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Grace [21]
3 years ago
15

Nada is making square coasters with sides of 3 inches. On each coaster is a circular design. What is the radius of the largest c

ircle that fits on one of the coasters?​
Mathematics
1 answer:
Brilliant_brown [7]3 years ago
4 0

Answer:

2.25π square inches [or 7.07 sq. in. rounded to 2 decimal places]

Step-by-step explanation:

The largest circle inscribed in a square would have DIAMETER EQUAL TO THE SIDE LENGTH OF THE SQUARE.

Since diameter is double of radius, we can find the radius to be:

diameter = 3 [side length of square]

radius = 3/2 = 1.5 inches

The area of a circle is  πr^2

THus, the largest circle area = πr^2 = π(1.5)^2 = π(2.25) = 2.25π square inches

You might be interested in
Is the solution of b x 5/6 = 25 greater than or less than 25
azamat

Answer:

Greater. (30)

Step-by-step explanation:

Simplest way to find out is divide.

Flip 5/6 and multiply.

25 x 6 = 150

150 / 5 = 30

8 0
3 years ago
A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 410 gram setting. It is
frozen [14]

Answer:

The decision rule for rejecting the null hypothesis is t < -1.721

Step-by-step explanation:

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 410 gram setting. It is believed that the machine is underfilling the bags.

At the null hypothesis, we test if the mean weight of the bag is the desired value of 410, that is:

H_0: \mu = 410

At the alternate hypothesis, we test if the bag is underfilled, that is, the mean weight is below the desired value, so:

H_0: \mu < 410

Type of test:

As we test if the mean is less than a value, we have a left-tailed test.

We have the standard deviation for the sample, which means that the t-distribution is used.

We have 22 - 1 = 21 degrees of freedom, with a level of significance of 0.05.

Using a calculator, the critical value is t_c = -1.721

Determine the decision rule for rejecting the null hypothesis.

We reject the null hypothesis if the test statistic is less than the critical value, so the decision rule for rejecting the null hypothesis is t < -1.721

3 0
3 years ago
What is the 8.356 rounded to the nearest hundredth
rodikova [14]

Answer:

8.356 rounded to the nearest hundredth=8.360

5 0
3 years ago
Read 2 more answers
So my another account got ban and I was wondering how long will it take to get unban I alright waited for 24 hours
Sati [7]
I think u can’t get unban u have to create a new account
7 0
3 years ago
Read 2 more answers
Brainliest to correct!! Please help :)
Zielflug [23.3K]

Answers:  2700 and 5300 in that order

Katie invested <u>$2700</u> at a rate of 3% and <u>$5300</u> at a rate of 4%

===============================================================

Explanation:

  • x = amount invested at a rate of 3%
  • y = amount invested at a rate of 4%

Those two amounts must add to 8000 because this is how much she invests total. So x+y = 8000 is the first equation to set up.

The formula we'll be using is the simple interest formula, which is,

i = p*r*t

where p is the amount deposited or principal, r is the interest rate, and t is the number of years. Luckily, we don't have to worry about the time value t because t = 1 so it effectively goes away. We just need to worry about p and r.

The variable p will be tied directly to the values of x and y, as these are deposit amounts. The r values are decimal forms of the percentages (eg: 3% converts to 0.03)

In short, Katie will earn

  • 0.03x dollars from the first account (3% account)
  • 0.04y dollars from the second account (4% account)

In total, she earns 0.03x+0.04y dollars combined. This is set equal to 293 as this is the stated interest she earns over the entire year.

So another equation to set up is 0.03x+0.04y = 293

This only works for simple interest. Compound interest may likely be a different story.

----------------------------------------------------

To summarize so far, we found these two equations:

  • x+y = 8000
  • 0.03x+0.04y = 293

We have a number of options on how to solve this system. I'll use substitution.

Solve the first equation for y

x+y = 8000

y = 8000-x

Then we'll plug this into the other equation to solve for x like so,

0.03x+0.04y = 293

0.03x+0.04( y ) = 293

0.03x+0.04( 8000-x ) = 293

0.03x+0.04(8000)+0.04(-x) = 293

0.03x+320-0.04x = 293

-0.01x+320 = 293

-0.01x = 293-320

-0.01x = -27

x = -27/(-0.01)

x = 2700

This tells us that Katie invested $<u>2700</u> at 3%

Use this x value to find y

y = 8000-x

y = 8000-2700

y = 5300

She also invested $<u>5300</u> at 4%

----------------------------

As a quick check,

  • x+y = 2700+5300 = 8000

so that works out

Also,

  • 0.03*x = 0.03*2700 = 81
  • 0.04*y = 0.04*5300 = 212
  • 0.03x+0.04y = 81+212 = 293

which also works out. The answers are fully confirmed.

7 0
3 years ago
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