What is 15 1/2 minus 11 3/8?

zlopas [31]

Step-by-step explanation:

transform the parent graph of f(x) = ln x into f(x) = - ln (x - 4) by shifting the parent graph 4 units to the right and reflecting over the x-axis

(???, 0): 0 = - ln (x - 4)

$\frac{0}{-1} = \frac{-ln (x - 4)}{-1}$

0 = ln (x - 4)

$e^{0} = e^{ln (x - 4)}$

1 = x - 4

+4 +4

5 = x

(5, 0)

(???, 1): 1 = - ln (x - 4)

$\frac{0}{-1} = \frac{-ln (x - 4)}{-1}$

1 = ln (x - 4)

$e^{1} = e^{ln (x - 4)}$

e = x - 4

+4 +4

e + 4 = x

6.72 = x

(6.72, 1)

Domain: x - 4 > 0

+4 +4

x > 4

(4, ∞)

Vertical asymptotes: there are no vertical asymptotes for the parent function and the transformation did not alter that

No vertical asymptotes

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transform the parent graph of f(x) = 3ˣ into f(x) = - 3ˣ⁺⁵ by shifting the parent graph 5 units to the left and reflecting over the x-axis

Domain: there is no restriction on x so domain is all real number

(-∞, ∞)

Range: there is a horizontal asymptote for the parent graph of y = 0 with range of y > 0. the transformation is a reflection over the x-axis so the horizontal asymptote is the same (y = 0) but the range changed to y < 0.

(-∞, 0)

Y-intercept is when x = 0:

f(x) = - 3ˣ⁺⁵

= - 3⁰⁺⁵

= - 3⁵

= -243

Horizontal Asymptote: y = 0 (explanation above)

5 0

4 years ago

What is the equation of the line in point slope form given a slope of -3 and a point of (-2,-5)?

Lelu [443]

Answer:

y = -3x - 11

Step-by-step explanation:

Use the given slope and point in the point-slope equation. Solving this will give us the y-intercept equation.

Point-slope formula: y - y = m(x - x)

Plug in the slope and point

y - (-5) = -3(x - (-2))

Subtracting negatives will make them positive. Multiply out the -3 to what is in the parentheses.

y + 5 = -3x - 6

Subtract the 5 from both sides

y = -3x - 11

The equation of the line is y = -3x - 11

7 0

3 years ago

Solve for x in the equation x2 - 8x+41 - 0

Liula [17]

Answer:

x= 4+5i

Step-by-step explanation:

7 0

3 years ago

"A study of the amount of time it takes a mechanic to rebuild the transmission for a 2005 Chevrolet Cavalier shows that the mean

Arada [10]

Answer:

85.31% probability that their mean rebuild time exceeds 8.1 hours.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sample means with size n of at least 30 can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 8.4, \sigma = 1.8, n = 40, s = \frac{1.8}{\sqrt{40}} = 0.2846$

If 40 mechanics are randomly selected, find the probability that their mean rebuild time exceeds 8.1 hours.

This is 1 subtracted by the pvalue of Z when X = 8.1. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{8.1 - 8.4}{0.2846}$

$Z = -1.05$

$Z = -1.05$ has a pvalue of 0.1469

1 - 0.1469 = 0.8531

85.31% probability that their mean rebuild time exceeds 8.1 hours.

4 0

3 years ago

Learning Task 1: Identify similar and dissimilar fractions. On your note- book write S if the fractions are similar and D if dis

Ronch [10]

<h2>Complete Question: </h2>

Learning Task 1: Identify similar and dissimilar fractions. On your note- book write S if the fractions are similar and D if dissimilar.

1. $\frac{2}{3} $ and $ \frac{1}{3}$

2. $\frac{3}{4} $ and $ \frac{1}4}$

3. $\frac{4}{7} $ and $ \frac{7}{8}$

4. $\frac{2}{5} $ and $ \frac{5}{11}$

5. $\frac{7}{13} $ and $ \frac{7}{9}$

<h2>The answers:</h2>

1. $\frac{2}{3} $ and $ \frac{1}{3}$ - Similar (S)

2. $\frac{3}{4} $ and $ \frac{1}4}$ - Similar (S)

3. $\frac{4}{7} $ and $ \frac{7}{8}$ - Dissimilar (D)

4. $\frac{2}{5} $ and $ \frac{5}{11}$ - Dissimilar (D)

5. $\frac{7}{13} $ and $ \frac{7}{9}$ - Dissimilar (D)

Note:

Similar fractions have the same denominator. i.e. the bottom value of both fractions are the same.
Dissimilar fractions have different value as denominator, i.e. the bottom value of both fractions are not the same.

Thus:

1. $\frac{2}{3} $ and $ \frac{1}{3}$ - They have equal denominator. Both fractions are similar (S).

2. $\frac{3}{4} $ and $ \frac{1}4}$ - They have equal denominator. Both fractions are similar (S).

3. $\frac{4}{7} $ and $ \frac{7}{8}$ - They have equal denominator. Both fractions are dissimilar (D).

4. $\frac{2}{5} $ and $ \frac{5}{11}$ - They have equal denominator. Both fractions are dissimilar (D).

5. $\frac{7}{13} $ and $ \frac{7}{9}$ - They have equal denominator. Both fractions are dissimilar (D).

Therefore, the fractions in 1 and 2 are similar (S) while those in 3, 4, and 5 are dissimilar (D).

Learn more here:

brainly.com/question/22099172

7 0

3 years ago