I need help with number 8

Solve the following inequality: 3x + 9 ≤7x -11.

m_a_m_a [10]

Answer:

x ≥ -3

Step-by-step explanation:

Step 1 :

Pulling out like terms :

1.1 Pull out like factors :

-4x - 12 = -4 • (x + 3)

Equation at the end of step 1 :

Step 2 :

2.1 Divide both sides by -4

Remember to flip the inequality sign:

Solve Basic Inequality :

2.2 Subtract 3 from both sides

x ≥ -3

Inequality Plot :

2.3 Inequality plot for

-4.000 X - 12.000 ≥ 0

6 0

3 years ago

Read 2 more answers

During his tennis career in singles play, John won 4 fewer tournament A titles than tournament B titles and 2 more tournament C

Dafna11 [192]

A-4=B
2+C=B
A+B+C=13

A=b+4
C=B-2
Plug in to equation 3
(B+4)+B+(B-2)=13
Rearrange
B=11/3
A=(11/3)+4= 23/3
C=(11/4)-2= 3/4

7 0

3 years ago

From a random sample of size 18, a researcher states that (11.1, 15.7) inches is a 90% confidence interval for mu, the mean leng

alexandr402 [8]

Complete Question

From a random sample of size 18, a researcher states that (11.1, 15.7) inches is a 90% confidence interval for mu, the mean length of bass caught in a small lake. A normal distribution was assumed. Using the 90% confidence interval obtain:

a. A point estimate of $\mu$ and its 90% margin of error.

b. A 95% confidence interval for $\mu$ .

Answer:

a

$\= x = 13.4$ . $E = 2.3$

b

$10.7 < \mu < 16.1$

Step-by-step explanation:

From the question we are told that

The sample size is n = 18

The 90% confidence interval is (11.1, 15.7)

Generally the point estimate of $\mu$ is mathematically evaluated as

$\= x = \frac{11.1 + 15.7 }{2}$

=> $\= x = 13.4$

Generally the margin of error is mathematically evaluated as

$E = \frac{15.7 - 11.1}{2 }$

=> $E = 2.3$

From the question we are told the confidence level is 90% , hence the level of significance is

$\alpha = (100 - 90 ) \%$

=> $\alpha = 0.10$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 1.645$

Generally the equation for the lower limit of the confidence interval is

$\= x - Z_{\frac{\alpha }{2} } * \frac{s}{\sqrt{18} } = 11.1$

=> $13.4 - 0.3877 s = 11.1$

=> $s = 5.932$

From the question we are told the confidence level is 95% , hence the level of significance is

$\alpha = (100 - 95 ) \%$

=> $\alpha = 0.05$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

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

Generally the margin of error is mathematically represented as

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

=> $E = 1.96 * \frac{5.932}{\sqrt{18} }$

=> $E = 2.7$

Generally 95% confidence interval is mathematically represented as

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

=> $13.4 - 2.7 < \mu < 13.4 + 2.7$

=> $10.7 < \mu < 16.1$

3 0

3 years ago

Whats 126/399 in its simplest form

marusya05 [52]

A common factor of both 126 and 399 is 3 so we can divide both numbers by 3.

126 / 3 = 42
399 / 3 = 133

A common factor for both 42 and 133 is 7 so we can divide both numbers by 7.

42 / 7 = 6
133 / 7 = 19

19 is a prime number so we can't reduce it anymore, therefore 126/399 in its simplest form is 6/19

4 0

3 years ago

Suppose we choose7 objects without replacement from 9 objects

stiks02 [169]

Answer:

Step-by-step explanation:

We have 9 choices for Choosing the first object

8 choices for Choosing the 2nd object

.

3 choices for Choosing the seventh object

Therefore if we want to choose7 objects without replacement from 9 objects we have : 9×8×7×6×5×4×3 = 181 440

Also ,we can calculate it this way :

9P7 = 181 440

7 0

2 years ago