The owner of a ballroom dance studio has 8 locations in the Houston area. Each studio is a 30 foot by 30 ft. room. If each couple requires 72 inch by 72 inch area, what is a reasonable estimate for the total number of people the dance company can accommodate in the city of Houston for all of it's locations? ​

The function is continuous only if m = 7.

If the function is continue, then the value of the function needs to be the same one in both pieces of the function when we evaluate in x = -2

That means that:

f(-2) = f(-2)  (trivially)

Replacing the two pieces of the function we will get:

m*(-2) - 6 = (-2)^2 + 10*(-2) - 4

now we can solve that equation for m.

-2m - 6 = 4 -20 - 4

-2m = -20 + 6 = -14

m = -14/-2 = 7

m = 7

that is the value of m.

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answer: the range is 41.

to find the range of this data set, we first need to find the minimum and maximum values - which are 59 and 100.

then we subtract the minimum from the maximum.

59 - 100 = 41.

Answer:

the son age is 13band Evans age is 52 years old at present day

Dan is 12 years old.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

let the Age of Dan is x years

Mr. Evans Age = 4x

If Mr. Evans was 46 years old 2 years ago

The, Present age of Mr. Evans = 48 years

So, Dan's Age = 48/4

                        = 12 years.

Hence, Dan is 12 years old.

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Answer:

19 + 6 = 25_ 25 - 3 = 22

Step-by-step explanation:

Good luck

The two distinct lines, line l and line m, have the following relationship with line n

A. The measure of the angle where line | meets line n is 90 degrees

B. The measure of the angle where line meets line n is 90 degrees

This is a term used to refer to lines that intersect at angle 90 degrees. perpendicular lines are also found in right angle triangle. Hence it is right to say that two sides of a right angled triangle are perpendicular to each other.

The features of perpendicularity also helps in defining a squire and rectangles. This is true because the sides meet at angle 90 degrees

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Answer: x = -3

Step-by-step explanation:

2 x 2 + x - 1 = 0

4 + x - 1 = 0

3 + x = 0

x = -3

Answer:

X=-3

Step-by-step explanation:

See steps below:)

The number of fidgets and pop bought was 15 each

From the information given, we have that;

1 fidget costs $3

1 Pop cost $4

Let the number of Fidgets be x

Let the number of Pop be y

Then, we have that a total of 20 fidgets and Pop cots $75

We have that;

20x + y = 75

Now, substitute the value of x as 3, we get;

20(3) + y= 75

expand the bracket

y = 75 - 60

y = 15

The number of fidgets is expressed as;

20x/4 = 20(3) /4 = 15

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Answer:

1.029 is greater than 1.0275

Step-by-step explanation:

Answer:

1.029

Step-by-step explanation:

What is greater 1.0275 or 1.029

.027 < .029

So, 1.029 is greater.

Answer:

45 degrees

Step-by-step explanation:

The 4 angles of a quadrilateral will add to 360.

We know 1 of them (angle B) is 90 degrees.

We can set up an equation to solve the others.

2x+3x+x+90 = 360

Now solve for x.

Start by combining the x terms together.

6x+90 = 360

6x = 360-90

6x = 270

(6x/6) = 270/6

x = 45 degrees

Check back to see if that makes sense and if the equation equals 360 when x is 45:

2x+3x+x+90 = 360

2(45)+3(45)+45+90=360.

Answer:−589.86

Step-by-step explanation:

let unknown number be x

Solve for x

655.4+x=65.54

Subtract 655.4 from both sides.

x=65.54−655.4

Subtract 655.4 from 65.54 to get −589.86.

x=−589.86

A sample size of [214] to be within 5 % of the true proportion of women over age 55 who are widows and be 900 % confident.

The term "standard deviation" (or "σ") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

We are given that recent study Indicated that 27% of the 142 women over age 55 in the study were widows

Margin of error  = 0.05 = E

z-score = z/2 = 1.645

n = 0.27 x 0.73 (1.645/ 0.05)²

n = 213.343

n=214

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Answer:

Therefore, the angle ∠CDA is 58°.

Step-by-step explanation:

∠CDA = 58°

In the given figure, let's consider the angle ∠CDA as x.

Since AB is the diameter of the circle, we know that the angle subtended by any diameter at any point on the circumference is always 90°. Therefore, ∠CAB = 90°.

In triangle CAD, the sum of angles is 180°. So, we have:

∠CAD + ∠CDA + ∠CAB = 180°

Substituting the known values:

32° + x + 90° = 180°

Combining like terms:

x + 122° = 180°

Subtracting 122° from both sides:

x = 180° - 122°

x = 58°

Answer: y=3.75x+1.9

Step-by-step explanation: the pick up fee would be the y-intercept and the per mile cost would be the slope.

The equation that can be used to determine the number of miles in the taxi ride is 1.90 + 3.75x = 80.65.

The number of miles traveled is 21 miles.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

Pick up fee charges = $1.90

Charges per mile = $3.75

Total fare = $80.65

The number of miles traveled = x

We can write an equation as:

1.90 + 3.75x = 80.65

The number of miles traveled:

1.90 + 3.75x = 80.65

Subtract 1.90 on both sides.

1.90 + 3.75x - 1.90 = 80.65 - 1.90

3.75x = 78.75

Divide both sides by 3.75.

x = 21.

Thus,

The equation that can be used to determine the number of miles in the taxi ride is 1.90 + 3.75x = 80.65.

The number of miles traveled is 21 miles.

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Divide total length by cut length:

9 / 2/3

= (9 x 3)/2 = 27/2 = 13.5

He can cut 13 pieces

The surface area of a cylinder with circular bases of radius r and height h is equal to the sum of the areas of the two circular faces and the area of the rectangular lateral surface:

A = 2πr² + 2πrh

If you know the height h, then you can solve the quadratic equation for r.

Answer:

5. (x,y) = (2.3)

Step-by-step explanation:

1/2x + 2 = x+1

x = 2

y = 2+1

y = 3

(x,y) + (2,3)

{3 = 1/2 x 2 + 2

{3 = 2 + 1

{3 = 3

{3 = 3

Answer:

  3. no solution

  5. (x, y) = (2, 3)

Step-by-step explanation:

  -5x +y = 1

  -10x +2y = -2

Multiply the first equation by -2 and add the second equation:

  -2(-5x +y) +(-10x +2y) = -2(1) +(-2)

  10x -2y -10x +2y = -2 -2 . . . . eliminate parentheses

  0 = -4 . . . . . . . . . no variable values will make this true: NO SOLUTION

(The lines graph as parallel lines.)

__

  y = 1/2x +2

  y = x +1

Subtract the first equation from the second:

  (y) -(y) = (x +1) -(1/2x +2)

  0 = 1/2x -1

  0 = x -2

  2 = x

  y = x +1 = 2 +1 = 3 . . . . use the second equation to find y

The solution is (x, y) = (2, 3).

Answer:

4(x - 1) = 6(x + 3)

x = -11

Step-by-step explanation:

x represents “the number” so we would substitute this with a variable.

(I hope this helps! Have a great day AND STAN BTS)

Answer:

The perimeter of rectangle JKLM is 16 units.

Step-by-step explanation:

Perimeter is the area around the shape, so if you look at the space between K and J, the units there are 7. Multiply 7 by 2 (since there are two sides), and then add 2. 2 + 14 = 16.

Answer:

17 units

Step-by-step explanation:

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The sum of the scores is equal to 160.

In Mathematics, a mean is sometimes referred to as an average and it can be defined as a ratio of the sum of the total number in a data set (population) to the frequency of the data set.

Mathematically, the mean for this set of scores can be calculated by using the following formula:

Mean = [F(x)]/n

For the total number of scores (data set), we have;

∑x = 20 + 60 + 30 + 50

∑x = 160.

Mean = [F(x)]/n = 160/4 = 40.

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Solve. Write the solution set in interval notation.

-2x > -8 and - 3x < 24

-2x > -8

divide both sides by -2

x < 4

And -3x < 24

divide both sides by -3

So, x > -8

So, x < 4 and x > -8

it can be written -8 < x < 4

So, the interval of solution is ( -8 , 4 )

and can be represented on the line of numbers as shown at the following figure :

Answer:

50.75

Step-by-step explanation:

We have:

\(E[g(x)] = \int\limits^{\infty}_{-\infty} {g(x)f(x)} \, dx \\\\= \int\limits^{1}_{-\infty} {g(x)(0)} \, dx+\int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx+\int\limits^{\infty}_{6} {g(x)(0)} \, dx\\\\= \int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x+3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x)\frac{2}{x} } \, dx + \int\limits^{6}_{1} {(3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {8} \, dx + \int\limits^{6}_{1} {\frac{6}{x} } \, dx\\\\\)

\(=8\int\limits^{6}_{1} \, dx + 6\int\limits^{6}_{1} {\frac{1}{x} } \, dx\\\\= 8[x]^{^6}_{_1} + 6 [ln(x)]^{^6}_{_1}\\\\= 8[6-1] + 6[ln(6) - ln(1)]\\\\= 8(5) + 6(ln(6))\\\\= 40 + 10.75\\\\= 50.74\)

The degree of the expression \(8ax^4\) is 4.

The degree of a monomial expression is defined as the highest exponent of the variable in that expression.

In this case, we have the expression \(8ax^4\), where x is the variable and its highest exponent is 4.

The coefficient 8a is just a constant multiple and does not affect the degree of the expression.

Therefore, the degree of the expression 8\(ax^4\) is 4. It is important to understand the concept of degree, as it helps us to classify polynomial expressions and determine their behavior.

Furthermore, by knowing the degree of an expression, we can also determine the number of possible roots or solutions of that expression.

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Question

"What is the degree of the expression 8ax^4?"

Note that the coordinates of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4). (Option B)

To rotate a point 90 degrees  clockwise about a given point,we can follow these steps -

Translate the coordinates   of the given point so that the center of rotation is at the origin.   In this case,we subtract the coordinates   of the center (0,1) from the coordinates of point A (5,4) to get (-5, 3).

Perform the rotation by swapping the x and y coordinates and changing the sign of the   new x coordinate. In this case,we  swap the x and y coordinates of (-5, 3)   to  get (3, -5).

Translate the coordinates back to their original position   by adding the coordinates of the center (0,1)  to the result from step 2. In   this case, we add (0,1) to (3, -5) to get (3, -4).

Therefore, the coordinates   of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4).

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Step-by-step explanation:

Types of fees and charges

Monthly account keeping or service fee. The fee you pay for an organisation to manage your bank account. ...

Internet banking fee. ...

EFTPOS transaction fee. ...

ATM transaction fee. ...

Non-bank or foreign ATM fee. ...

Telephone banking transaction fee. ...

Branch withdrawal fee. ...

Cheque withdrawal fee.

Answer:

We can solve this problem using the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the legs (the sides adjacent to the right angle) is equal to the square of the length of the hypotenuse (the side opposite the right angle).

Let's let "h" be the height of the tree before it broke, and "x" be the distance from the base of the tree to where it broke. Then, we can set up the following equation using the Pythagorean theorem:

h^2 = x^2 + (h-7)^2

We also know that the top of the tree rests 23 feet from the base of the tree, so we can set up another equation:

x + 23 = h

Now we have two equations with two unknowns, which we can solve simultaneously. Rearranging the second equation, we get:

x = h - 23

Substituting this into the first equation, we get:

h^2 = (h-23)^2 + (h-7)^2

Expanding the squares and simplifying, we get:

0 = -46h + 552

Solving for h, we get:

h = 12

Therefore, the height of the tree before it broke was approximately 12 feet. Since none of the answer choices match this result, we cannot cross out any of the choices.

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{m = 9}}}}}\)

Option A is the correct option

Step-by-step explanation:

\( \sf{5m + 3m - 8 = 64}\)

Collect like terms

⇒\( \sf{8m - 8 = 64}\)

Move 8 to right hand side and change it's sign

⇒\( \sf{8m = 64 + 8}\)

Add the numbers

⇒\( \sf{8m = 72}\)

Divide both sides of the equation by 8

⇒\( \sf{ \frac{8m}{8} = \frac{72}{8} }\)

Calculate

⇒\( \sf{m = 9}\)

Hope I helped!

Best regards!!

Answer:

\(\Huge \boxed{m=9}\)

Step-by-step explanation:

\(5m + 3m - 8 = 64\)

Combining like terms.

\(8m - 8 = 64\)

Adding 8 to both sides.

\(8m=72\)

Dividing both sides by 8.

\(m=9\)

Answer:

k = 25

Step-by-step explanation:

Given the following data;

Volume = 325 in³

Length = 13 inches

To find the constant of proportionality, k;

Mathematically, direct proportion is given by the expression;

V = kL

k = V/L

Substituting into the formula, we have;

k = 325/13

k = 25