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3 years ago

Express the inequality using interval notation.−4≤x≤0

Mathematics

1 answer:

Aleonysh [2.5K]3 years ago

4 0

Answer:

[-4,0]

Step-by-step explanation:

we use closed bracket to show " it includes" and -4 and 0 are included in the solution set

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The ability of lizards to recognize their predators via tongue flicks can often mean life or death for lizards. Seventeen juveni

Sloan [31]

Answer:

Confidence level is (380.7133, 533.2867)

Step-by-step explanation:

Responses in number of tongue flicks per 20 minutes of lizards, are: 727,217, 268, 438, 625, 319, 200, 591, 574, 727, 693, 336, 302, 761, 268, 353, 370

n = 17

Mean (μ) is:

$\mu=\frac{{\Sigma}x}{n} = \frac{727+217+ 268+ 438+ 625+ 319+ 200+ 591+ 574+ 727+ 693+ 336+ 302+ 761+ 268+ 353+ 370}{17} = 439.3529$

Standard deviation (σ) is:

$\sigma=\sqrt{\frac{\Sigma(x-\mu^2)}{n} } =\sqrt{\frac{(727-457)^2+(217-457)^2+...+(370-457)^2}{17} } =191.2$

The confidence interval (c) = 90% = 0.9

$\alpha=1-0.9=0.1\\\frac{\alpha }{2} = 0.05\\Z_{\frac{\alpha }{2} }=1.64$

Margin of error (e) = $=Z_{\frac{\alpha}{2} }*\frac{\sigma}{\sqrt{n} }=1.64*\frac{191.2}{\sqrt{17} }=76.2867$

Confidence level = μ ± e = 457 ± 76.2867 = (380.7133, 533.2867)

8 0

4 years ago

Find c to complete the perfect trinomial x2 + 4x + c

sladkih [1.3K]

Answer:

Step-by-step explanation:

I assume that is supposed to be x squared. A perfect trinomial is the product of a perfect square, (x times a number) squared. With these trinomials, you can look at them as: ax squared times bx + c. When a is 1, the fastest way to get c to make a perfect square is to divide b by 2. In this case, it's 4/2 = 2. The last step is to square that number. 2 squared = 4.

8 0

3 years ago

Use decimals to answer the question what is 6% of 225

ElenaW [278]

Answer:

13.5

Step-by-step explanation:

(Are you meaning this as the answer is a decimal?)

3/50 * 225/1

Cross-cancel 50 and 225 by cancelling out 25.

3/2 * 9/1

Rewrite this so it is a single fraction.

(3 * 9)/2

Multiply 3 by 9 to get 27.

27/2

Divide 27 by 2 to get 13.5.

13.5

6% of 225 is 13.5.

8 0

3 years ago

Read 2 more answers

a line with a slope of 0 passes through the point (6, 4). what is its equation in slope intercept form

anygoal [31]

Answer:

y = 4

Step-by-step explanation:

A line with a slope of zero is a horizontal line parallel to the x- axis with equation

y = c ( c is the value of the y- coordinates the line passes through )

the line passes through (6, 4 ) with y- coordinate 4 , then

y = 4 ← equation of line

8 0

2 years ago

Solve for x in the equation 3 x squared minus 18 x + 5 = 47.

Lana71 [14]

Answer:

first option

Step-by-step explanation:

3x² - 18x + 5 = 47 ( subtract 5 from both sides )

3x² - 18x = 42 ( divide through by 3 )

x² - 6x = 14

Using the method of completing the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 3)x + 9 = 14 + 9

(x - 3)² = 23 ( take square root of both sides )

x - 3 = ± $\sqrt{23}$ ( add 3 to both sides )

x = 3 ± $\sqrt{23}$

6 0

3 years ago