What is the solution to this linear equation? 4b + 6 = 2

PLS I NEED HELP BRAINLIEST IS UP FOR GRABS

Gwar [14]

Answer:

(a) x > 4 (b) y < -2

Step-by-step explanation:

Domain is referring to the x-values while the range is referring to the y-values.

Since the function (the line) has a circle at the point (4, -2), the function will be exclusive at that coordinate.

The line goes to infinity for the x-values from 4, so you write x > 4 or ∞ > x > 4.

Similarly, the line goes to infinity for the y-values from -2, so you write y < -2 or -∞ < y < -2.

7 0

3 years ago

A theatre has 1,450 seats. If 42% of these are balcony seats. How many balcony seats does the theatre have?

kirill115 [55]

Answer:

609

Step-by-step explanation:

All you must do is multiply 1450 by 0.42. That would give you the total.

5 0

2 years ago

Read 2 more answers

Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true

IgorLugansk [536]

Answer:

(a) 95% confidence interval for the true average porosity of a certain seam is [4.52 , 5.18].

(b) 98% confidence interval for the true average porosity of a another seam is [4.12 , 4.99].

Step-by-step explanation:

We are given that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation 0.75.

(a) Also, the average porosity for 20 specimens from the seam was 4.85.

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 average porosity = 4.85

$\sigma$ = population standard deviation = 0.75

n = sample of specimens = 20

$\mu$ = true average porosity

Here for constructing 95% confidence interval we have used One-sample z test statistics as we know about population standard deviation.

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

= [ $4.85-1.96 \times {\frac{0.75}{\sqrt{20} } }$ , $4.85+1.96 \times {\frac{0.75}{\sqrt{20} } }$ ]

= [4.52 , 5.18]

Therefore, 95% confidence interval for the true average porosity of a certain seam is [4.52 , 5.18].

(b) Now, there is another seam based on 16 specimens with a sample average porosity of 4.56.

The pivotal quantity for 98% 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 average porosity = 4.56

$\sigma$ = population standard deviation = 0.75

n = sample of specimens = 16

$\mu$ = true average porosity

Here for constructing 98% confidence interval we have used One-sample z test statistics as we know about population standard deviation.

So, 98% confidence interval for the true mean, $\mu$ is ;

P(-2.3263 < N(0,1) < 2.3263) = 0.98 {As the critical value of z at 1% level

of significance are -2.3263 & 2.3263}

P(-2.3263 < $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < 2.3263) = 0.98

P( $-2.3263 \times {\frac{\sigma}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $2.3263$ ) = 0.98

P( $\bar X-2.3263 \times {\frac{\sigma}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.3263 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.98

98% confidence interval for $\mu$ = [ $\bar X-2.3263 \times {\frac{\sigma}{\sqrt{n} } }$ , $\bar X+2.3263 \times {\frac{\sigma}{\sqrt{n} } }$ ]

= [ $4.56-2.3263 \times {\frac{0.75}{\sqrt{16} } }$ , $4.56+2.3263 \times {\frac{0.75}{\sqrt{16} } }$ ]

= [4.12 , 4.99]

Therefore, 98% confidence interval for the true average porosity of a another seam is [4.12 , 4.99].

7 0

3 years ago

What value makes 3(x-1) +2 = 6x-2

Vikentia [17]

Answer:

x = 1/3

Step-by-step explanation:

3x-1=6x-2

3x-1+1=6x-2+1

3x=6x-1

3x-6x=6x-1-6x

-3x=-1

x=1/3

6 0

3 years ago

In a random sample of 74 women at a company, the mean salary is $39,902 with a standard deviation of $3270 in a random sample of

ValentinkaMS [17]

The correct answer is the first choice, ($1818.30, $5077.70.)

To find this, we first find the z-score based on the confidence level:
Convert 95% to a decimal: 95%=95/100 = 0.95
Subtract from 1: 1-0.95 = 0.05
Divide by 2: 0.05/2 = 0.025
Subtract from 1: 1-0.025 = 0.975

Using a z-table (http://www.z-table.com) we see that this value is associated with a z-score of 1.96.

Next, we identify
$\overline{x_1}=39902; \overline{x_2}=36454; n_1=74; n_2=40; \sigma_1=3270; \sigma_2=4677$

Next we find
$(\overline{x_1}-\overline{x_2})=(39902-36454) = 3448$

Next we find
$\sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}
\\
\\=\sqrt{\frac{3270^2}{74}+\frac{4677^2}{40}}=\sqrt{\frac{10692900}{74}+\frac{21874329}{40}}
\\
\\=831.479$

Next, we multiply this value by z:
1.96(831.479) = 1629.70

The confidence interval is given by
$3448\pm1629.70
\\
\\=(3448-1629.70, 3448+1629.70)
\\
\\=(1818.30, 5077.70)$

5 0

3 years ago

What is the solution to this linear equation? 4b + 6 = 2 - b + 4