What is the median of this set of data? 66, 51, 77, 68, 60, 75, 54, 80

The rate of the boat that travels 66 miles in 2 hours is approximately 2904 feet per minute.

Given:

Distance traveled = 66 miles

Time taken = 2 hours

We know that:

1 mile =  5280 feet

66 miles = 66 [tex]\times[/tex] 5280

                  348,480 feet

Next, we'll convert the time from hours to minutes.

 1 hour = 60 minutes,

2 hours = 120 minutes

Now, we can calculate the rate in feet per minute:

Rate (feet per minute) =  [tex]\dfrac{ Distance \ in\ feet}{Time\ in\ minutes}[/tex]

                    Rate             =        [tex]\dfrac{348480}{120}[/tex]

Rate   ≈ 2904 feet per minute

So, the rate of the boat is approximately 2904 feet per minute.

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1.a. -19 at x = -4 for f(x) = 5x + 1.

2.a.  8x + y = -18 the standard form of the equation.

A line has no definite length it can extend in both the directions indefinitely.

According to the given question a functions f(x) = 5x + 1 is given and we have to find the value of this function when x = -4.

Given f(x) = 5x + 1

f(-4) = 5(-4) + 1

f(-4) = -20 + 1

f(-4) = -19.

In the second question we have to write an equation of the line passing through the point (-2,-2) with slope -8.

We know equation of a line in slope intercept form is y = mx + b.

∴ -2 = (-8)(-2) + b

  -2 = 16 + b

   b = - 18.

So, y = -8x -18 OR 8x + y = -18.

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To write the expression 4 log x − 6 log (x + 2) as a single logarithm, apply the properties of logarithms.

To write the expression 4 log x − 6 log (x + 2) as a single logarithm, we can make use of the following logarithmic properties:

Using these properties, we can simplify the given expression as follows:

4 log x − 6 log (x + 2) = log(x^4) - log((x + 2)^6)

Therefore, the expression can be written as the single logarithm log(x^4) - log((x + 2)^6).

Answer:

Option A -distributive property

Step-by-step explanation:

Given : expression     -3 + 2(2 + x + 3)

Step 1: = -3 + 2(x + 2 + 3)

Step 2: = -3 + 2(x + 5)

Step 3: = -3 + 2x + 10

Step 4: = 2x + (-3) + 10

Step 5: = 2x + 7

In step 3 distributive property is applied i.e. c(a+b)=ca+cb

in step 2- 2(x+5) when we apply distributive property it became

2x+10

Therefore, option A is correct

Answer:

commutative property of addition

Step-by-step explanation:

The dilation of a rectangle with a scale factor of 4 will result in each side of the rectangle being multiplied by 4, thus the perimeter will also be quadrupled.

When a rectangle undergoes a dilation with a scale factor of 4, the lengths of all sides of the rectangle are multiplied by 4. Since perimeter is the sum of all the side lengths of a rectangle, the perimeter will also be affected by the scale factor. Therefore, if the original perimeter of the rectangle is P, the new perimeter after dilation will be 4 × P.

Using the property of dilations, the new dimensions of the rectangle will be proportional to the original dimensions. For example, if the original length l and width w of the rectangle are scaled by a factor of 4, the new dimensions will be 4l and 4w respectively. Subsequently, the new perimeter will be 2(4l + 4w) which is the same as saying 4 × (2l + 2w), proving the perimeter is scaled by the same factor of 4.

Answer:

First of all, each slice represents an intersecting plane at that level.

For example, y = 2 is a plane that passes thorugh that level and cuts the volume given by [tex]x^{2} -y^{2}+z^{2}=2[/tex]

We replace this value in the given volume.

[tex]x^{2} -y^{2}+z^{2}=2\\x^{2} -(2)^{2}+z^{2}=2\\x^{2}+z^{2}=2+4\\x^{2}+z^{2}=6[/tex]

So, results in a circumference with radius [tex]\sqrt{6}[/tex], because a circumference is defind as [tex]x^{2} +y^{2} =r^{2}[/tex]. (On plane XY).

We repeat the process.

[tex](1)^{2} -y^{2}+z^{2}=2\\z^{2}-y^{2}=2-1\\z^{2}-y^{2}=1[/tex]

It forms a horizontal hyperbola on plane ZY.

[tex]x^{2} -0^{2}+z^{2}=2\\x^{2}+z^{2}=2[/tex]

Another circle with radius of [tex]\sqrt{2}[/tex] on plane XZ.

[tex](2)^{2} -y^{2}+z^{2}=2\\z^{2}-y^{2}=2-4\\z^{2}-y^{2}=-2\\\frac{z^{2}-y^{2}}{-2} =\frac{-2}{-2} \\\frac{y^{2} }{2} -\frac{z^{2} }{2} =1[/tex]

It forms a hyporbola on plane YZ.

Final answer:

Bobby can buy 5 cups of coffee at $2.25 each and 3 cups of hot chocolate at $1.50 each to meet his budget of $15.75 for 8 cups in total. We find this by solving a system of equations.

Explanation:

Bobby wants to buy a total of 8 cups of coffee and hot chocolate for his co-workers with a budget of $15.75. Since each cup of coffee costs $2.25 and each cup of hot chocolate costs $1.50, we need to find out how many cups of each he can buy.

Let's denote the number of cups of coffee as C and the number of cups of hot chocolate as H.

The total cost for coffee will be $2.25 × C and for hot chocolate $1.50 × H.

The total amount spent is $15.75, and the total number of cups is 8, so we have two equations: 2.25C + 1.50H = 15.75 and C + H = 8.

We can solve this system of equations using substitution or elimination. For simplicity, we'll use substitution.

From C + H = 8, we can express H in terms of C: H = 8 - C.

Substitute H in the cost equation: 2.25C + 1.50(8 - C) = 15.75.

Simplify and solve for C: 2.25C + 12 - 1.50C = 15.75, which simplifies to 0.75C = 3.75, and therefore C = 5.

Now, plug C = 5 into H = 8 - C to find H: H = 3.

Bobby can buy 5 cups of coffee and 3 cups of hot chocolate.

The ratio 60 cents: $2 simplifies to 3:10 after converting dollars to cents and dividing both terms by the greatest common divisor, which is 20.

To simplify the ratio 60 cents: $2, we need to first express both quantities in the same units. Since 1 dollar is equal to 100 cents, $2 is equivalent to 200 cents. Thus, the ratio becomes 60 cents : 200 cents.

Next, we simplify the ratio by dividing both sides by the greatest common divisor. In this case, both 60 and 200 are divisible by 20, which is the greatest common divisor. So we divide both sides by 20:

[tex]\frac{60}{20}[/tex] = 3

[tex]\frac{200}{20}[/tex] = 10

Therefore, the simplified ratio is 3:10.

The inequality would be equal to n  ≥ 7.

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.

We are given that the phrase as;

"A number n is at least 7"

Therefore, the inequality would be;

n  ≥ 7

Or

n = 7

Thus, the inequality would be equal to n  ≥ 7.

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