Please help me with this

Write 3.01 (1 repeating) as a mixed fraction?

Advocard [28]

Answer:

3 1/100

Step-by-step explanation:

4 0

2 years ago

Hey ^-^ can someone please help me with this problem:

soldi70 [24.7K]

Answer: 8 (Pi - sqrt(3))

Discussion:

The area of the shaded region is that of the semicircle minus the area of the triangle..

Area of semicircle = 1/2 * Pi * R^2

Where R^2 is the square of the radius of the circle. In our case, R ( = OC)

= 4 so the semicircle area is

(1/2) * Pi * (4^2) = (1/2) * Pi * 16 = 8 Pi

Area of triangle.

First of all, angle ACB is a right angle ( i.e. 90 degrees).

* This is the Theorem of Thales from elementary Plane Geometry. *

so by Pythagoras

AC^2 + BC^2 = AB^2

But CB = 4 (given) and AB = 4*2 = 8 ( the diameter is twice the radius).

Substituting these in Pythagoras gives

AC^2 + 4^2 = 8^2 or

AC^2 = 8^2 - 4^2- = 64 - 16 = 48

Hence AC = sqrt(48) = sqrt (16*3) = 4 * sqrt(3)

We are almost done! The area of the triangle is given by

(1/2) b * h = (1/2) BC * AC = (1/2) 4 * (4 * sqrt(3)) = 8 sqrt(3)

We conclude the area area of the shaded part is

8 PI - 8 sqrt(3) = 8 (Pi - sqrt(3))

Note that sqrt(3) is approx 1.7 so (PI - sqrt(3)) is a positive number, as it better well be!

6 0

2 years ago

A survey of 225 students showed the mean number of hours spent studying per week was 20.6 and the standard deviations was 2.7

LekaFEV [45]

Answer:

The margin of error is approximately 0.3

Step-by-step explanation:

The following information has been provided;

The sample size, n =225 students

The sample mean number of hours spent studying per week = 20.6

The standard deviation = 2.7

The question requires us to determine the margin of error that would be associated with a 90% confidence level. In constructing confidence intervals of the population mean, the margin of error is defined as;

The product of the associated z-score and the standard error of the sample mean. The standard error of the sample mean is calculated as;

$\frac{sigma}{\sqrt{n} }$

where sigma is the standard deviation and n the sample size. The z-score associated with a 90% confidence level, from the given table, is 1.645.

The margin of error is thus;

$1.645*\frac{2.7}{\sqrt{225}}=0.2961$

Therefore, the margin of error is approximately 0.3

5 0

2 years ago

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A scuba diver is descending at an average rate of 44.5 feet per minute.

finlep [7]

Scuba diver has done 102.35 feet below sea level.

The diver is:

descending at a speed of 44.5 feet per minute.
has descended for 2.3 minutes

The distance the scuba diver has gone in that time is:

Distance = Speed x time

Solving for distance gives us:

= 44.5 feet per minute x 2.3 minutes

= 102.35 feet

Because the diver is going down, they are going below sea level. This means that the diver has gone 102.35 feet below sea level.

Find out more at brainly.com/question/24720718.

5 0

1 year ago

The quadratic function y = –10x2 + 160x – 430 models a store’s daily profit (y) for selling a T-shirt priced at x dollars. What

inn [45]

x2-16x+48=0 Two solutions were found : x = 12 x = 4

Step by step solution :Step 1 :Trying to factor by splitting the middle term

1.1 Factoring x2-16x+48

The first term is, x2 its coefficient is 1 .
The middle term is, -16x its coefficient is -16 .
The last term, "the constant", is +48 

Step-1 : Multiply the coefficient of the first term by the constant 1 • 48 = 48

Step-2 : Find two factors of 48 whose sum equals the coefficient of the middle term, which is -16 .

-48 + -1 = -49 -24 + -2 = -26 -16 + -3 = -19 -12 + -4 = -16 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -12 and -4
 x2 - 12x - 4x - 48

Step-4 : Add up the first 2 terms, pulling out like factors :
 x • (x-12)
 Add up the last 2 terms, pulling out common factors :
 4 • (x-12)
Step-5 : Add up the four terms of step 4 :
 (x-4) • (x-12)
 Which is the desired factorization

Equation at the end of step 1 : (x - 4) • (x - 12) = 0 Step 2 :Theory - Roots of a product :

2.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

2.2 Solve : x-4 = 0

Add 4 to both sides of the equation :
 x = 4

Solving a Single Variable Equation :

2.3 Solve : x-12 = 0

Add 12 to both sides of the equation :
 x = 12

Supplement : Solving Quadratic Equation DirectlySolving x2-16x+48 = 0 directly

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Parabola, Finding the Vertex :

3.1 Find the Vertex of y = x2-16x+48

5 0

2 years ago

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