A cut piece of ribbon is 21 inches long. The piece of ribbon is 15% of the original length of the ribbon.How long was the original length of ribbon?

Answers

Answer 1
Answer:

Answer:

The original length of the rope is 140

Step-by-step explanation:

21x (100/15)

Answer 2
Answer:

Answer:

140

Step-by-step explanation:

.


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Of interest is whether the percent of managers at High Tech Inc. that pay over $8 per day for lunch is the same as the percent of technicians. Sixty managers are surveyed and forty-six of them pay over $8 per day for lunch. One hundred forty-nine technicians are surveyed and ninety-eight of them pay over $8 per day for lunch. The hypothesis test to use is Group of answer choices matched or paired samples two proportions independent group means, population standard deviations unknown independent group means, population standard deviations known.

Answers

Answer:

comparison of two sample proportions independent

Step-by-step explanation:

Given that the percent of managers at High Tech Inc. that pay over $8 per day for lunch is the same as the percent of technicians.

The data can be given as follows:

The samples are as follows

Managers             60                149

Who paid >8        46                  98

Hence we compare sample proportions here.

The appropriate test would be

comparison of two sample proportions independent

A telephone company charges 50 cents for along distance call for the first two minutes, and
30 cents for each additional minute. Find the cost
of a 15-minute call.

Answers

Answer: $4.40 is the cost for the call

PLEASE HELP ASAP
Add the complex numbers: (4 + 8i) + (–2 – i)

Answers

Answer:

2 + 7i

Step-by-step explanation:

(4 + 8i) + (-2 - i)

open the brackets

4 + 8i - 2 - i

add or subtract like terms

2 + 7i

Answer:

2+7i

Step-by-step explanation:

Open the brackets.

4+8i-2-i

You will get…

2+7i

Find the length of side
x in simplest radical form with a rational denominator.

Answers

The length of sides x in the simplest radical form is 2√2

Properties of a right angled triangle:

  • One of the angle is equals to 90 degree.
  • The sides can be found using Pythagoras theorem
  • Trigonometric ratios can be used to find the angles.

Let's find x using trigonometric ratios

sin ∅ = opposite / hypotenuse

Therefore,

sin 30° = √2 / x

x sin 30° = √2

x = √2 / sin 30°

x = (√(2) )/((1)/(2) )

x = √(2) × 2

x = 2√2

learn more on right angle triangle: brainly.com/question/15948053?referrer=searchResults

Write the equation of a parabola whose directrix is y=9.75 and has a focus at (8, 0.25).

Answers

Answer:

y = (-1/19)(x - 8)² + 1521/76

Step-by-step explanation:

A parabola moves in such a way that it's distance from it's focus and directrix are always equal.

Now, we are given that directrix is y = 9.75 and focus is at (8, 0.25). Focus can be rewritten as (8, ¼) and directrix can be rewritten as y = 39/4

If we consider a point with the coordinates (x, y), it means the distance from this point to the focus is;

√((x - 8)² + (y - ¼)²)

Distance from that point to the directrix is; (y - 39/4)

Thus;

√((x - 8)² + (y - ¼)²) = (y - 39/4)

Taking the square of both sides gives;

((x - 8)² + (y - ¼)²) = (y - 39/4)²

(x - 8)² + y² - ½y + 1/16 = y² - (39/2)y + (39/4)²

Simplifying this gives;

(x - 8)² - (39/4)² = (½ - 39/2)y

(x - 8)² - 1521/4 = -19y

(x - 8)² - 1521/4 = -19y

Divide both sides by -19 to get;

y = (-1/19)(x - 8)² + 1521/76

The sphere at the right fits snugly inside a cube with 4-in. edges. What is the approximate volume of the space between the sphere and cube?

Answers

As given by the question

There are given that the inside edge is 4 in.

Now,

Since sphere fits snugly inside a cube therefore diameter of sphere will be equal to side of the cube

So,

\begin{gathered} \text{diameter}=4\text{ inches} \n \text{radius}=(dameter)/(2) \n \text{radius}=(4)/(2) \n \text{radius}=2 \end{gathered}

Then,

Volume of the sphere is given by:

\begin{gathered} (4)/(3)*\pi* r^3=(4)/(3)*3.14*2^3 \n =(4)/(3)*3.14*8 \n =33.5 \end{gathered}

And,

The volume of a cube is:

\begin{gathered} \text{Volume of cube=side}* side* side \n =4*4*4 \n =64\text{ inches} \end{gathered}

Then,

The volume of the space between the sphere and cube = 64-33.5 = 30.5.

Hence, the answer is 30.5 cube inches.