3/2x-2=19 What does x equal?

(CO6) From a random sample of 68 businesses, it is found that the mean time that employees spend on personal issues each week is

satela [25.4K]

Answer:

(1) (4.82, 4.98)

(2) Large sample size

(3) Yes, the temperature is within the confidence interval of (37.40, 37.60)

(4) (15.083, 15.117)

Step-by-step explanation:

Confidence Interval (CI) = mean + or - (t×sd)/√n

(1) mean = 4.9, sd = 0.35, n = 68, degree of freedom = n-1 = 68 - 1 = 67

t-value corresponding to 67 degrees of freedom and 95% confidence level is 1.9958

CI = 4.9 + (1.9958×0.35)/√68 = 4.98

CI = 4.9 - (1.9958×0.35)/√68 = 4.82

CI is (4.82, 4.98)

(2) Error margin = (t-value × standard deviation)/√sample size

From the formula above, error margin varies inversely as the square root of the sample size. Since the relationship between the error margin and sample size is inverse, increase in one (sample size) will conversely lead to a decrease in the other (error margin)

(3) mean = 37.5, sd = 0.6, n= 100, degree of freedom = n-1 = 100-1 = 99

t-value corresponding to 99 degrees of freedom and 90% confidence level is 1.6602

CI = 37.5 + (1.6602×0.6)/√100 = 37.5 + 0.10 = 37.60

CI = 37.5 - (1.6602×0.6)/√100 = 37.5 - 0.10 = 37.40

37.53 is within the confidence interval (37.40, 37.60)

(4) mean = 15.10, sd =0.08, n = 104, degree of freedom = n-1 = 104-1 = 103

t-value corresponding to 103 degrees of freedom and 97% confidence interval is 2.2006

CI = 15.10 + (2.2006×0.08)/√104 = 15.10 + 0.017 = 15.117

CI = 15.10 - (2.2006×0.08)/√104 = 15.10 - 0.017 = 15.083

CI is (15.083, 15.117)

4 0

3 years ago

Find the vertex of the graph of the function.

lapo4ka [179]

Answer: The correct options are (1) (5,10), (2) (3,-3), (3) x = -1, (4) $y=(x+2)^2+3$ , (5) 21s and (6) 0, -1, and 5.

Explanation:

Te standard form of the parabola is,

$f(x)=a(x-h)^2+k$ .....(1)

Where, (h,k) is the vertex of the parabola.

(1)

The given equation is,

$f(x)=(x-5)^2+10$

Comparing this equation with equation (1),we get,

$h=5$ and $k=10$

Therefore, the vertex of the graph is (5,10) and the fourth option is correct.

(2)

The given equation is,

$f(x)=3x^2-18x+24$

$f(x)=3(x^2-6x)+24$

To make perfect square add $(\frac{b}{2a})^2$ , i.e., $9$ . Since there is factor 3 outside the parentheses, so subtract three times of 9.

$f(x)=3(x^2-6x+9)+24-3\times 9$

$f(x)=3(x-3)^2-3$

Comparing this equation with equation (1),we get,

$h=3$ and $k=-3$

Therefore, the vertex of the graph is (3,-3) and the fourth option is correct.

(3)

The given equation is

$f(x)=4x^2+8x+7$

$f(x)=4(x^2+2x)+7$

To make perfect square add $(\frac{b}{2a})^2$ , i.e., $1$ . Since there is factor 4 outside the parentheses, so subtract three times of 1.

$f(x)=4(x^2+2x+1)+7-4$

$f(x)=4(x+1)^2+3$

Comparing this equation with equation (1),we get,

$h=-1$ and $k=3$

The vertex of the equation is (-1,3) so the axis is x=-1 and the correct option is 2.

(4)

The given equation is,

$y=x^2+4x+7$

To make perfect square add $(\frac{b}{2a})^2$ , i.e., $2^2$ .

$f(x)=x^2+4x+4+7-4$

$f(x)=(x+2)^2+3$

Therefore, the correct option is 4.

(5)

The given equation is,

$h=-16t^2+672t$

It can be written as,

$h=-16(t^2-42t)$

It is a downward parabola. so the maximum height of the function is on its vertex.

The x coordinate of the vertex is,

$x=\frac{b}{2a}$

$x=\frac{42}{2}$

$x=21$

Therefore, after 21 seconds the projectile reach its maximum height and the correct option is first.

(6)

The given equation is,

$f(x)=3x^3-12x^2-15x$

$f(x)=3x(x^2-4x-5)$

Use factoring method to find the factors of the equation.

$f(x)=3x(x^2-5x+x-5)$

$f(x)=3x(x(x-5)+1(x-5))$

$f(x)=3x(x-5)(x+1)$

Equate each factor equal to 0.

$x=0,-1,5$

Therefore, the zeros of the given equation is 0, -1, 5 and the correct option is 2.

3 0

3 years ago

If f(x)= 3x^2 + 3x^1/2 +3x what is the value of f(-9)

Dahasolnce [82]

Answer:

216 + 9i

Step-by-step explanation:

Given: f(x) = 3x² + 3 $x^{1/2}$ + 3x

When x = -9, f(x) equals to;

3(-9)² + 3(-9 $)^{1/2}$ + 3(-9)

243 + 3(3i) - 27

243 + 9i - 27

216 + 9i

4 0

3 years ago

Dane goes to a fast food restaurant and orders some tacos t and burritos b. write a story that matches the system of equation's

r-ruslan [8.4K]

Ouch becuase ouctastic

8 0

3 years ago

Simplifiy the given epression<br> (-3.2)^0

siniylev [52]

Answer:

(-3.2)^0 = 1

Step-by-step explanation:

Anything to the power of 0 equals 1.

6 0

3 years ago

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