How do I solve this radical?

When you solve a word problem involving a quadratic equation which of the following is not a number of solutions can you possibl

Nady [450]

It depends on the value of the discriminant of the quadratic.

If you are familiar with the quadratic formula...

x=(-b±√(b^2-4ac))/(2a)

The part under the radical sign (b^2-4ac) is called the discriminant of the quadratic (of the form ax^2+bx+c)

If the discriminant is less than zero there are no REAL solutions (however there are two imaginary solutions)

If the discriminant is equal to zero, there is just one solution

If the discriminant is greater than zero, there are two real solutions.

So depending on context, if you are to exclude imaginary solutions (which we often do) you can have 0,1, or 2 real solutions.

However you will NEVER have three solutions. (real or imaginary)

6 0

3 years ago

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The diameters of aluminum alloy rods produced on an extrusion machine are known to have a standard deviation of 0.0001 in. A ran

Murljashka [212]

Complete Question

The complete question is shown on the first uploaded image

Answer:

The null hypothesis is rejected this means that $\mu \ne 0.5025$

The 95% confidence interval is $0.5045608 < \mu < 0.5046392$

Step-by-step explanation:

From the question we are told that

The standard deviation is s= 0.0001

The sample size is n = 25

The sample mean is $\= x = 0.5046 \ in$

The population mean is $\mu = 0.5025 \ in$

The null hypothesis is $H_o : \mu = 0.5025$

The alternative hypothesis is $H_a : \mu \ne 0.5025$

The test statistics is mathematically represented as

$t = \frac{0.5046 - 0.5025}{ \frac{0.0001}{\sqrt{25} } }$

$t = 105$

So the p-value from the z-table is mathematically represented as

$p-value = 2 * P( z > 105)$

$p-value = 0.000$

seeing that

$p-value < \alpha$ we reject the null hypothesis

The critical value of

$\frac{\alpha }{2}$ obtained from the normal distribution table is

$Z_{\frac{\alpha }{2} } = 1.96$

The margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} }*\frac{s}{\sqrt{n} }$

=> $E = 1.96 *\frac{0.0001}{\sqrt{25} }$

=> $E =3.92 *10^{-5}$

The 95% confidence level is mathematically represented as

$\= x - E < \mu < \= x + E$

=> $0.5046 - 3.92 *10^{-5} < \mu < 0.5046 + 3.92 *10^{-5}$

=> $0.5045608 < \mu < 0.5046392$

8 0

3 years ago

Please help I'm very confused.

Diano4ka-milaya [45]

Answer: So the area of the square is 100 while the sides are all equal to 10 leaving a perimeter of 40 since the square has 4 sides so 4*10=40

Step-by-step explanation: So for this questions you want to look at the bigger picture and what I mean by that is the larger square BHFD outside of square ACEG right. So if you look carefully you'll see 4 triangles labeled something like ABC, AHG, CDE, and GEF. using these triangles and there sides we can solve for the hypotenuse which is also the side of the square ACEG and since all the triangles have the same dimensions we only need to solve for one of them. So using pythagorean theroem 8^2+6^2=c^2 where in this case c = a side of the square ACEG so c = 10. Now that we have the sides all equal 10 the area or length times width = 10*10=100. Hope it helps :)

7 0

2 years ago

A 7th grade classis selling packages of cotton candy at a festival for $2.95 each. Each package costs them $0.95 to make.They ex

Luden [163]

Answer:

Answer C.

Step-by-step explanation:

The class sells them for $2.95, assuming $0.95 manufacturing cost per, leaving $2.00 profit per bag. If they sell 900-1000 packages at $2.00, it leaves $1800-$2000 profit.

6 0

3 years ago

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Triangle ABC is a right triangle with leg lengths of 5 and 12 inches. Find the length of the hypotenuse. Round answer to the nea

stiv31 [10]

(AB)^2+(BC)^=(AC)^2
5^2+12^2=AC^2
25+144=AC^2
169=AC^2
AC=13inches

8 0

3 years ago

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