A five-question multiple-choice quiz has five choices for each answer. Use the random number table provided, with 0’s representing incorrect answers and 1’s representing correct answers, to answer the following question:

What is the probability of correctly guessing at random exactly one correct answer? Round your answer to the nearest whole number.

Answer:

3rd option

Step-by-step explanation:

[tex]\frac{3x^2-3}{x^2-5x+4}[/tex] ( factorise numerator and denominator )

3x² - 3 ← factor out 3 from each term

= 3(x² - 1²) ← x² - 1 is a difference of squares and factors in general as

a² - b² = (a - b)(a + b)

x² - 1

= x² - 1²

= (x - 1)(x + 1) , then

3x² - 3 = 3²(x - 1)(x + 1) ← in factored form

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

x² - 5x + 4

consider the factors of the constant term (+ 4) which sum to give the coefficient of the x- term (- 5)

the factors are - 1 and - 4 , since

- 1 × - 4 = + 4 and - 1 - 4 = - 5 , then

x² - 5x + 4 = (x - 1)(x - 4)

then

[tex]\frac{3x^2-3}{x^2-5x+4}[/tex] = [tex]\frac{3(x-1)(x+1)}{(x-1)(x-4)}[/tex] ← in factored form

Answer:

a^2 + b^2 = c^2

Step-by-step explanation:

a^2 + b^2 = c^2

Answer:

[tex]\Longrightarrow: \boxed{\sf{A^2+B^2=C^2}}[/tex]

Step-by-step explanation:

In the Pythagorean theorem, the formula is:

[tex]\underline{\text{PYTHAGOREAN THEOREM FORMULA:}}}[/tex]

[tex]\Longrightarrow: \sf{A^2+B^2=C^2}[/tex]

Thus, the Pythagorean theorem's formula is "a²+b²=c²".

I hope this helps. Let me know if you have any questions.

Answer:

29.3 degrees

Step-by-step explanation:

90 - 60.7 = 29.3 degrees

Answer:

Step-by-step explanation:

Answer:

See below:

Step-by-step explanation:

At x axis intercepts, the value of y = 0

0 = -3/5 ( x+7)^2   + 6

-6(-5/3) =   (x+7)^2

 10 = (x+7)^2

x =  -7 +- sqrt (10)

Answer:

[tex] x = -7 \pm \sqrt{10 [/tex]

Step-by-step explanation:

The x-intercepts occur where y = 0.

-3/5(x + 7)² + 6 = 0

-3(x + 7)² + 30 = 0

-3(x² + 14x + 49) + 30 = 0

-3x² - 42x - 147 + 30 = 0

3x² + 42x + 117 = 0

[tex] x = \dfrac{-42 \pm \sqrt{42^2 - 4(3)(117)}}{2(3)} [/tex]

[tex] x = \dfrac{-42 \pm \sqrt{360}}{6} [/tex]

[tex] x = \dfrac{-42 \pm 6\sqrt{10}}{6} [/tex]

[tex] x = -7 \pm \sqrt{10 [/tex]

Answer:

Step-by-step explanation:

Given points P(4, 2) and Q(13, 14), you want the length of PQ and its midpoint.

The length of PQ is given by the distance formula ...

  d = √((x2 -x1)² +(y2 -y1)²)

  d = ((13 -4)² +(14 -2)²) = √(9² +12²) = √225

  d = 15

The length of PQ is 15 units.

The midpoint is halfway between the end points. It is conveniently found as the average of the coordinates of the end points.

  M = (P +Q)/2

  M = ((4, 2) +(13, 14))/2 = (4+13, 2+14)/2 = (17, 16)/2

  M = (8.5, 8)

The midpoint of PQ is M(8.5, 8).

__

Additional comment

The length of PQ is the hypotenuse of a right triangle with side lengths 9 and 12 units. You recognize this ratio as 3:4, so the triangle is a 3-4-5 right triangle, scaled up by a factor of 3. The length PQ is 3·5 = 15.

{3, 4, 5} is one of several Pythagorean triples commonly seen in textbook problems. Others include {5, 12, 13}, {7, 24, 25}, {8, 15, 17}.

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Answer:

4n-10, Answer is D

Step-by-step explanation:

First we will use n as any number.

the difference between each of the numbers is +4

This creates first part of the formula.

4n...

If you do 4n and replace n as one (For the first number of the sequence) then 4×1=4. You then have to find out how much you need to add or subtract to get -6 so the difference between 4 and -6 is -10.

This creates the second part of our formula.

4n - 10

You can check this by doing the same thing for the second number and replacing n with 2.

2×4=8

8 - 10= -2 which is the second number in the sequence which confirms this is correct.

Answer:

To find the directional derivative in the direction of the vector (1,2), we need to find a unit vector in the direction of the vector (1,2). We simply divide by the magnitude of (1,2). u=(1,2)∥(1,2)∥=(1,2)√12+22=(1,2)√5=(1/√5,2/√5).

Answer:To find the directional derivative in the direction of the vector (1,2), we need to find a unit vector in the direction of the vector (1,2). We simply divide by the magnitude of (1,2). u=(1,2)∥(1,2)∥=(1,2)√12+22=(1,2)√5=(1/√5,2/√5).

Step-by-step explanation:

Answer:

10%

Step-by-step explanation: there are 5 numbers from 5 to 50 ending in 9. 5 is 10% of 50. Hope this helped

The money account is doubled at an interest rate of 5.2 % compunded quarterly, that is, under the model of compound interest in a time period of about 3.5 years.

The compound interest takes into account the change of money deposited in time in contrast with the simple interest, which only takes the initial amount of money into account. Please notice that four quarters equals a year.

The compound interest formula is described below:

C = C' · (1 + r/100)ⁿ     (1)

Where:

If we know that C = 2 · C' and r = 5.2, then the doubling time is:

n = /㏒ C/C'/㏒ (1 + r/100)

n = ㏒ 2/㏒ 1.052

n ≈ 13.674

The money account is doubled at an interest rate of 5.2 % compunded quarterly, that is, under the model of compound interest in a time period of about 3.5 years. [tex]\blacksquare[/tex]

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Answer:

answer is equal to 73 degrees

Option C is correct.

1 : 3 and 6 : 3                                              1 : 3 and 3 : 6

1 : 3 and 2 : 1                                               1 : 3 and 1 : 2

not proportional                                       not proportional

3 : 1 and 9 : 3                                               3 : 1 and 3 : 9

3 : 1 and 3 : 1                                                3 : 1 and 1 : 3

proportional                                               not proportional

Answer:

Step-by-step explanation:

ac = adjacent

ab = hypotenuse

cb = opposite

= cb/ab

= 9/41

HAVE A NICE DAY

STAY SAFE

if this is the answer then pls give BRAINLIST

Answer:

Step-by-step explanation:

Answer:

Absolute value is the magnitude of a real number regardless of sign. When you take the absolute value of something, it is the positive value of the number being evaluated

|21| = 21

also...

|−21| = 21

Step-by-step explanation:

Hope This Helps

Have A Great Day

~Zero~

Answer:

b

Step-by-step explanation:

it has to add the two cost of the flowers and it has to be less than or equal to 50 dollars

Answer:

When used as a diacritic mark, the term dot is usually reserved for the interpunct, or to the glyphs "combining dot above" and "combining dot below" which may be combined with some letters of the extended Latin alphabets in use in Central European languages and Vietnamese

Answer:

hope it can help you

brainliest pls

Step-by-step explanation:

the volume of a figure bases always on a calculation that multiplies 3 dimensions.

while a surface area bases always on a calculation that multiplies 2 dimensions.

since the figures are similar, that means that all dimensions or side lengths of one figure correlate to the corresponding dimensions or side lengths of the other figure via the same scale factor f.

and that means that

large side length = small side length × f.

and that means that f has to be multiplied in 3 times for the volume and 2 times for the surface area (once for every dimension).

so,

large volume = small volume × f × f × f =

= small volume × f³

1536 = 648 × f³

f³ = 1536/648 = 64/27

f = 4/3

and

large surface = small surface × f×f =

= small surface × f²

small surface = large surface / f² = 864 / 16/9 =

= 864 × 9/16 = 54 × 9 = 486 m²

Answer:

42 feet

Step-by-step explanation:

1 inch = 6 feet

  then multiply both sides by 7

7 inches = 42 feet

Answer:

Step-by-step explanation:

Here,

→We get 1620 products every 30 seconds

→We get 1620/30=54 products in every 1 second

→We get 54×60=3240 products in every 60 seconds(1 minute)

As we have

60seconds=1min

60 minutes=60 seconds ×60

Now,

→We get 3240×60=194400 products in every 60 minutes

Also,

→We get 450 products every 7 seconds

→We get 450/7=64.28 products in every 1 second

→We get 64.28×60 products in every 60 seconds

→We get 3856.8×60=231408 products in 60 minutes

It is found that the time it takes for the projectile to hit the ground would be after 20 seconds.

The projectile would hit the ground when its height h(t), is equal to zero.

The given function that models its height is given by:

[tex]h(t) = -4.9t^2 + 98t.[/tex]

where h is the height in meters and t is the elapsed time in seconds.

Then,

h(t) = 0

[tex]-4.9t^2 + 98t = 0\\-4.9t(t - 20) = 0\\\\t - 20 = 0[/tex]

t = 20

Thus, The projectile hits the ground after 20 seconds.

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Answer:

6

Step-by-step explanation:

There is no perfect square root of 40 but when calculated it would be 6.33 which rounds down to 6.

Answer:

The answer is x=3 and the extraneous is x=-1

Step-by-step explanation:

56000 is the actual park in square yards.

If Faleye Consulting’s WACC is 10% and both “projects” can be repeated indefinitely, the system that should be chosen is System A, and its EAA is $2,866.91.

The EAA of a project is the Equivalent Annual Annuity.  The EAA can be determined using the following formula.

EAA = r x NPV1 - (1 + r)-n

Where the EAA = Equivalent Annual Annuity

r = interest rate per period

n = project duration

NPV = Net present value of project

We can also compute the EAA by using an online finance calculator as follows:

                                                System A        System B

After-tax cost                           $19,000         $13,000

After-tax cash flows                 $6,000           $6,000

Equipment duration                 6 years           3 years

WACC = 10%

Annuity factor                            4.355              2.487

Present value of cash flows $26,130          $14,922 ($6,000 x 2.487)

NPV                                          $7,130           $1,922 ($14,922 - $13,000)

EAA (an online calculator)    $2,866.91        $800.966

Thus, using the EAA rule, the computer system that should be chosen is System A because it has a higher EAA than System B.

Learn more about the equivalent annual annuity at https://brainly.com/question/20566589