1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
guapka [62]
3 years ago
13

Determine the nature of the roots: 4x^2 + 32x + 64 = 0

Mathematics
2 answers:
DENIUS [597]3 years ago
6 0

Answer:

b. a unique real solution

Step-by-step explanation:

A quadratic equation ax² + bx + c = 0 ,

Has two distinct real roots,

If discriminant, D=b^2 - 4ac > 1

Has two equal real roots,

If D = 0,

Has two imaginary roots or no real roots,

if D < 1,

Here. the given qudratic equation,

4x^2 + 32x + 64=0

By comparing,

a = 4, b = 32, c = 64,

\implies D = 32^2 - 4\times 4\times 64 = 1024 - 1024 = 0

Hence, the equation has two equal real roots or a unique real solution.

i.e. OPTION 'b' is correct.

zloy xaker [14]3 years ago
5 0

Answer:

A unique real solution

Step-by-step explanation:

You might be interested in
Best known for its testing program, ACT, Inc., also compiles data on a variety of issues in education. In 2004 the company repor
GarryVolchara [31]

Answer:

\mu_p -\sigma_p = 0.74-0.0219=0.718

\mu_p +\sigma_p = 0.74+0.0219=0.762

68% of the rates are expected to be betwen 0.718 and 0.762

\mu_p -2*\sigma_p = 0.74-2*0.0219=0.696

\mu_p +2*\sigma_p = 0.74+2*0.0219=0.784

95% of the rates are expected to be betwen 0.696 and 0.784

\mu_p -3*\sigma_p = 0.74-3*0.0219=0.674

\mu_p +3*\sigma_p = 0.74+3*0.0219=0.806

99.7% of the rates are expected to be betwen 0.674 and 0.806

Step-by-step explanation:

Check for conditions

For this case in order to use the normal distribution for this case or the 68-95-99.7% rule we need to satisfy 3 conditions:

a) Independence : we assume that the random sample of 400 students each student is independent from the other.

b) 10% condition: We assume that the sample size on this case 400 is less than 10% of the real population size.

c) np= 400*0.74= 296>10

n(1-p) = 400*(1-0.74)=104>10

So then we have all the conditions satisfied.

Solution to the problem

For this case we know that the distribution for the population proportion is given by:

p \sim N(p, \sqrt{\frac{p(1-p)}{n}})

So then:

\mu_p = 0.74

\sigma_p =\sqrt{\frac{0.74(1-0.74)}{400}}=0.0219

The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ). Broken down, the empirical rule shows that 68% falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ).

\mu_p -\sigma_p = 0.74-0.0219=0.718

\mu_p +\sigma_p = 0.74+0.0219=0.762

68% of the rates are expected to be betwen 0.718 and 0.762

\mu_p -2*\sigma_p = 0.74-2*0.0219=0.696

\mu_p +2*\sigma_p = 0.74+2*0.0219=0.784

95% of the rates are expected to be betwen 0.696 and 0.784

\mu_p -3*\sigma_p = 0.74-3*0.0219=0.674

\mu_p +3*\sigma_p = 0.74+3*0.0219=0.806

99.7% of the rates are expected to be betwen 0.674 and 0.806

5 0
3 years ago
The base of S is the region enclosed by the parabola y = 8 − 8x2 and the x-axis. Cross-sections perpendicular to the x-axis are
Elena-2011 [213]

The base of a solid is the region in the first quadrant bounded by the y-axis, the x-axis, the graph of y=ex, and the vertical line x=1. For this solid, each cross section perpendicular to the x-axis is a square. What is the volume of the solid?

Step-by-step explanation:

Answer: Sometimes I dont want to be happy.

8 0
1 year ago
Am i doing this right
klasskru [66]
Good luck >>>>>>>>>>>>>>

5 0
2 years ago
Two arithmetic means between 3 and 24 are -
defon

The value of two arithmetic means which are inserted between 3 and 24 are 24/9 and 75/9.

<h3>What is arithmetic mean?</h3>

Arithmetic mean is the mean or average which is equal to the ratio of sum of all the group numbers to the total numbers.  

The two arithmetic means between 3 and 24 are has to be inserted.

3, A₂, A₃, 24

All the four numbers are in arithmetic progression. The nth terms of AM can be found using the following formula:

t(n)=a(n-1)d

Here, d is the common difference a is the first terms and n is the total term.  The first term, a=3 and t₄=24. Thus, the common difference is;

t(n)=a(n-1)d\\t(4)=3(4-1)d\\24=3(3)d\\24=9d\\d=\dfrac{24}{9}

The second and 3rd term are:

A₂=3+\dfrac{24}{9}=\dfrac{51}{9}\\ A₃=\dfrac{51}{9}+\dfrac{24}{9}=\dfrac{75}{9}

Thus, the value of two arithmetic means which are inserted between 3 and 24 are 24/9 and 75/9.

Learn more about the arithmetic mean here;

brainly.com/question/14831274

#SPJ1

8 0
2 years ago
Why is a stick of gum like a sneeze
patriot [66]

why?

ωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωω

7 0
2 years ago
Other questions:
  • Probability help!!!!!
    14·1 answer
  • Simply this expression. Which like terms can she combine 12-4x+3
    10·1 answer
  • In need of help! ASAP!!!!!!!!!!!!!!!
    6·1 answer
  • At noon on tuesday in Chicago the temperature in degrees Fahrenheit was -2 Fahrenheit at noon on Wednesday the temperature was 8
    7·2 answers
  • Cameron Indoor Stadium at Duke University is one of the most revered sites in all of college basketball, as well as in all of sp
    14·1 answer
  • the difference of two positive numbers is 8. the larger is twice the smaller decreased by 7. find the two numbers
    15·1 answer
  • What is the range of the function on the graph?
    15·1 answer
  • Andrea ordered a computer
    13·1 answer
  • Evaluate the expression for u = –8 and v = 2.<br><br> uv − u
    9·2 answers
  • A recipe for dessert calls for 1/3 cup of powdered sugar and 2/6 cup of brown
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!