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3 years ago

Which of the following could be the solution set to 8x² - 2x = 1?

Mathematics

2 answers:

Elanso [62]3 years ago

7 0

The answer is B: (-1/4, 1/2)

Ray Of Light [21]3 years ago

4 0

Answer:

$\text{The solution set is }\{\frac{-1}{4}, \frac{1}{2}\}$

Step-by-step explanation:

Given the equation

$8x^2-2x=1$

we have to find the solution of above equation.

Expression: $8x^2-2x=1$

$8x^2-2x-1=0$

$8x^2-4x+2x-1=0$

$4x(2x-1)+1(2x-1)=0$

$(4x+1)(2x-1)=0$

$x=\frac{-1}{4}, \frac{1}{2}$

$\text{The solution set is }\{\frac{-1}{4}, \frac{1}{2}\}$

Option B is correct

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If a student randomly guesses at 20 multiple-choice questions, find the probability that the student gets exactly four correct.

ad-work [718]

Answer:

Probability = 0.190

Step-by-step explanation:

Given:

Number of questions, 'n' = 20

Each question has four choices.

Let event of choosing correct answer be success and its probability be represented by 'p'.

Therefore, event of choosing wrong answer is failure and its probability be represented by 'q'.

Now, probability of success is choosing one correct answer out of 4 options. So, $p=\frac{1}{4}=0.25$

Now, 'p' and 'q' are complements of each other. Therefore,

$q=1-p=1-0.25=0.75$

Now, we need 4 successes. Therefore, $x=4$

Using Bernoulli's theorem to find 'x' successes from 'n' questions, we get:

$P(x)=_{x}^{n}\textrm{C}p^xq^{n-x}$

Plug in 4 for 'x', 20 for 'n', 0.25 for 'p' and 0.75 for 'q'. Solve.

$P(4)=_{4}^{20}\textrm{C}(0.25)^4(0.75)^{20-4}\\P(4)=_{4}^{20}\textrm{C}(0.25)^4(0.75)^{16}\\P(4)=4845\times (0.25)^4\times (0.65)^{16}\\\\P(4)=0.1896\approx0.190$

Therefore, the probability of getting 4 correct answers out of 20 questions is 0.190.

6 0

2 years ago

The tax rate as a percent, r, charged on an item can be determined using the formula – 1 = r, where c is the final cost of the i

melisa1 [442]

The correct answer is:

$43.20

Explanation:

The formula we have is

c = p(1+r), where c is the total cost, p is the price of the item before tax, and r is the tax rate written as a decimal. This formula comes from the fact that adding a percent tax to the cost of an item takes 100% of the price and adds r% to it; this is why we multiply the price by (1+r).

Since our tax rate is 8%, r = 8% = 8/100 = 0.08. The price of the item is $40. Using this information, we have:

c = 40(1.08) = $43.20

3 0

3 years ago

Read 2 more answers

5(p - 3) = 63 Who ever get this right Cash app 300 dollars to u

lesya [120]

Answer:

oh wait nevermind

8 0

3 years ago

Read 2 more answers

if Mr Green drives 100 miles in 2 hours. he continues to drive at the same speed if he doesn't stop how long will it take mr gre

Anton [14]

Answer:

8 hours

Step-by-step explanation:

1 - 50 miles

2 - 100 miles

3 - 150 miles

4 - 200 miles

5 - 250 miles

6 - 300 miles

7 - 350 miles

8 - 400 miles

and so on hope this helps

5 0

2 years ago

Gabby received change worth $2.10. She received 3 more dimes than nickels and 4 less quarters than nickels. How many of each kin

xz_007 [3.2K]

Answer:

Gabby received

7 nickels

10 dimes

3 quarters

Step-by-step explanation:

Let

x----> the number of dimes

y----> the number of nickels

z---> the number of quarters

Remember that

1 dime=$0.10

1 nickel=$0.05

1 quarter=$0.25

we know that

0.10x+0.05y+0.25z=2.10 ------> equation A

x=y+3-----> equation B

z=y-4 -----> equation C

substitute equation B and equation C in equation A and solve for y

0.10(y+3)+0.05y+0.25(y-4)=2.10

0.10y+0.30+0.05y+0.25y-1=2.10

0.40y=2.10-0.30+1

0.40y=2.80

y=7 nickels

Find the value of x

x=y+3 -----> x=7+3=10 dimes

Find the value of z

z=y-4 -----> z=7-4=3 quarters

therefore

Gabby received

7 nickels

10 dimes

3 quarters

6 0

3 years ago