*Ahem* HELP ME PLEASE! WILL GIVE BRAINLIEST

A clairinet case is shaped like a rectangular prisim the case is 8 inches tall 3 inches wide and has a volume of 312 cubic inche

diamong [38]

Answer:

13 inches

Step-by-step explanation:

A clarinet case is shaped like a rectangular prism the case is 8 inches tall 3 inches wide and has a volume of 312 cubic inches what is the length of the clarinet case

The volume of a rectangular prism = Length × Width × Height

Length of the rectangular prism = Volume/ Width × Height

= 312 in³/ 3 in × 8 in

= 312 in³/24 in²

= 13 in

Length = 13 inches

8 0

2 years ago

The lifetime of a battery in a certain application is normally distributed with mean μ = 16 hours and standard deviation σ = 2 h

DaniilM [7]

Answer:

Probability that a battery will last more than 19 hours is 0.0668.

Step-by-step explanation:

We are given that the lifetime of a battery in a certain application is normally distributed with mean μ = 16 hours and standard deviation σ = 2 hours.

Let X = lifetime of a battery in a certain application

So, X ~ N( $\mu=16,\sigma^{2} =2^{2}$ )

The z-score probability distribution for normal distribution is given by;

Z = $\frac{ X -\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = mean lifetime = 16 hours

$\sigma$ = standard deviation = 2 hours

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.

So, the probability that a battery will last more than 19 hours is given by = P(X > 19 hours)

P(X > 19) = P( $\frac{ X -\mu}{\sigma}$ > $\frac{19-16}{2}$ ) = P(Z > 1.50) = 1 - P(Z $\leq$ 1.50)

= 1 - 0.9332 = 0.0668

Now, in the z table the P(Z $\leq$ x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.50 in the z table which has an area of 0.9332.

Hence, the probability that a battery will last more than 19 hours is 0.0668.

5 0

3 years ago

which of the functions have a range of real numbers greater than or equal to 1 or less than or equal to-1

lilavasa [31]

The question is incomplete. Here is the complete question:

Which of the functions have a range of all real numbers greater than or equal to 1 or less than or equal to -1? check all that apply.

A. $y=\sec x$

B. $y= \tan x$

C. $y= \cot x$

D. $y= \csc x$

Answer:

A. $y=\sec x$

D. $y=\csc x$

Step-by-step explanation:

Given:

The range is greater than or equal to 1 or less than or equal to -1.

The given choices are:

Choice A: $y=\sec x$

We know that, the $\sec x=\frac{1}{\cos x}$

The range of $\cos x$ is from -1 to 1 given as [-1, 1]. So,

$|\cos x|\leq 1\\\textrm{Taking reciprocal, the inequality sign changes}\\\frac{1}{|\cos x|}\geq 1\\|\sec x|\geq 1$

Therefore, on removing the absolute sign, we rewrite the secant function as:

$\sec x\leq -1\ or\ \sec x\geq 1\\$

Therefore, the range of $y=\sec x$ is all real numbers greater than or equal to 1 or less than or equal to-1.

Choice B: $y= \tan x$

We know that, the range of tangent function is all real numbers. So, choice B is incorrect.

Choice C: $y= \cot x$

We know that, the range of cotangent function is all real numbers. So, choice C is incorrect.

Choice D: $y=\csc x$

We know that, the $\csc x=\frac{1}{\sin x}$

The range of $\sin x$ is from -1 to 1 given as [-1, 1]. So,

$|\sin x|\leq 1\\\textrm{Taking reciprocal, the inequality sign changes}\\\frac{1}{|\sin x|}\geq 1\\|\csc x|\geq 1$

Therefore, on removing the absolute sign, we rewrite the cosecant function as:

$\csc x\leq -1\ or\ \csc x\geq 1\\$

Therefore, the range of $y=\csc x$ is all real numbers greater than or equal to 1 or less than or equal to-1.

6 0

3 years ago

What is the explicit formula for this sequence? −7, −4, −1, 2, 5, …

VikaD [51]

The explicit formula for the sequence is 3n -10

<h3>What is an Arithmetic Sequence ?</h3>

An arithmetic sequence is a series of terms which have common difference between its consecutive numbers.

The sequence given is

−7, −4, −1, 2, 5, …

The common difference between each term is d =3

-4-(-7) = 3

-1-(-4) =3

The nth term for a sequence is given by

$\rm T_n = a +(n-1)d$

Here a is the first term = -7

n is the no. of terms = n

d is the common difference = 3

Therefore the equation will be

$\rm T _n = -7 + (n-1) * 3$

$\rm T _n$ = -7 +3n -3

$\rm T _n$ = 3n -10

Therefore the explicit formula for the sequence is 3n -10 .

To know more about Arithmetic Sequence

brainly.com/question/15412619

#SPJ1

7 0

1 year ago

If gasoline costs 2.14 per gallon and you drive 500 miles in a car that gets 30 mpg, what is the cost of gasoline

Vlad [161]

Answer:

35.7

Step-by-step explanation:

First, you would calculate how many gallons of gasoline the car gets. To do this, divide your total mileage of 500 miles by the mpg (30). Now you know how many gallons of gasoline will be used by the car. After calculating, you get 16.67. Multiply this by how much it costs per gallon of gasoline, and you get an answer of $35.7.

8 0

3 years ago