is  -210+ 12m

This expression  represents a submarine that began at a depth of 210 feet below sea level and ascended at a rate of 12 feet per minute.

We need to find the depth of the submarine after 9 ​minutes

m=9

Now put m value in the expression

-210+12(9)

-210+108

-108

Hence, -108 is the depth of the submarine after 9 ​minutes.

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A simple correlation between two variables when there is no obvious third variable that could be causing changes in both a and b.

A measure of the degree to which two variables vary together or the strength of the link between two variables is simple linear correlation. Correlation is frequently misused. You must provide evidence that one variable is really having an impact on another. and when we compare r to the relevant crucial value in the table, the association is statistically significant. The correlation coefficient is significant if it is greater than zero and does not fall between the positive and negative critical values.

the possibility that a reported correlation between two variables may not actually reflect any underlying relationship (in a causal sense) between the two variables, but rather the shared correlation between each of the variables and a third variable.

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The perimeter of the floor in the scale drawing is 42 inches.

To find the scale factor, we can use the length of the room in the original and the scaled drawing:

scale factor = length in scale drawing / length in original = 10 inches / 30 feet

Since 1 foot = 12 inches, we can convert the length of the room to inches:

30 feet * 12 = 360 inches

So, the scale factor is 10 inches / 360 inches = 1/36.

To find the length of the room in the scaled drawing, we can use the scale factor:

length in scale drawing = scale factor * length in original = (1/36) * 360 inches = 10 inches

And the width in the scaled drawing would be:

width in scale drawing = scale factor * width in original = (1/36) * 33 feet * 12 inches/foot = (1/36) * 396 inches = 11 inches

Finally, to find the perimeter of the room in the scaled drawing, we add up the lengths of all four sides:

perimeter = 2 * (length in scale drawing) + 2 * (width in scale drawing) = 2 * 10 inches + 2 * 11 inches = 20 inches + 22 inches = 42 inches.

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Answer:

Step-by-step explanation:

To convert 20 cm to meters, we divide by 100, because 1 meter = 100 centimeters.

So, 20 cm = 20/100 m = 0.2 m

To convert 0.2 m to meters in the lowest form, we divide by 15, because 1 meter = 15 units.

So, 0.2 m = 0.2/15 m = 0.013 m

So the final answer is 0.013 m.

The distance between the two jet when one is in the 108miles of east and second one 214miles in the north is equal to 239.7 miles ( nearest tenth ).

Location of the first jet at 5:45 p.m. is :

=  108 miles in the east of the city.

Location of the second jet at  5:45 p.m. is :

= 214 miles in the north of the city.

Let 'x' miles  be the distance between the jets.

East and north from a city forms a right angled triangle.

'x' represents the hypotenuse.

Using Pythagoras theorem we have,

x² = 108² + 214²

⇒ x² = 11664 + 45796

⇒x² = 57460

⇒ x = 239.708 miles

⇒ x = 239.7 miles (nearest tenth )

Therefore, the distance between the two jets as per given condition is equal to 239.7 miles

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Answer:

Step-by-step explanation:

To find a sinusoidal function that matches the given graph, we need to find the amplitude (A), period (T), phase shift (h), and vertical shift (k) of the function.

Since the graph goes through the points (-9,0) and (5,0), we know that the maximum value of the function is located at the average of the x-values, which is -2, and that the minimum value of the function is located at the average of the x-values, which is (9+5)/2 = 7. The amplitude of the function can be found by taking half the difference of the maximum and minimum y-values, which is 0 - (-2)/2 = 1.

The period of the function can be found by taking the difference of the x-values of two consecutive maxima or minima, which is 5-(-9) = 14.

The phase shift can be found by noting the horizontal shift of the graph from its standard form, which is usually given by the equation y = A sin(x). In this case, the graph is shifted 2 units to the right, so the phase shift is 2.

The vertical shift can be found by noting the location of the midline of the graph, which is half way between the maximum and minimum y-values. In this case, the midline is at y = -1.

Putting all these values together, we can write a sinusoidal function that matches the given graph as:

f(x) = 1 sin(x + 2π/14) - 1

This function has amplitude 1, period 14, phase shift 2π/14 to the right, and a vertical shift of -1 down.

Answer:

64%

Step-by-step explanation:

"Percent" means per hundred. So Lamar has completed 32 out of 50 deliveries.

32/50 is the same as 64/100.

64/100 is 64%

Without mental math, if you can use a calculator, divide

32÷50

You'll get 0.64, times by 100 (or move the decimal point two places to the right) to get 64%

By several orders of magnitude, the role that money plays in the rate of urbanization and various economic activities is significant.

The proportion of people who live in towns and cities growing is known as urbanization. People relocate to urban areas from rural (countryside) areas, which causes urbanization (towns and cities). This typically happens when a nation is still growing.

Urban areas can expand due to a rise in the population or because people move there. Urbanization causes habitat loss, deforestation, and freshwater extraction from the environment, which can reduce natural things and change species ranges and interactions.

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Answer:

$50, and $250

Step-by-step explanation:

Answer:

Step-by-step explanation:

Grouping terms in mathematics refers to the process of combining like terms, which are terms that have the same variable raised to the same power.

For example, consider the expression 2x + 3x. The terms 2x and 3x are like terms because they both have the variable x, so they can be grouped together:

2x + 3x = (2 + 3)x = 5x

When grouping terms, it's important to simplify each group of like terms before combining them. For example, consider the expression 2x^2 + 3x^2 + 4x^3. The terms 2x^2 and 3x^2 are like terms because they both have x raised to the power of 2, but they are not like terms with 4x^3 because it has x raised to a different power. To group the terms correctly, we simplify each group of like terms first:

2x^2 + 3x^2 = (2 + 3)x^2 = 5x^2

2x^2 + 3x^2 + 4x^3 = 5x^2 + 4x^3

Once all like terms are grouped and simplified, the expression can be simplified further by combining the groups of like terms:

5x^2 + 4x^3 = 5x^2 + 4x^3

This final expression is the simplified form of the original expression.

Answer:

x = 3

y = -1

Step-by-step explanation:

5x + 3y = 12

x - 4y= 7

Times the second equation by -5

5x + 3y = 12

-5x + 20y = -35

23y = -23

y = -1

Now put -1 back in for y and solve for x

x - 4(-1) = 7

x + 4 = 7

x = 3

Let's check

3 - 4(-1)= 7

3 + 4 = 7

7 = 7

So, x = 3 and y = -1 is the correct answer.

Since triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−1, −1), B′(1, 1), C′(0, 1), the scale factor used is: D. 1/3.

In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):

Scale factor = Dimension of image (new figure)/Dimension of pre-image(original figure)

Substituting the given parameters into the scale factor formula, we have the following;

Scale factor = Dimension of image (new figure)/Dimension of pre-image(original figure)

Scale factor = -1/-3

Scale factor = 1/3.

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Answer: D = 1/3

Step-by-step explanation: Took the test and got it right :>

the dimension of The diagonal ad of the rectangle will be 40.24 units.

In Mathematics, a polygon can be defined as a two-dimensional geometric figure that consists of straight line segments and a finite number of sides. Additionally, some examples of a polygon include the following:

• Triangle

• Quadrilateral

• Pentagon

• Hexagon

and so on

Given data of a quadrilateral. Since the type of quadrilateral is not provided.

we will assume it to be a rectangle as shown in the figure.

From the general formula of diagonal:

Diagonal = √sum of the square of sides

Thus,

Diagonal (ad) = √(36² + 18²)

ad = 40.24

Therefore the dimension of The diagonal ad of the rectangle will be 40.24 units.

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The triangle third side may be 6 or 9 metres long, or it may be between 9 and 15 metres long.

Depending on the lengths of the other two sides, the triangle's third side can have a variety of lengths. The third side's length could range from 9 to 15 metres if the first two sides are 6 and 9 metres, respectively. The reason for this is that the length of any two sides of a triangle must always be greater than the length of the third side; in this instance, the sum of the two sides is 15 metres, or 6 and 9 metres. As a result, the triangle's third side must be either less than or equal to 15 metres. A triangle can also have two equal sides, so the third side could also be equal to 6 or 9 metres. In conclusion, the third side of the triangle may be anywhere between 9 and 15 metres long, or it could be 6 or 9 metres long.

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Option C is correct : y = ±3x + 8, represents a function because it satisfies the vertical line test.

"y = ±3x + 8" represents a function. A function is a mathematical relationship between a set of inputs (in this case, x) and a set of outputs (in this case, y). In this equation, for each value of x there is exactly one corresponding value of y, which means that it represents a function.

"y = ±2x + 3" is not a function because for each value x, there are two possible values y (one positive and one negative). This is not the definition of a function, as a function must have exactly one output value for each input value.

Options B, D, and E do not represent functions because they do not have an equal sign between the x and y variables, which is the defining characteristic of a mathematical function.

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The correct statement regarding the function is given as follows:

As you move closer to the center of the whirlpool, the speed of the current approaches infinity.

The function for this problem is defined as follows:

s = 300/d.

In which:

As d approaches 0, the equation has the following format:

s = 300/0.

The division by a number that is very close to zero means that the output assumes a value close to infinity, hence the third option is the correct option in the context of this problem.

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The common region or overlapped region in the graph of both the inequalities represents the number of cats and dogs that can be at the store.

Given is that  Priya’s Pet Store never has more than a combined total of 20 cats and dogs and never more than 8 cats. This is represented by the inequalities x + y ≤ 20 and x ≤ 8.

The number of cats and dogs that can be at the store on a graph can be represented by the common region in the graph of both the inequalities.

Therefore, the common region or overlapped region in the graph of both the inequalities represents the number of cats and dogs that can be at the store.

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The value of [tex]w^{-1}(3)[/tex] is -0.75

We know that the function is a well defined relation between input and output values in which each input is related to exactly one output.

An inverse function is  nothing but a function that returns the original value for which a function has given the output.

If two functions f and g are inverse functions, then f(x) = y if and only if g(y) = x

Here, the table of values for function is:

  x             w(x)

 -3             8

-0.75          3

  3             0.2

 6.5          -3

  7              1

From above table we can observe that for input x = -0.75, the value of function w(x) is 3

This means, that the inverse of 3 for function w is -0.75

Therefore,  [tex]w^{-1}(3)[/tex] = -0.75

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