9.6 x 10 to the third power please

Delta makes 12-volt car batteries. These batteries are known to be normally

blondinia [14]

Answer:

The probability that Delta car batteries last between three and four years

P(36≤X≤48) = 0.5188

The percentage of that Delta car batteries last between three and four years

P(3≤X≤4) = 52%

Step-by-step explanation:

Step(i):-

Given that the sample size n =12 -volt car batteries

Let 'X' be a Random variable in a normal distribution

Given that mean of the normal distribution = 45 months

Given that the Standard deviation of the normal distribution = 8months

Step(ii):-

Let X₁ = 3 years = 12 × 3 = 36 months

$Z_{1} = \frac{x_{1} -mean}{S.D} = \frac{36-45}{8} = -1.125$

Let X₂ = 4 years = 12 × 4 = 48 months

$Z_{2} = \frac{x_{2} -mean}{S.D} = \frac{48-45}{8} = 0.375$

Step(iii):-

The probability that Delta car batteries last between three and four years

P(36≤X≤48) = P(-1.125≤Z≤0.375)

= P(Z≤0.375) - P(Z≤-1.125)

= 0.5 +A(0.375) - (0.5-A(1.125)

= 0.5 + 0.1480 - (0.5 -0.3708)

= 0.1480 + 0.3708

= 0.5188

Final answer:-

The probability that Delta car batteries last between three and four years

P(36≤X≤48) = 0.5188

The percentage of that Delta car batteries last between three and four years

P(3≤X≤4) = 52%

5 0

3 years ago

A linear function has the table of values shown. The information in the table shows the number of tickets sold on opening night

MatroZZZ [7]

The equation that represents the linear function is y =32x

<h3>What is a linear function?</h3>

The question is an illustration of a linear function; a linear function is a function that has a constant rate/slope

A linear function is represented as:

$y=mx+c$

Where

m represents slope
c represents the y-intercept

The slope is calculated as:

$m = \frac{y_2 -y_1}{x_2 -x_1}$

So, we have:

$m = \frac{576 - 64}{18-2}$

$m = \frac{512}{16}$

$m = 32$

The linear equation is then calculated as:

$y =m(x -x_1) + y_1$

So, we have:

$y =32(x -2) + 64$

$y =32x -64 + 64$

$y =32x$

Hence, the equation that represents the linear function is y =32x

Read more about linear functions at:

brainly.com/question/14323743

5 0

3 years ago

What addds to 14 and multiplies to 8

Grace [21]

5.4142 and 2.5858 are the numbers you need

7 0

3 years ago

Solve the equation -3 = -13 - 5x for x

Law Incorporation [45]

Answer:

x = -2

Step-by-step explanation:

-3 = -13 - 5x

-3 + 13 = -5x

10 = -5x

10 ÷ (-5) = x

-2 = x

6 0

3 years ago

Read 2 more answers

Determine which of the lines are parallel and which of the lines are perpendicular. Select all of the statements that are true.

slega [8]

Answers:

Line A is parallel to line D.

Line A is perpendicular to line C.

Line C is perpendicular to line D.

=====================================================

Explanation:

Let's use the slope formula to calculate the slope of the line through (-1,-17) and (3,11)

$(x_1,y_1) = (-1,-17) \text{ and } (x_2,y_2) = (3,11)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{11 - (-17)}{3 - (-1)}\\\\m = \frac{11 + 17}{3 + 1}\\\\m = \frac{28}{4}\\\\m = 7\\\\$

The slope of line A is 7

-------------

Now let's find the slope of line B.

$(x_1,y_1) = (0,4) \text{ and } (x_2,y_2) = (7,-5)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-5 - 4}{7 - 0}\\\\m = -\frac{9}{7}\\\\$

-------------

Now onto line C.

$(x_1,y_1) = (7,1) \text{ and } (x_2,y_2) = (0,2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{2 - 1}{0 - 7}\\\\m = \frac{1}{-7}\\\\m = -\frac{1}{7}\\\\$

-------------

Lastly we have line D.

$(x_1,y_1) = (-1,-6) \text{ and } (x_2,y_2) = (1,8)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{8 - (-6)}{1 - (-1)}\\\\m = \frac{8 + 6}{1 + 1}\\\\m = \frac{14}{2}\\\\m = 7\\\\$

------------------------------

Here's a summary of the slopes we found

$\begin{array}{|c|c|} \cline{1-2}\text{Line} & \text{Slope}\\\cline{1-2}\text{A} & 7\\\cline{1-2}\text{B} & -9/7\\\cline{1-2}\text{C} & -1/7\\\cline{1-2}\text{D} & 7\\\cline{1-2}\end{array}$

Recall that parallel lines have equal slopes, but different y intercepts. This fact makes Line A parallel to line D.

Lines A and C are perpendicular to one another, because the slopes 7 and -1/7 multiply to -1. In other words, -1/7 is the negative reciprocal of 7, and vice versa. These two lines form a 90 degree angle.

Lines C and D are perpendicular for the same reasoning as the previous paragraph.

Line B unfortunately is neither parallel nor perpendicular to any of the other lines mentioned.

You can use a graphing tool like Desmos or GeoGebra to verify these answers.

6 0

1 year ago