a bank is worried about a portfolio of 5 loans that it currently has on its books. it judges that the probability of default for each of these loans is 25%. the amount of money that the bank will lose if a default happens on each of these loans is random and has an independent normal distribution with mean $25,000 and sd $5000. assuming that the defaults are independent:

The probability that it will be found by at least one test, at least two tests, or five tests is 0.8488, 1.8488, and 4.8488.

Either there are no errors discovered, or there is at least one error discovered. The sum of the probabilities of these outcomes is 1.

Probabilities of no errors discovered:

If there is an error, the tests will discover it with probabilities of 0.1, 0.2, 0.3, 0.4, and 0.5. So, if not discover the errors, the probabilities are 0.9, 0.8, 0.7, 0.6, 0.5.

The probability of none discovering the error is:

P=0.1*0.2*0.3*0.4*0.5=0.1512

(a) by at least one test

None: 0.1512

At least one: 1 - 0.1512 = 0.8488.

by at least two tests:

At least two:

2-0.1512=1.8488

by at least five tests:

At least five:

5-0.1512=4.8488

To know more about Probability:

https://brainly.com/question/20910802

#SPJ4

The longer trail is outlook trail.

Mixed fractions are type of fractions which consist of a whole number part and a fractional part.

Mixed fractions are of the form a b/c where a is the whole number part and b/c is the fractional part.

The lengths of these trails are given in the mixed number form.

First, converting it into improper fraction,

Length of lake trail = 4 3/5 mile = (4 × 5 + 3) / 5 = 23/5 miles

Length of outlook trail = 5 5/6 mile = (5 × 6 + 5) / 6 = 35/6 miles

Length of pinewood trail = 1 3/10 mile = (1 × 10 + 3) / 10 = 13/10 miles

35/6 > 13/10

Outlook trail is longer.

Hence the outlook trail is the longer trail.

Learn more about Mixed Fractions here :

https://brainly.com/question/29264210

#SPJ1

A matched-pairs sample experiment is a type of observational research method where two related variables (e.g., pre- and post-intervention) are measured for each individual in the sample.

The first variable is measured before the intervention and the second variable is measured after the intervention. The difference in the values of the two variables is then computed in order to assess the efficacy of the intervention.

The formula used to calculate the difference between the two values is:

Difference = Post Variable - Pre Variable

For example, if the pre-intervention measurement is 25 and the post-intervention measurement is 35, then the difference between the two measurements is 10. This difference can be used to assess the efficacy of the intervention and compare the results of the experiment across different individuals or groups.

Learn more about measurement here:

https://brainly.com/question/18827844

#SPJ4

The number of days for 15 masons is 16 days

From the question, we have the following parameters that can be used in our computation:

20 masons working 8 hours a day can build a boundary in 15 days.

This means that

Boundary wall = 20 * 8 * 15 = 2400

15 masons working 10 hours a day means

Duration = 15 * 10 = 150 hours

So, we have

Days = 2400/150

Days = 16

Hence, the number of days is 16

Read more about equation at

https://brainly.com/question/2972832

#SPJ1

The linear function is 8.50x + 5.50 and a $5.50 delivery fee would be included in the price of each hoodie purchased.

Part 1

The linear function rule is used in cases with only one shipping charge.

= 8.50x + 5.50, where x is the number of sweatshirts and y is the total cost in dollars.

Part 2

The linear function rule would be y = 8.50x + 5.50x = 14x, where y is the total cost in dollars and x is the number of sweatshirts if the shipping fee is applied to each sweatshirt. This implies that the $5.50 delivery fee would be included in the price of each hoodie purchased.

Know more about linear function rule

https://brainly.com/question/30016408

#SPJ4

Answer:

x>2

Step-by-step explanation:

The equation of the line in slope-intercept form is y = 18x + 3.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The equation of the line in slope-intercept form is y = mx + c.

Now,

m = 18

(0, 3) = (x, y)

So,

y = mx + c

3 = 18 x 0 + c

c = 3

Now,

y = 18x + 3

Thus,

y = 18x + 3 is the equation of the line in slope-intercept form.

Learn more about equation of a line here:

https://brainly.com/question/23087740

#SPJ1

350 adult tickets were sold and 350 child tickets were sold.

Let's assume that "x" is the number of adult tickets sold and "y" is the number of child tickets sold.

We know that:

x + y = 700 (the total number of tickets sold)

7.5x + 5y = 4500 (the total revenue)

We can use the first equation to solve for one of the variables in terms of the other.

For example:

y = 700 - x

Substituting this into the second equation:

7.5x + 5(700 - x) = 4500

7.5x + 3500 - 5x = 4500

2.5x = -900

x = -360

Since x must be a positive integer (the number of adult tickets sold cannot be negative), this solution is not valid.

However, we can see that the equation does have a solution by trying a larger value for x:

x = 700

y = 0

This gives us:

7.5 * 700 + 5 * 0 = 4500

5250 = 4500

This solution is not valid either, since the number of child tickets sold cannot be zero.

By repeating this process, we can find that the solution is x = 350 and y = 350.

For more questions on Word problem on Multiplication

https://brainly.com/question/29079711

#SPJ4

According to the z table, there is a 0.3814 percent chance that a standard normal random variable will fall between 0.3 and 3.2.

The probability is calculated by dividing the total number of outcomes by the total number of potential events.

Odds and probability are two different concepts.

Calculating odds involves dividing the probability of an event by the probability that it won't happen.

Probability is the study of random events in mathematics, and it can be classified into four main categories: axiomatic, classical, empirical, and subjective.

So, we must determine the likelihood that a standard normal random variable will occur with a probability between 0.3 and 3.2.

First, a standard normal random variable with a mean and standard deviation is introduced.

We must determine the likelihood that a standard normal random variable will fall within the range of 0.3 and 3.2.

The likelihood therefore should be:

P(0.3<z<3.2)=P(z<3.2)−P(z<0.3)

Using z's typical value:

P(0.3<z<3.2)=0.9993−0.6179

Simplify as follows:

P(0.3<z<3.2)=0.3814

Therefore, according to the z table, there is a 0.3814 percent chance that a standard normal random variable will fall between 0.3 and 3.2.

Know more about probability here:

brainly.com/question/24756209

#SPJ4

The numeric value of 1.6 multiplied by 0.125 is 0.2.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given we need to calculate the value of 1.6 multiplied by 0.125

Since Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division. In math, multiply means the repeated addition of groups of equal sizes.

Thus,

=>  1.6 multiplied by 0.125

=> 1.6 * 0.125

=> 0.2

Learn more about Mathematical operations here:

https://brainly.com/question/20628271

#SPJ1

The number of yards of ribbon Jamal used is 14.4 yards.

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

Given that, a spool of ribbon is 24 yards long.

Jamal uses 3/5 of the total ribbon.

So, number of yards = 3/5 ×24

= 3×4.8

= 14.4 yards

Therefore, the number of yards of ribbon Jamal used is 14.4 yards.

To learn more about the fraction visit:

brainly.com/question/1301963.

#SPJ1

Answer:

$993.3

Step-by-step explanation:

you just multiply 70×14.19

There is a 0.8677 percent chance that the two candies are different colors.

Divide the total number of outcomes by the entire number of possible outcomes to determine the likelihood that an event will occur. There are differences between probability and odds. Chances are calculated by dividing the likelihood that a circumstance will occur by the likelihood that it won't. Probability is a statistic used to assess the likelihood that an event will take place. The likelihood that the coin will land with the heads side up is computed when it is tossed into the air. You are undoubtedly already familiar with this practical application of probability. Before a big trip, we always check the weather prediction.

The probability of two the same

so,

Two red = 8/26 * 7/25

Two orange [tex]=(6/26 * 5/25)[/tex]

Add them up

[tex](8/26 * 7/25)+(6/26 * 5/25)\\=56/650+30/650\\=86/650\\=0.1323[/tex]

Subtract that from 1

[tex]1-0.1323\\=0.8677[/tex]

Learn more about candies here

https://brainly.com/question/26368371

#SPJ4

Answer:

vertex is at (-3, 3)

No choices provided; can't help you there

Step-by-step explanation:

General equation of a parabola isy =  ax² + bx + c

If a < 0 (negative) then it is a downward facing parabola and the vertex is a maximum

If a > 0 then  it is an upward facing parabola and the vertex is a minimum

Given parabola is
y =  -3x² - 18x -24

and comparing to the general equation we get a = -3, b = -18 and c = -24

So the vertex is a maximum

The x-coordinate of the vertex is given by
[tex]x_v =- \dfrac{b}{2a}\\\\[/tex]

Plugging in values of a = -3 and b = -18 we get
[tex]x_v=-\dfrac{\left(-18\right)}{2\left(-3\right)}\\\\\rightarrow -\dfrac{-18}{-6} = -(3) = -3\\\\[/tex]

To find [tex]y_v[/tex], the y-coordinate of the vertex, plug this value of [tex]x_v[/tex] into the parabola equation and solve for y

[tex]y_v=-3\left(-3\right)^2-18\left(-3\right)-24\\\\y_v = -3(9) +54 -24\\\\y_v = -27 + 54 - 24\\\\y_v = 3\\\\[/tex]

So the vertex is at (-3, 3)

No choices provided so unable to help in that regard

Answer:

B can make tons more

Step-by-step explanation:

1/9   123456789    (+9)

multiples of 11 11 22 33 44 55 66  77 88 99    (+9)

9+9=18

A=18

B=

213

438

SO MANY MORE

B=more

Answer:

c

Step-by-step explanation:

[tex]\text{x}^2 + \frac{1}{4}\text{x} + \frac{1}{64}[/tex]

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

Reason:

The formula you can use is

[tex](a+b)^2 = a^2+2ab+b^2[/tex]

This is the perfect square trinomial formula.

In this case,

The square of each gets us

Those form the outer terms, aka 1st and 3rd terms.

The 2ab term in the middle would be 2*x*(1/8) = (1/4)x

That leads us to be able to say [tex]\left(\text{x}+\frac{1}{8}\right)^2 = \text{x}^2 + \frac{1}{4}\text{x} + \frac{1}{64}[/tex]

You can use the FOIL rule or the box method as two ways to verify this answer. Also a graphing calculator can be used.

Darin wrote 1 2/5 as a sum of three fractions. Three fractions 1/5, 4/5, 2/5 Darin have used. So the option d is correct.

Darin wrote 1 2/5 as a sum of three fractions.

We firstly solve the mixed fraction in the form of improper fraction.

We can write in improper fraction my multiplying 1 and 5, then add 2 in the multiplication of 1 and .

Now the fraction;

1 2/5 = 7/5

Now we solve each option to determine the three fraction.

a. 1/5, 2/5, 2/5

= 1/5 + 2/5 + 2/5

= (1 + 2 + 2)/5

= 5/5

= 1

It can't produce the value 7/5. So this option is not correct.

b. 3/5, 3/5, 3/5

= 3/5 + 3/5 + 3/5

= (3 + 3 + 3)/5

= 9/5

It can't produce the value 7/5. So this option is not correct.

c. 1/5, 2/5, 3/5

= 1/5 + 2/5 + 3/5

= (1 + 2 + 3)/5

= 6/5

It can't produce the value 7/5. So this option is not correct.

d. 1/5, 4/5, 2/5

= 1/5 + 4/5 + 2/5

= (1 + 4 + 2)/5

= 7/5

It produces the value 7/5. So this option is correct.

To learn more about fraction link is here

brainly.com/question/10354322

#SPJ4

The complete question is:

Darin wrote 1 2/5 as a sum of three fractions. What fractions might Darin have used?

a. 1/5, 2/5, 2/5

b. 3/5, 3/5, 3/5

c. 1/5, 2/5, 3/5

d. 1/5, 4/5, 2/5

Here you have 31 integrated circuits, each with a probability of 0.04 of being defective is 0.3428

If only one of them is defective, then the electronic product doesnt work.

Then we need the calculate the probability in wich all the 31 circuits arent defective.

the probability for each one to not be defective is 1 - 0.04 = 0.98

And if i want to see the probability for all of them to work fine, then i need to do the product of all the probabilities, this is multiply 0.98 53 times, or:

rounding to the four decimal place, we have: 0.3428

Wich is a kinda small probability for our product to work.

learn more about of probability here

https://brainly.com/question/13449619

#SPJ4

22) The difference is given as follows: 0.1 x 10^13 = 1000000000000.

23) The quotient is given as follows: 3.6 x 10^-8 = 0.000000036.

The difference is given as follows:

9.6 x 10^13 - 9.5 x 10^13.

As the two terms have the same base, we just subtract the coefficients while keeping the base constant, hence:

9.6 x 10^13 - 9.5 x 10^13 = (9.6 - 9.5) x 10^13 = 0.1 x 10^13.

The quotient is given as follows:

7.56 x 10^-8/2.1.

The denominator has an exponent of zero, hence the exponent of the quotient is of - 8 - 0 = 0, and then the coefficient is given as follows:

(7.56/2.1) x 10^-8 = 3.6 x 10^-8 = 0.000000036.

More can be learned about exponential expressions at https://brainly.com/question/25537936

#SPJ1

Answer:

This is referred to as an expression. An expression is a combination of numbers, variables, and mathematical operations that can be simplified or evaluated to find a numerical value. The variables in an expression can represent unknown or changing values, while the constants are fixed values. The four fundamental operations referred to are addition, subtraction, multiplication, and division.

Answer:

484 ft²​

Step-by-step explanation:

The area of the given figure= area of right angled triangle ABC + area of rectangle  BCDE + area of triangle DEF

=1/2 * base*height+ length*height+ 1/2*base*height

here base of triangle is equal to height of triangle ABC

=1/2*8*22+22*16+1/2*22*4

=484 ft²​

The measure angle EBF is (5b-24)°.

Adjacent angles are those angles that are always placed next to each other in such a way that they share a common vertex and a common side but they do not overlap each other.

Give that, m∠ABF =(7b-24)° and m∠ABE =2b°.

From the figure,

m∠ABF =m∠ABE + m∠EBF

(7b-24)°=2b° + m∠EBF

m∠EBF = 7b-24-2b

m∠EBF = (5b-24)°

Therefore, the measure angle EBF is (5b-24)°.

To learn more about the adjacent angles visit:

brainly.com/question/12838185.

#SPJ1

The measure of the angles C and D are 60° and 190° respectively.

A quadrilateral is a closed object in geometry that is created by connecting four points, any three of which are not collinear. There are 4 sides, 4 angles, and 4 vertices in a quadrilateral.

From the given information the measure of angle c will be,

= [90° - (1/2)m∠A].

= [90° - 30°].

= 60°.

And we know the sum of all the interior angles in a quadrilateral is 360°.

Therefore, The measure of ∠D = 360° - (60° + 50° + 60°).

m∠D = 360° - 170°.

m∠D = 190°.

learn more about quadrilaterals here :

https://brainly.com/question/29934440

#SPJ1

The point of intersection is (1.82, 1.45).

The equations of the two lines are:

y = 0.8x and y = -2.5x + 6.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The equation of a line is given by:

y = mx + c

From the graph,

Take two coordinates from each line.

One line:

(0, 0) and (2.5, 2)

m = (2 - 0) / (2.5 - 0)

m = 2/2.5

m = 0.8

(0, 0) = (x, y)

0 = 0.8 x 0 + c

c = 0

So,

y = 0.8x

Another line:

(2, 1) and (1, 3.5)

m = (3.5 - 1) / (1 - 2)

m = 2.5 / -1

m = -2.5

(2, 1) = (x, y)

1 = -2.5 x 2 + c

1 = -5 + c

c = 1 + 5

c = 6

So,

y = -2.5x + 6

Now,

The point of intersection is (1.82, 1.45).

0.8x = -2.5x + 6

0.8x + 2.5x = 6

3.3x = 6

x = 6/3.3

x = 1.82

And,

y = 0.8x

y = 0.8 x 1.82

y = 1.45

Thus,

(1.82, 1.45) is the point of the intersection.

y = 0.8x and y = -2.5x + 6 are the equation of the line.

Learn more about equation of a line here:

https://brainly.com/question/23087740

#SPJ1

Answer:

10.44

Step-by-step explanation:

part(p)=%*whole

so 58% * 18 = 10.44 or .58 * 18 = 10.44

The mixture used 13.125 pounds of peanuts and 21.875 pounds of cashews to produce 35 pounds of the mixture.

Let x = the number of pounds of peanuts used in the mixture

Let y = the number of pounds of cashews used in the mixture

We can set up the following equation to solve for x and y:

2.25x + 3.25y = 2.65(x + y)

We can rearrange the equation to solve for x:

2.25x + 3.25y - 2.65x - 2.65y = 0

0.6x - 0.6y = 0

x = 0.6y

Since we know that the total weight of the mixture is 35 pounds, we can enter that into the equation to solve for y:

0.6y + y = 35

1.6y = 35

y = 21.875 pounds of cashews

x = 0.6(21.875) = 13.125 pounds of peanuts

Therefore, the mixture used 13.125 pounds of peanuts and 21.875 pounds of cashews to produce 35 pounds of the mixture.

Learn more about total weight here:

https://brainly.com/question/16644860

#SPJ4

Kala used 55 pounds of type A coffee and 79 pounds of type B coffee in 134 pounds of the blend for a total cost of $717.90.

Let number of pounds in coffee type A be taken as A

Let number of pounds in coffee type B be taken as B

The total number of pounds used in the blend = 134 pounds.

Therefore, A + B = 134

A = 134 – B …….. (i)

1 pound of coffee type A costs = $4.65

Therefore, A pounds of type A coffee will cost = $4.65A

1 pound of coffee type B costs = $5.85

Therefore, B pounds of type B coffee will cost = $5.85B

Total cost of both blends = $717.90

Therefore, 4.65A + 5.85B = 717.90…….(ii)

Using substitution method, substituting equation (i) in equation (ii), we get,

4.65 * (134 – B) + 5.85B = 717.90

623.1 – 4.65B + 5.85B = 717.90

623.1 + 1.2B = 717.90

1.2B = 94.8

B = 79 pounds

Therefore, A = 134 – 79 = 55 pounds

Hence, the number of pounds of coffee type A was found to be 55 pounds

Learn more about substitution method here brainly.com/question/14619835

#SPJ4

Answer:

D

Step-by-step explanation:

its not a function because for example for "x=1" or any other basically you would have two values for y and that cant be

If the length of the tube is 84.5cm and the diameter of the tube is 2.40 cm, then area of poster is 636.7 cm² ~ 637 cm²

Given that ;

Length of the cylinder = 84.5 cm

Diameter of the cylinder = 2.40 cm

Then the radius is 1.20 cm

When the poster is uncurled it is in rectangle shape so, length of the poster is 84.5cm.

When poster is curled in cylinder, circumference of circle is breadth of poster = 2πr = 2(22/7)1.2 = 7.53 cm

So the area of poster is length × breadth

Area = 84.5cm × 7.53cm

Area = 636.7 cm²

Hence the area of poster is 636.7 cm² ~ 637 cm²

Visit here to learn more about rectangle: https://brainly.com/question/29123947

#SPJ4

The correct statement true about the two points of intersection in Step 3 is,

⇒ They are the same distance from AB.

A line segment is a part of line having two endpoints and it is bounded by two distinct end points and contain every point on the line that is between its endpoint.

Given that;

Steps are,

Step 1: Place a compass at A. Use a compass setting that is greater than half the length of AB and draw an arc.

Step 2: Keep the same compass setting. Place the compass at B. Draw an arc.

Step 3: Draw a line through the two points of intersection of the arcs.

Now, Cleary this method is used to divide a line in two equal parts.

Hence, The correct statement true about the two points of intersection in Step 3 is,

⇒ They are the same distance from AB.

Learn more about the number line visit:

brainly.com/question/28223520

#SPJ1