There are fewer than 8 gallons of gas in the tank how do I write an inequality for that

Answer: 3.6651

Step-by-step explanation:

The formula to convert [tex]\theta[/tex] degrees to radians is given by :-

[tex]\dfrac{\pi}{180^{\circ}}\times\theta[/tex]

Given : Angle : [tex]\theta=210^{\circ}[/tex]

Then , the measure of angle in radians is given by :-

[tex]\dfrac{\pi}{180^{\circ}}\times210^{\circ}[/tex]

Using the value of [tex]\pi=3.14159[/tex], we get

[tex]\dfrac{3.14159}{6}\times7\approx3.6651[/tex]

The calculated value of the constant of proportionality that relates the variable y, to x, is 1/6

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

x 12 24 36 48

y 2 4 6 8

The constant of proportionality (k) is calculated as

k = y/x

So, we have

k = 2/12

Evaluate

​k =  1/6

Hence, the constant of proportionality is 1/6

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Answer with Step-by-step explanation:

As we can see from the graph:

A=(0,0)  and A'=(2,1)

Distance between (x1,y1) and (x2,y2) is given by:

    [tex]\sqrt{{(x1-x2)}^2+{(y1-y2)}^2}[/tex]

Here (x1,y1)=(0,0)  and (x2,y2)=(2,1)

Hence, distance between A and A' is:

    [tex]\sqrt{{(0-2)}^2+{(0-1)}^2}[/tex]

=   [tex]\sqrt{4+1}[/tex]

=   [tex]\sqrt{5}[/tex]

Hence, distance AA'=√5

The method to find the other x-intercept for the function f(x) = ax² + bx + c is given in the explanation below the answer.

The other x-intercept is; ((-b/2a - 3), 0)

We are given the equation of the function;

f(x) = ax² + bx + c

where a, b and c are real numbers and non - zero

Now, this is a quadratic equation that has 2 roots and it means there will be two x-intercepts.

Also, in quadratic equations, the formula to find the x-coordinate of the line of symmetry of the graph is;

x = -b/2a

The line of symmetry divides the graph curve into 2 equal parts at the vertex. This means the two x - intercepts will be the same distance from the x-coordinate of the vertex or line of symmetry but on opposite sides.

Thus, if one x-intercept is at ((-b/2a + 3), 0), then the other coordinate using the line of symmetry reason above is; ((-b/2a - 3), 0)

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Given is the square whose area is 1/64 squared miles, and it says to find the side of the square.

We know the formula for area of square is given by :-

Area of square = (side)²

[tex] (side)^{2} = \frac{1}{64} \\\\
side = \sqrt{\frac{1}{64}} \\\\
side = \frac{1}{8} = 0.125\; miles [/tex]

Hence, side of the square would be 1/8 miles or 0.125 miles.

Final answer:

The original price of the diamond earrings before a 50% markup that led to a final selling price of $198.00 was $132.00.

Explanation:

The question asks us to find the original price of the diamond earrings before a 50% markup that resulted in a final selling price of $198.00. To solve this, we use the markup formula, which is Final Price = (Original Price) × (1 + Markup Percentage). Here, the Final Price is $198.00 and the Markup Percentage is 50%, or 0.50 when expressed as a decimal.

First, we rearrange our formula to solve for the Original Price:
Original Price = Final Price ÷ (1 + Markup Percentage). Plugging in the given values, we have: Original Price = $198.00 ÷ (1 + 0.50) = $198.00 ÷ 1.50.

Doing the computation: Original Price = $132.00. Therefore, the earrings were priced at $132.00 before the 50% markup.

We have a circle A and a line segment BQ is passing through the circle A such that it forms a triangle ABQ.

From the diagram, we have some information about the angles of triangle ΔABQ as follows :-

angle QAB = 36 degrees and angle BAQ = 54 degrees.

We know about the Triangle Sum theorem which states "The sum of all interior angles of any triangle is 180 degrees".

We can use this theorem to find the third angle of the triangle ΔABQ.

∠ABQ + ∠BQA + ∠QAB = 180 degrees

∠ABQ + 54° + 36° = 180°

∠ABQ + 90° = 180°

∠ABQ = 180° - 90°

∠ABQ = 90 degrees

If any line makes a right angle with the radius of any circle, then this line must be a tangent to that circle.

So, BQ would be a tangent line because angle ∠ABQ = 90 degrees. Hence, option A is correct.

Answer:

square is the answer

N=0.5

1x0.5=0.5 which is less than 1 but greater than 0

The possible value of n is,

⇒ n = 1/2

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The statement is,

1×n is less than 1 but greater than 0

Now, We can write as;

⇒ 0 < 1 × n < 1

Simplify as;

⇒ 0 < n < 1

Thus, The possible value of n is,

⇒ n = 1/2

⇒ n = 0.5

Thus, The possible value of n is,

⇒ n = 1/2

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Diversification means wide variety of different investment options available in the portfolio so that it becomes lesser risky towards minimizing losses in down market.

It provides better protection towards common issues like inflation, market instability, war effects, hike in exchange rates, interest rates reduction etc. So, we can conclude that :-

Diversification is the method to make investments less vulnerable to a catastrophic loss.

Hence, option A is best answer from given choices.

When no specific speed limit is posted, the default speed limit applies. These defaults are set by local or state law and can vary. Drivers must adhere to these limits and drive safely for conditions.

In most areas, when specific traffic speed limit signs are not posted, what's known as the default speed limit applies. These default speed limits are not posted on signs and instead are set by local or state law. It's important to stay aware of these limits in different areas, as they can vary. For instance, in many cities, the default speed limit is 25 mph unless otherwise posted. However, it should be noted that these default limits may not protect you from being pulled over if the police deem your speed unsafe for the current conditions. Thus, it's recommended to always drive at a speed that is appropriate for the conditions, even if you are technically within the speed limit.

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Final answer:

The median is a number that measures the center of the data. To find the median, arrange the data in ascending order and determine the middle value. If the data has an even number of values, the median is the average of the two middle values.

Explanation:

The median is a number that measures the center of the data. It separates the data into two halves, with half the values being smaller or equal to the median and the other half being larger or equal to it. To find the median, you need to arrange the data in ascending order and then determine the middle value.

If the data has an even number of values, the median is the average of the two middle values.

Answer: [tex]16\pi\ \text{ units}^2[/tex]

Step-by-step explanation:

We know that the circumference of a circle is given by :-

[tex]\text{Circumference}=2\pi r[/tex], where r is the radius of the circle.

Given : The circumference of a circle = [tex]8\pi[/tex]

Then , the circumference of a circle will be :-

[tex]8\pi=2\pi r\\\\\Rightarrow\ r=4\text{ units}[/tex]

Now, the area of circle is given by :-

[tex]A=\pi r^2\\\\\Rightarrow\ A=\pi(4)^2\\\\\Rightarrow\ A =16\pi\ \text{ units}^2[/tex]

Final answer:

To find the height of the lamppost given the girl's height, distance from the lamp post, and shadow length, set up a proportion to calculate the lamp post's height.

Explanation:

A girl stands 160 cm tall and stands 360 cm away from a lamp post at night. Her shadow from the light is 90 cm long. How high is the lamppost?

Set up a proportion: Lamp post height / Girl's height = Lamp post shadow length / Girl's shadow length.

Substitute the values: Lamp post height / 160 cm = 360 cm / 90 cm.

Solve for the lamp post height: Lamp post height = (360 cm * 160 cm) / 90 cm = 640 cm.

Answer:

26 1/4

Step-by-step explanation:

took the test 100% 4.08 Quiz: Finding the Volume of Rectangular Prisms and Problem Solving