This is a tricky one<br>n ÷ 9 = 14

What is the value of n when (9)^2n-1 = (27)^n+2

Elis [28]

$9^{2n-1} = 27^{n+2} \\ ( {3}^{2} ) ^{2n - 1} = ( {3}^{3} )^{ n + 2} \\ {3}^{4n - 2} = {3}^{3n + 6} \\ 4n - 2 = 3n + 6 \\ 4n - 3n = 6 + 2 \\ n = 8$

Answer: n=8

5 0

3 years ago

Among the thirty largest U.S. cities, the mean one-way commute time to work is 25.8 minutes. The longest one-way travel time is

Dafna11 [192]

Answer:

A. 0.9015

B. 0.1658

C. 0.0132

Step-by-step explanation:

Given

Mean, μ of commuting time in New York is 39.7 minutes

Standard Deviation, σ = 7.5 minutes

Let x represent the commute time

For Normal Distribution, z = (x - μ) /σ

A. x is less than 30 minutes

P(x<30) = P(x - μ < 30 - μ)

P(x<30) = P((x - μ)/ σ < (30 - μ)/ σ)

P(x<30) = P(z < (30 - μ)/ σ)

P(x<30) = P(z < (30 - 39.7) / 7.5)

P(x<30) = P(z < (-9.7/7.5)

P(x<30) = P(z < -1.29)

P(x<30) = P(z > 1.29)

P(x<30) = 0.9015 -------- From z table

B. x is between 30 and 35

P(30>x<35) = P(30 -μ > x - μ < 35 - μ)

P(30>x<35) = P((30 -μ)/σ < (x - μ)/σ < (35 - μ) / σ)

P(30>x<35) = P((30 -μ)/σ < z < (35 - μ) / σ)

P(30>x<35) = P((30 -39.7)/7.5 < z < (35 - 39.7) / 7.5)

P(30>x<35) = P(-9.7/7.5 < z < -4.7/7.5)

P(30>x<35) = P(-1.29 < z < -0.63)

There are two points on the same side here; we calculate both probabilities and subtract to give

P(30>x<35) = P(-1.29 < z < 0) - P(0 < z < -0.63)

P(30>x<35) = P(0 < z < 1.29) - P(0 < z < 0.63)

P(30 > x < 35) = 0.9015 - 0.7357

P(30 > x < 35) = 0.1658

C. x is between 30 and 50

P(30>x<50) = P(30 -μ > x - μ < 50 - μ)

P(30>x<50) = P((30 -μ)/σ < (x - μ)/σ < (50 - μ) / σ)

P(30>x<50) = P((30 -μ)/σ < z < (50 - μ) / σ)

P(30>x<50) = P((30 -39.7)/7.5 < z < (50 - 39.7) / 7.5)

P(30>x<50) = P(-9.7/7.5 < z < 10.3/7.5)

P(30>x<50) = P(-1.29 < z < 1.37)

There are two points on different sides here; calculate both probabilities and add to give

P(30>x<50) = P(-1.29 < z < 0) + P(0 < z < 1.37)

P(30>x<50) = -P(0 < z < 1.29) + P(0 < z < 1.37)

P(30 > x < 50) = -0.9015 + 0.9147

P(30 > x < 50) = 0.0132

8 0

3 years ago

A student modify the relationship in the table with the equation x=4y explain the students error write an equation that correctl

umka2103 [35]

The students error is that they flipped where the x and y should be. so instead of x=4y it should be y=4x. or, the students error is that they forget to make it a fraction. so, it could also be x=1/4y. an equation that models this relationship is y=4x or x=1/4y

5 0

2 years ago

Divide 0.23 by 1,000. (Do not round off)

Tom [10]

The answer is 0.00023 due to the decimal going to the left because of the 3 zeros in 1000

4 0

3 years ago

Read 2 more answers

A straight line has an x intercept -2 and passes through the point (-4,6) Find its equation

Illusion [34]

The x-intercept is the point where the line crosses the x-axis. That point has a y-coordinate of 0. The coordinates of the x-intercept are (-2, 0). You are also given point (-4, 6), so you have two points on the line.

You can use the two-point form of the equation of a line to find its equation.
The two points are $(x_1, y_1)$ and $(x_2, y_2)$

$y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1)$

$y - 0 = \dfrac{6 - 0}{-4 - (-2)}(x - (-2))$

$y = \dfrac{6}{-2}(x + 2)$

$y = -3(x + 2)$

$y = -3x - 6$

4 0

3 years ago

This is a tricky onen ÷ 9 = 14 ​

This is a tricky onen ÷ 9 = 14