All categories

3 years ago

Solve 7x + 2 < 9x - 4

Mathematics

1 answer:

Alexus [3.1K]3 years ago

5 0

Answer:

$\boxed{\bold{x>3}}$

Step By Step Explanation:

Subtract 2 From Both Sides

$\bold{7x+2-2$

Simplify

$\bold{7x$

Subtract 9x From Both Sides

$\bold{7x-9x$

Simplify

$\bold{-2x$

Multiply Both Sides By -1 (Reverse Inequality)

$\bold{\left(-2x\right)\left(-1\right)>\left(-6\right)\left(-1\right)}$

Simplify

$\bold{2x>6}$

Divide Both Sides By 2

$\bold{\frac{2x}{2}>\frac{6}{2}}$

Simplify

$\bold{x>3}$

- Mordancy

You might be interested in

Can y’all help me on question nine?!

Fudgin [204]

Answer:

Step-by-step explanation:

x=2

x³+7x+2

2³+14+2

8+14+2

5 0

3 years ago

The National Center for Education Statistics surveyed a random sample of 4400 college graduates about the lengths of time requir

Paha777 [63]

Answer:

95% confidence interval for the mean time required to earn a bachelor’s degree by all college students is [5.10 years , 5.20 years].

Step-by-step explanation:

We are given that the National Center for Education Statistics surveyed a random sample of 4400 college graduates about the lengths of time required to earn their bachelor’s degrees. The mean was 5.15 years and the standard deviation was 1.68 years respectively.

Firstly, the pivotal quantity for 95% confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean time = 5.15 years

$\sigma$ = sample standard deviation = 1.68 years

n = sample of college graduates = 4400

$\mu$ = population mean time

Here for constructing 95% confidence interval we have used One-sample z test statistics although we are given sample standard deviation because the sample size is very large so at large sample values t distribution also follows normal.

So, 95% confidence interval for the population mean, $\mu$ is ;

P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5%

level of significance are -1.96 & 1.96}

P(-1.96 < $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < 1.96) = 0.95

P( $-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ < $\mu$ < $\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.95

95% confidence interval for $\mu$ = [ $\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ , $\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ]

= [ $5.15-1.96 \times {\frac{1.68}{\sqrt{4400} } }$ , $5.15+1.96 \times {\frac{1.68}{\sqrt{4400} } }$ ]

= [5.10 , 5.20]

Therefore, 95% confidence interval for the mean time required to earn a bachelor’s degree by all college students is [5.10 years , 5.20 years].

8 0

3 years ago

Evaluate 3-5 using a number line.

Alekssandra [29.7K]

Step-by-step explanation:

= 3 - 5

= -2

line in the picture

4 0

3 years ago

ZABC and ZDEF are complementary angles.

Marat540 [252]

Answer:

x = 36

Step-by-step explanation:

Complementary angles add to 90 degrees

54+x = 90

x = 90-54

x = 36

4 0

2 years ago

Read 2 more answers

(x+6)(x-2)(x-1)=60 write a polynomial

enot [183]

For this case what you should do is:
1) Multiplication of terms within parentheses correctly.
2) Rewrite the expression respecting power properties.
3) Add or subtract terms of equal power.
Note: See attached image.
Answer:
x ^ 3 + 3x ^ 2 -16x - 48 = 0

8 0

3 years ago