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3 years ago

Sketch the graph of the inequality. 9. 7y − 2x + 3 < 17

Mathematics

1 answer:

ohaa [14]3 years ago

5 0

$7y-2x+3 < 17\ \ \ \ |-3\\\\7y-2x < 14\ \ \ \ |+2x\\\\7y < 2x+14\ \ \ \ |:7\\\\y < \dfrac{2}{7}x+2\\\\y=\dfrac{2}{7}x+2\\\\for\ x=0\to y=\dfrac{2}{7}(0)+2=2\to(0,\ 2)\\\\for\ x=-7\to y=\dfrac{2}{7}(-7)+2=0\to(-7,\ 0)$

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In a large lecture class, the professor announced that the scores on a recent exam were normally distributed with a range from 5

iVinArrow [24]

Answer:

The standard deviation of the scores on a recent exam is 6.

The sample size required is 25.

Step-by-step explanation:

Let X = scores of students on a recent exam.

It is provided that the random variable X is normally distributed.

According to the Empirical rule, 99.7% of the normal distribution is contained in the range, μ ± 3σ.

That is, P (μ - 3σ < X < μ + 3σ) = 0.997.

It is provided that the scores on a recent exam were normally distributed with a range from 51 to 87.

This implies that:

P (51 < X < 87) = 0.997

So,

μ - 3σ = 51...(i)

μ + 3σ = 87...(ii)

Subtract (i) and (ii) to compute the value of σ as follows:

μ - 3σ = 51

(-)μ + (-)3σ = (-)87

______________

-6σ = -36

σ = 6

Thus, the standard deviation of the scores on a recent exam is 6.

The (1 - α)% confidence interval for population mean is given by:

$CI=\bar x\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

The margin of error of this interval is:

$MOE = z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

Given:

MOE = 2

σ = 6

Confidence level = 90%

Compute the z-score for 90% confidence level as follows:

$z_{\alpha/2}=z_{0.10/2}=z_{0.05}=1.645$

*Use a z-table.

Compute the sample required as follows:

$MOE = z_{\alpha/2}\frac{\sigma}{\sqrt{n}}\\2=1.645\times \frac{6}{\sqrt{n}}\\n=(\frac{1.645\times 6}{2})^{2}\\n=24.354225\\n\approx 25$

Thus, the sample size required is 25.

4 0

3 years ago

PLZ HELP ME

poizon [28]

Answer:

Step-by-step explanation:

x for black fabric , y for green fabric

6x+4y≤ 60 ( the cost is no more than 60 dollars)

x≥3 , y≥ 4 (at least 3 yards of black fabric, at least 4 yards of green fabric,

x+y≥10 ( at least 10 yards of fabric overall)

27) : graph in the screen shot ,( blue picture is simplified one)

note : point lies in the solution:(4,7) , (5,6)

( where is 28)

3 0

3 years ago

Determine the equation of the circle graphed below

faltersainse [42]

Equation of the circle is (x - 6)² +(y-7)² = 4.

<h3>What is a Circle ?</h3>

A figure having round shape and all the points lie on the same plane is called a circle.

Equation of a circle can be formed using centre of the circle and radius of the circle.

(x-h)² +(y-k)² = r²

where (h,k) is the vertex and 'r' is the radius.

From the given graph the centre of the circle is at (6,7)

and radius of the circle is 2 units

(h,k) is (6,7)

and r= 2

Substituting all the values

The equation of the circle

(x - 6)² +(y-7)² = 2² = 4

Equation of the circle is (x - 6)² +(y-7)² = 4

To know more about Circle

brainly.com/question/11833983

#SPJ1

7 0

2 years ago

Evaluate the expression when x=48 and y=3 x/8-y

Vlad1618 [11]

Answer:

$9\frac{3}{5}$

Step-by-step explanation:

$\frac{x}{8-y}=\frac{48}{8-3}=\frac{48}{5}=9\frac{3}{5}$

4 0

2 years ago

Read 2 more answers

N76 [4]

Alicia would have to walk 42 yards, as north and south are opposite ways of eachother, so 30 - 72 = -42, and to get back to her starting point eould mean walking those 42 yards back.

6 0

2 years ago