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3 years ago

If a^b=x, what is a^(b+2)?

1 answer:

3 0

$\bf \boxed{a^b=x}\implies \sqrt[b]{a^b}=\sqrt[b]{x}\implies \boxed{a=\sqrt[b]{x}}\\\\
-------------------------------\\\\
a^{b+2}\implies a^b\cdot a^2\implies \boxed{x}\cdot \left( \boxed{\sqrt[b]{x}} \right)^2\implies x\cdot \sqrt[b]{x^2}\implies x\sqrt[b]{x^2}$

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Write the equation of the line in slope-intercept that has passes through the points (2,-5) and (8, 13).

const2013 [10]

Answer:

The equation of the straight line in Slope- intercept form

y = 3 x - 11

Step-by-step explanation:

<u><em>Explanation:-</em></u>

Given points are (2,-5) and (8, 13)

The Slope of the line

$m = \frac{y_{2} -y_{1} }{x_{2} -x_{1} } = \frac{13-(-5)}{8-2} = \frac{18}{6} =3$

Equation of the line having slope 'm' and given point

$y - y_{1} = m (x - x_{1} )$

(x₁ , y₁) = ( 2, -5 )

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

y + 5 = 3x - 6

The equation of the straight line in slope intercept form

y = m x + c

y = 3 x - 6-5

y = 3 x - 11

<u><em>Final answer:</em></u>-

The equation of the straight line in Slope- intercept form

y = 3 x - 11

8 0

3 years ago

The graph of y = f(x) is shown below. According to the graph, what is f(-2)

iris [78.8K]

Answer:

x = 4

Step-by-step explanation:

Find 8 on the y-axis. Draw a horizontal line through y =8. Determine the x value for which the graph intersects this horizontal line y = 8. It is x = 4

4 0

2 years ago

A married man filing serpartly with a taxable income of 167,000

erastovalidia [21]

Sorry I don't see a question here but .

Knowing your income tax rate can help you calculate your tax liability for unexpected income, retirement planning or investment income. This calculator helps you estimate your average tax rate, your tax bracket, and your marginal tax rate for the current tax year.

4 0

2 years ago

Read 2 more answers

your family is driving from cincinnati to st louis. the graph relates your distance from st.louis d in miles and travel time h (

rewona [7]

The solution is about a distance-time graph. The interpretation of the graph is that it took the family 6 hours to travel a distance of 360 miles. Note that the distance is plotted on y-axis and time on the x-axis.

<h3>What is a distance-time graph?</h3>

A distance time graph is a simple graph that shows the relationship between the time travelled the distance covered while doing do.

The slope-intercept form is

y= mx+b−⋯(1)

The y-intercept is 360

⇒b = 360; and m = −60

Substituting the value of m = −60

and b = 360

in (1) above,

⇒y = −60x +360

The x-intercept is

y = 0,

⇒0= −60x+360

hence, x=6

The y-intercept is

x=0

⇒y=−60(0)+360

⇒y=360

In conclusion, the x - intercept is the time in hours between Cincinnati and St. Loui: and

The y - intercept is the distance between Cincinnati and St. Louis.

Learn more about distance-time graphs at:
brainly.com/question/13877898
#SPJ1

6 0

1 year ago

In October of 2012, Apple introduced a much smaller variant of the Apple iPad, known at the iPad Mini. Weighing less than 11 oun

sveticcg [70]

Answer:

a. $f_X(x) = \dfrac{1}{3.5}8.5$

b. the probability that the battery life for an iPad Mini will be 10 hours or less is 0.4286 which is about 42.86%

c. the probability that the battery life for an iPad Mini will be at least 11 hours is 0.2857 which is about 28.57 %

d. the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours is 0.5714 which is about 57.14%

e. 86 should have a battery life of at least 9 hours

Step-by-step explanation:

From the given information;

Let X represent the continuous random variable with uniform distribution U (A, B) . Therefore the probability density function can now be determined as :

$f_X(x) = \dfrac{1}{B-A}A$

where A and B are the two parameters of the uniform distribution

From the question;

Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours

So; Let A = 8,5 and B = 12

Therefore; the mathematical expression for the probability density function of battery life is :

$f_X(x) = \dfrac{1}{12-8.5}8.5$

$f_X(x) = \dfrac{1}{3.5}8.5$

b. What is the probability that the battery life for an iPad Mini will be 10 hours or less (to 4 decimals)?

The probability that the battery life for an iPad Mini will be 10 hours or less can be calculated as:

F(x) = P(X ≤x)

$F(x) = \dfrac{x-A}{B-A}$

$F(10) = \dfrac{10-8.5}{12-8.5}$

F(10) = 0.4286

the probability that the battery life for an iPad Mini will be 10 hours or less is 0.4286 which is about 42.86%

c. What is the probability that the battery life for an iPad Mini will be at least 11 hours (to 4 decimals)?

The battery life for an iPad Mini will be at least 11 hours is calculated as follows:

$P(X\geq11) = \int\limits^{12}_{11} {\dfrac{1}{3.5}} \, dx$

$P(X\geq11) = {\dfrac{1}{3.5}} (x)^{12}_{11}$

$P(X\geq11) = {\dfrac{1}{3.5}} (12-11)$

$P(X\geq11) = {\dfrac{1}{3.5}} (1)$

$P(X\geq11) = 0.2857$

the probability that the battery life for an iPad Mini will be at least 11 hours is 0.2857 which is about 28.57 %

d. What is the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours (to 4 decimals)?

$P(9.5 \leq X\leq11.5) =\int\limits^{11.5}_{9.5} {\dfrac{1}{3.5}} \, dx$

$P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} \, (x)^{11.5}_{9.5}$

$P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} (11.5-9.5)$

$P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} (2)$

$P(9.5 \leq X\leq11.5) =0.2857* (2)$

$P(9.5 \leq X\leq11.5) =0.5714$

Hence; the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours is 0.5714 which is about 57.14%

e. In a shipment of 100 iPad Minis, how many should have a battery life of at least 9 hours (to nearest whole value)?

The probability that battery life of at least 9 hours is calculated as:

$P(X \geq 9) = \int\limits^{12}_{9} {\dfrac{1}{3.5}} \, dx$

$P(X \geq 9) = {\dfrac{1}{3.5}}(x)^{12}_{9}$

$P(X \geq 9) = {\dfrac{1}{3.5}}(12-9)$

$P(X \geq 9) = {\dfrac{1}{3.5}}(3)$

$P(X \geq 9) = 0.2857*}(3)$

$P(X \geq 9) = 0.8571$

NOW; The Number of iPad that should have a battery life of at least 9 hours is calculated as:

n = 100(0.8571)

n = 85.71

n ≅ 86

Thus , 86 should have a battery life of at least 9 hours

3 0

3 years ago