Suppose the time a child spends waiting at for the bus as a school bus stop is exponentially distributed with mean 5 minutes. Determine the probability that the child must wait between 4 and 6 minutes on the bus on a given morning.
a) 0.3519
b) 0.8519
c) 0.3481
d) 0.4493
e) 0.1481
f) None of the above

Answer:

120

Step-by-step explanation:

First, you notice that both the angles add up to 180 degrees because it is a straight line.  Therefore, 2x+x+90=180.  Now you have an equation to solve!  Subtract 90 from both sides and combine like terms.  3x=90.  Therefore, x=30.  Now you plug x back in to find out m<DBC.  DBC=x+90 which is 30+90= 120.  

Answer:

4:50 hrs to school activities

Step-by-step explanation:

the entire school day 6:10 hrs (with breaks)

so if we remove the breaks (which are 1:20hrs in total) we'll have 4:50hrs.

the equation would be: (the time the full day is)-(the total of breaks)= the school activity time.

so: 6:10hrs-1:20hrs= 4:50hrs

there's your answer. 4:50 hrs

*just remember i am working in the hrs format meaning 60 mins= 1hrs*

Answer:

x  =  10.60660171

x  =  15 √ 2  over 2

Step-by-step explanation:

Answer:

-0.5

Step-by-step explanation:

\(\frac{f}{g} =\frac{f(n)}{g(n)} = \frac{4n}{n^2-3n}\)

\(\frac{4(-5)}{(-5)^2-3(-5)} =\frac{-20}{40} =\frac{-1}{2}\)

Answer:

-104 is the answer .....

The solution to the initial-value problem y' = (1/2)y2, y(0) = 0.5y(1) is y = -2/x + 4.

a. Differential equations are used to model change. They represent the change in a variable y with respect to the change in another variable x. By looking at the differential equation of the form y' = ky, where k is a constant, you can say that the solution of the equation y is decreasing (or equal to 0) on any interval on which it is defined.

b. The given family of solutions y = 2/(x + C) is of the form y = k/(x + C), where k = 2 is a constant and C is the arbitrary constant of integration. The derivative of y with respect to x is y' = -k/(x + C)

2. Substituting this into the given differential equation y' = ky, we have:-k/(x + C)2 = k/k(x + C)y, which simplifies to y = 2/(x + C).

Therefore, all members of the family y = 2/(x + C) are solutions of the given differential equation.

c. To find a solution of the initial-value problem y' = (1/2)y2, y(0) = 0.5y(1), we need to solve the differential equation and use the initial condition y(0) = 0.5y(1).

Separating the variables and integrating both sides, we get:

dy/y2 = (1/2)dx.

Integrating both sides, we get:-1/y = (1/2)x + C, where C is the constant of integration.

Solving for y, we get:

y = -1/(1/2)x - C = -2/x - C.

We know that y(0) = 0.5y(1), so substituting x = 0 and x = 1 in the solution above, we get:-2/C = 0.5y(1), and y(1) = -2 - C.

Substituting C = -4, we have y = -2/x + 4. Therefore, the solution to the initial-value problem y' = (1/2)y2, y(0) = 0.5y(1) is y = -2/x + 4.

To know more about derivatives visit:

https://brainly.com/question/23819325

#SPJ11

(a) Given differential equation is `(1/2) y²`. For a solution of differential equation `y = f(x)`, the function `y = f(x)` must satisfy the differential equation.  

By looking at the differential equation, we can say that the function Y must be decreasing (or equal to 0) on any interval on which it is defined. Thus, the correct option is (A).

The differential equation is `(1/2) y²`. Let `y = f(x)`, then `(1/2) y²` can be written as,`dy/dx = y dy/dx`Dividing by `y²`, we get,`dy/y² = dx/2`Integrating both sides, we get,`-1/y = (x/2) + C`

Where C is the constant of integration. Rearranging the terms, we get,`y = -2/(x + C)`

This is the general solution of the differential equation. Now, we need to verify that all members of the family `y = 2/(x + C)` are solutions of the equation in part (a).(b) Let `y = 2/(x + C)`, then `y' = -2/(x + C)²`.

Substituting these values in the differential equation, we get,`(1/2) [2/(x + C)]² (-2/(x + C)²) = -1/(x + C)²`Simplifying, we get,`-1/(x + C)² = -1/(x + C)²`This is true for all values of x.

Hence, all members of the family `y = 2/(x + C)` are solutions of the equation in part (a).(c) We need to find a solution of the initial-value problem: `y' = y²/2, y(0) = 0.5 y(1)`.

We know that `y = 2/(x + C)` is the general solution of the differential equation. To find the particular solution that satisfies the initial condition, we substitute `x = 0` and `y = 0.5 y(1)` in the general solution, we get,`0.5 y(1) = 2/(0 + C)`or, `C = 4/y(1)`

Substituting this value of C in the general solution, we get,`y = 2/(x + 4/y(1))`

Hence, the solution of the initial-value problem is `y = 2/(x + 4/y(1))`.

To know more about integration ,visit

https://brainly.com/question/31744185

#SPJ11

Jesse can make 3.3141 liters of juice.

First, we need to calculate the volume of the can of juice concentrate:

The radius of the circular base is half the diameter, so r = 7.5 / 2 = 3.75 cm

The volume of a cylinder is V = πr^2h, where h is the height of the cylinder.

So, the volume of the can is

V = π(3.75 cm)^2(20 cm) ≈ 4,418.77 cubic centimeters.

Next, we need to calculate the volume of one can of water. We know that Jesse needs to mix the contents of the can of juice concentrate with three cans of water, so the total volume of the juice will be four times the volume of the can of juice concentrate.

To convert cubic centimeters to liters, we divide by 1000. So, the volume of the can of juice concentrate in liters is V = 4,418.77 / 1000 = 4.41877 liters.

Divide this by 4 to get the volume of one can of juice: 4.41877 / 4 = 1.1047 liters.

Therefore, Jesse can make 3 cans of water x 1.1047 liters per can = 3.3141 liters of juice.

To learn more about litres, click here:

https://brainly.com/question/25546396

#SPJ11

The required domain of g ( x ) = 3 x - 1 is R ( real nos . ) .

Given : g ( x ) = 3 x - 1

To find : Domain of function

Domain : The set of all possible values of input variable  ( x in this case ) is called the domain of the function .

Calculating domain :

g ( x ) = 3 x - 1

Since , it is a polynomial function with degree 1 , therefore it's domain will be real nos .

Hence , domain of g ( x ) = 3 x - 1 is R .

To learn more on domain and range follow link :

https://brainly.com/question/2264373

#SPJ4

Answer:

$3600

Step-by-step explanation:

Given:

Total income T = $18,000

Fraction of income spent on house rent f1 = 1/5

Fraction of income spent on other expenditures f2 = 3/5

Fraction of income saved is;

f = 1 - (1/5+3/5) = 1 - 4/5

f = 1/5

The Amount he save is A;

A = fraction saved × total amount = f × T

Substituting the values

A = 1/5 × $18,000

A = $3,600

The Amount he save is $3,600

Answer: Varun saves 3,600 every month

Step-by-step explanation: Varun's income in the first instance is fixed at 18000, and out of this amount he spends 1/5 on house rent. We shall now determine the amount represented by 1/5 as follows;

Total income = 18000

House rent = 1/5

Rent expense = 1/5 of 18000

Rent expense = 1/5 * 18000

Rent expense = 3600

he also spends 3/5 on other expenditure

Other expenditure = 3/5 of 18000

Other expenditure = 3/5 * 18000

Other expenditure = (3 * 18000)/5

Other expenditure = 54000/5

Other expenditure = 10800

His expenses therefore have been derived as

Total expenditure = 3600 + 10800

Total expenditure = 14400

His savings per month therefore is derived as;

Total income - total expenditure = savings

18000 - 14400 = savings

3600 = savings

Therefore, Varun saves 3,600 every month

A direct relationship between two variables is reflected in a "POSITIVE" correlation coefficient.

Correlation is a statistical technique for measuring and describing the relationship between two variables.

The variables move in the same direction when they have a positive correlation. In other words, as one variable increases, so does the other, and conversely, as one variable decreases, so does the other.

Typically, the two variables are simply observed rather than manipulated. Two scores from the same individuals are required for the correlation.

Find more on correlation coefficient at : https://brainly.com/question/28213588

#SPJ4

Answer:

30.1°

Step-by-step explanation:

Let A = angle of elevation

tan A = 55/95

A = arctan 55/95

    = 30.1°

The proportion of school-aged children who are overweight is  108.

a) We are given that 21.4% of school-aged children aged 6-11 years are overweight.

The shape of the sampling proportion is approximately normal, i.e., the sampling distribution of the sample proportion can be approximated by a normal distribution since the sample size is greater than 30 (98 > 30).

b) Mean = µp = 21.4%

= 0.214

Standard deviation = σp

= sqrt [p(1 - p) / n]

= sqrt [(0.214)(1 - 0.214) / 98]

= 0.0456c)

In a random sample of 98 school-aged children, the probability that at least 23% are overweight is found using the formula:

z = (x - µ) / σp

= (0.23 - 0.214) / 0.0456

= 0.3509

Using the z-table, the probability that at least 23% are overweight is:

P(z > 0.3509) = 0.3632d)

A random sample of 98 school-aged children resulted in 20 overweight children.

The sample proportion is:

p = x / n = 20 / 98 = 0.204

The sample proportion (0.204) is close to the population proportion (0.214).

E = z(α/2) * sqrt [p(1 - p) / n]

= 1.96 * sqrt [(0.214)(1 - 0.214) / 98]

= 0.0929 ≈ 0.093f)

E = z(α/2) * sqrt [p(1 - p) / n]n

= [z(α/2) / E]2 * p(1 - p)

= [1.645 / 0.03]2 * 0.214(1 - 0.214)

= 763.05

≈ 764 (rounded up)j)

The sample size (n) that should be used with 90% confidence assuming no prior information suggesting a possible value of the proportion of school-aged children who are overweight is found using the formula:

n = [z(α/2) / E]2

= [1.645 / 0.05]2

= 107.18

≈ 108 (rounded up)

For more related questions on proportion:

https://brainly.com/question/31548894

#SPJ8

If two coplanar lines are cut by a transversal so that a pair of alternate interior angles are equal then the two lines are parallel.

The four sets of opposing angles that each have their own vertex point, are on different sides of the transversal and are both either internal or exterior are called alternate angles.

In geometry, a transversal line is one that cuts across the plane in two places. It does so at two spots where two lines meet. Many right angles are produced when two transverse lines meet. There are four types of similar angles: matching, alternative interior, alternate exterior, and co-interior.

In geometry, two lines are considered parallel if and only if all pairs of alternative interior angles in any transversal are equal.

Learn more about the alternative interior angles -

https://brainly.com/question/20344743

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

point 1 (0 , 0 ) x1 = 0 y1 = 0

point 2 (2 , -3) x2 = 2 y2 = -3

equation of the line = ?

Step 02:

Slope formula

Slope-intercept form of the line

y = mx + b

b = y-intercept = 0

m = - 3/2

y = -3/2 x + 0

y = -3/2 x

The answer is:

y = -3/2 x

If Cynthia keeps up her pace, she will finish the 248-mile bike race in approximately 7.29 hours.

To determine how many hours Cynthia will finish the 248-mile bike race given her pace of 68 miles in 2 hours, follow these steps:

1. Calculate her speed by dividing the distance by the time:

speed = 68 miles / 2 hours

speed = 34 miles per hour.

2. Divide the total distance of the race (248 miles) by her speed (34 miles per hour) to find the time:

time = 248 miles / 34 miles per hour

time ≈ 7.29 hours.

Thus, we can state that if Cynthia keeps up her pace, she will finish the 248-mile bike race in approximately 7.29 hours.

To learn more about distance visit : https://brainly.com/question/26550516

#SPJ11

Answer:

X = 7

Step-by-step explanation:

because of you do 5+2 = 7 then you minus 3 which you get 4.

the. if you have a production of around 10 you will get 7.

or you can do.

3+2 which is 5 and then you multiply that by 2 which is 10 and then you comprised that number therefore you will get 6 but you have to find X so we youndelie (think that's how u spell it) X which will equal to 1 and 6+1 is 7. once you get it it's quite simple

Answer:

150u+90

Step-by-step explanation:

..

Answer:

In (5u+3) 5 is a constant

Step-by-step explanation:

Answer:

(7, -1)

Step-by-step explanation:

3x + 7y = 14

y = x - 8

3x + 7(x - 8) = 14

3x + 7x - 56 = 14

10x - 56 = 14

Add 56 to both sides.

10x = 70

Divide both sides by 10.

x = 7

3(7) + 7y = 14

21 + 7y = 14

Subtract 21 from both sides.

7y = -7

Divide both sides by 7.

y = -1

(7, -1)

Answer:

i believe it's 8

Step-by-step explanation:

if the problem is 7+j-k

7+2-1

=8

hope this helps

please mark brainiest

Answer:

Opcion C

Step-by-step explanation:

I think Maybe it could be

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

\(y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{2}{3}}x-\cfrac{4}{5}\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)

so we're really looking for the equation of a line whose slope is 2/3 and that it passes through (-3 , 2) in standard form

standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

\((\stackrel{x_1}{-3}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{2}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{ \cfrac{2}{3}}(x-\stackrel{x_1}{(-3)}) \implies y -2= \cfrac{2}{3} (x +3)\)

\(\stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3(y-2)=3\left( \cfrac{2}{3} (x +3) \right)}\implies 3y-6=2(x+3)\implies 3y-6=2x+6 \\\\\\ 3y=2x+12\implies -2x+3y=12\implies {\Large \begin{array}{llll} 2x-3y=-12 \end{array}}\)

Step-by-step explanation:

A is the answer to the question

A) r^2 - 2rs+s^2

...............................

We need at least 96 rectangular tiles of dimensions 2 inches by 3 inches to cover a square region that is 2 feet on each side.

First, we need to convert the dimensions of the square region from feet to inches. Since there are 12 inches in a foot, a square region that is 2 feet on each side would be 24 inches on each side (2 feet x 12 inches/foot = 24 inches).

To find the least number of tiles needed to cover the square region, we need to determine how many tiles can fit horizontally and vertically on the 24-inch side of the square.

Since the tiles are 2 inches by 3 inches, we can fit 12 tiles horizontally (24 inches ÷ 2 inches per tile = 12 tiles). Similarly, we can fit 8 tiles vertically (24 inches ÷ 3 inches per tile = 8 tiles).

Therefore, we need at least 12 x 8 = 96 tiles to completely cover the square region.

To learn more about rectangular please click on below link        

https://brainly.com/question/21334693

#SPJ1

0.688 will be the probability of getting a nickel from the jar.

Given,

Probability;-

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

Here,

The number of fortunate situations divided by the total number of coins would be the product between the probability of each occurrence and the likelihood of each event.

Therefore,

P(nickel) = 19/69

P(penny) = 17/68

That is,

P = 19/69 × 17/68

P = 323/4692

P = 0.0688

That is,

The probability of getting nickel from the jar is 0.06888

Learn more about probability here;

https://brainly.com/question/29087823

#SPJ4

Answer: Tasha

Step-by-step explanation:

9/10 = .900 avg

12/15 = .800 avg

If you standardize the ratios to 30, then:

27/30 = .900 avg

24/30 = .800 avg

Answer:

Step-by-step explanation:

radius of semicircle = 5

area of semicircle = πr² = 25π

area of rectangle = 10×14 = 140

total area = 140 + 25π ≅ 218.54 square units

Hi, your question appears to be unclear. However, I inferred this to be a linear programming problem.

Answer:

$500

Step-by-step explanation:

To begin we need to state the system of inequalities for this situation (constraints):

From the question, we note we are required to find the maximum revenue that the craftsman can take in. In other words, the optimization equation is \(5b+7.5n\) = maximum revenue (taking note that a bracelet costs $5 and a necklace costs $7.50)

Next, we are to plot the inequalities on a graph to determine the feasible region: Doing so should give us these main vertices: (0,0) (0,40) (40,30 (100,0).

By substituting the vertices into the optimization equation (replacing b, and n) we can determine which quantity gives the maximum revenue:

For (0,40) ⇒ 5(0) + 7.5(0) = $0

For (0,40) ⇒ 5(0) + 7.5 (40) = $300

For (40, 30) ⇒ 5(40) + 7.5 (30) = $425

For (100, 0) ⇒ 5(100)+7.50(0) = $500

We notice that at point  (100, 0) we have a maximum revenue of $500.