Andrew invests $2834 in a savings account with a fixed annual rate of 2.5% compounded daily. What will the account balance be after 28 years?

The applicants who are granted admission is 0.8413, The applicants who will score 860 or higher is 0.0228, and there will be 2023 applicants that are expected to be qualified to the university.

a) The scores in this problem are known to be normally distributed with a mean of 700 and a standard deviation of 80. To find the proportion of all applicants taking the exam who are granted admission, we must compute the Z-score of 620.

We then need to find the area under the normal curve to the right of this Z-score.1. Z-score of 620: (620 - 700)/80 = -1.00Therefore, P(X ≥ 620) = P(Z ≥ -1.00) = 0.8413 (using a standard normal table)

So, the proportion of all applicants taking the exam who are granted admission is approximately 0.8413.

b) To find the proportion of all applicants who will score 860 or higher on the exam, we must compute the Z-score of 860.

We then need to find the area under the normal curve to the right of this Z-score.2. Z-score of 860: (860 - 700)/80 = 2.00

Therefore, P(X ≥ 860) = P(Z ≥ 2.00) = 0.0228 (using a standard normal table)So, the proportion of all applicants who will score 860 or higher on the exam is approximately 0.0228.

c) Using the proportions calculated in parts (a) and (c), we can expect the following number of applicants to be qualified for admission to the university.

Qualified applicants = (2400)(0.8413) = 2023 (rounded to the nearest whole number)

Therefore, we expect 2023 applicants to be qualified for admission to the university.

Learn more about probability here:

https://brainly.com/question/30448794

#SPJ11

The number of different sets of three points of this grid can be the three vertices of an isosceles triangle is 36.

An isosceles triangle is one with two equal sides. The two angles that face the two equal sides are also equal. An isosceles triangle, in other words, is a triangle whose two sides are equal in length.

By using the Permutation formula,

Number of isosceles triangle to be formed is,

9!/(7!x2!) = 9x8x7!/7!x2!

= 9x8/2

= 36

So number of isosceles triangle that can be formed of this 3-by-3 grid is 36.

When a square is described as a 3 x 3 Magic square, it has three rows and three columns. An illustration of a 3 by 3 magic square with the magic constant.

Learn more about 3-by-3 grid:

https://brainly.com/question/27890591

#SPJ4

Answer:

9

Step-by-step explanation:

3^4= 81

3^2= 9

81/9=9

hope this helped!!!! :)

Answer:

3^4 / 3^2 =

3^2 =

9

Answer:8

Step-by-step explanation:

Answer:

3, 5, 7, 9, 11

Step-by-step explanation:

the recursive formula allows a term to be found by adding 2 to the previous term, that is

u₁ = 3

u₂ = u₁ + 2 = 3 + 2 = 5

u₃ = u₂ + 2 = 5 + 2 = 7

u₄ = u₃ + 2 = 7 + 2 = 9

u₅ = u₄ + 2 = 9 + 2 = 11

the first 5 terms are 3, 5, 7, 9, 11

Overall fraction of sold seats is 0.63333...

First we use the fact that 2/3 of the seats are located on the main floor and the number of seats on the main floor is 600, so the total number of seats can be calculated as follows:

Total number of seats = 600 / (2/3) = 900 seats

Next, we can find the number of seats in the balcony:

Balcony seats = Total number of seats - Main floor seats = 900 - 600 = 300 seats

Next, we can find the number of sold floor seats:

Sold floor seats = 4/5 * 600 = 480 seats

And the number of sold balcony seats:

Sold balcony seats = 1/2 * 300 = 150 seats

Finally, to find the overall fraction of sold seats in the theater, we add the number of sold floor seats and the number of sold balcony seats and divide by the total number of seats:

Overall fraction of sold seats = (480 + 150) / 900 = 0.63333... (rounded to the nearest hundredth)

Learn more about  overall fraction here: brainly.com/question/28699958

#SPJ1

Answer:

21,704

Step-by-step explanation:

Find the volume of both the top of the silo (hemisphere) and the end bit of the silo (cylinder)

V = \(\frac{2}{3}\) \(\pi\)\(r^{3}\) is the formula for finding the volume of a hemisphere

V = \(\pi\)\(r^{2}\)h is the formula for finding the volume of a cylinder

Let's find the hemisphere first.

We're using 3.14 for pi, so the equation would look like this

V = \(\frac{2}{3}\) x 3.14 x \(12^{3}\)

V = \(\frac{2}{3}\) x 3.14 x 1728

V = 3617.28 \(ft^{3}\)

Now let's find the volume of the cylinder.

V = 3.14 x \(12^{2}\) x 40

V = 3.14 x 144 x 40

V = 18,086.4 \(ft^{3}\)

Last, you add both volumes together.

3617.28 + 18,086.4 = 21,703.68

Round it to make it 21,704.

The total number of cubic feet of grain or volume of the grain that the silo can hold is 28947.41 .

The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

Given that the top of a silo is a hemisphere

Radius(r) = 12 ft.

Then, the volume of a hemisphere is,

V = 2/3πr³

V = 2/3 x 3.14 x 12³

V = 10851.84 feet³

And, the bottom of the silo is a cylinder with

height (h) = 40ft.

the volume of a cylinder is,

V = πr²h

V = 3.14 x 12² x 40

V = 18095.57

So, the total volume is

V = 10851.84 + 18095.57

V = 28947.41

Then, total volume = total number of cubic feet of grain

Hence, the required answer is, 28947.41 .

To learn more about the volume visit:

brainly.com/question/24372707

#SPJ2

Given that sin(x) = 2/3 and x is in Quadrant II, we can use trigonometric identities to find the values of cos(2x), sin(2x), and tan(2x). In two lines.

To find cos(2x), sin(2x), and tan(2x), we can use the double-angle identities: cos(2x) = cos^2(x) - sin^2(x), sin(2x) = 2sin(x)cos(x), and tan(2x) = (2tan(x))/(1 - tan^2(x)). By substituting the given value of sin(x) = 2/3 into these formulas and applying the Pythagorean identity sin^2(x) + cos^2(x) = 1, we can calculate cos(2x), sin(2x), and tan(2x) using trigonometric calculations. The values of cos(2x), sin(2x), and tan(2x) can then be determined.

Learn more about Quadrant here:

https://brainly.com/question/29298581

#SPJ11

Answer:

Step-by-step explanation:

y = a * x(x - 3)(x + 1)^2

2,12 is used to find the value of a

y = a (2)(2 - 3)(2 + 1)^2

12 = a (2)(-1)(3)^2

12 = a (2) (-1) (9)

12 = - 18*a

12/-18 = a

a = - 2/3

y = (-2/3)*x*(x - 3)(x + 1)^2

The probability that Robert is approved on both the written application and the interview is approximately 0.5531

To find the probability that Robert is approved on both the written application and the interview, we can use the formula for conditional probability

P(A and B) = P(B | A) × P(A)

where A and B are events, P(A) is the probability of event A, and P(B | A) is the probability of event B given that event A has occurred.

Let's define the events

A = "Robert is approved on the written application"

B = "Robert is approved by the interview committee"

We know that P(A) = 0.67, and P(B | A) = 0.83. We want to find P(A and B), which represents the probability that both events A and B occur.

Using the formula for conditional probability, we have

P(A and B) = P(B | A) × P(A)

P(A and B) = 0.83 × 0.67

P(A and B) = 0.5531

Learn more about probability here

brainly.com/question/11896081

#SPJ4

Answer:

513.881

Explanation: (Credits to jessy276)

= 5*100+3+10+8*0.1+9*0.009

= 500+3+10+8*0.1+9*0.009

= 500+3+10+0.8+9*0.009

= 500+3+10+0.8+0.081

= 503+10+0.8+0.081

= 513+0.8+0.081

= 513.8+0.081

= 513.881

Answer:

The answer is 513.881

Step-by-step explanation

The additional time it will take for the liquid's temperature to decrease from 64°F to 32°F is 2 minutes, considering a rate of temperature decrease of 16°F per minute.

To find the additional time it will take for the liquid's temperature to decrease from 64°F to 32°F, we can consider the rate at which the temperature is decreasing.

From the given information, we know that the liquid's temperature decreases from 160°F to 64°F in 6 minutes. This means that the temperature decreases by 160°F - 64°F = 96°F in 6 minutes.

Therefore, the rate of temperature decrease is 96°F / 6 minutes = 16°F per minute.

To find the additional time it will take for the temperature to decrease from 64°F to 32°F, we can calculate the difference in temperature and divide it by the rate of temperature decrease

Temperature difference = 64°F - 32°F = 32°F

Additional time = Temperature difference / Rate of temperature decrease

Additional time = 32°F / 16°F per minute = 2 minutes

Therefore, it will take an additional 2 minutes for the temperature to decrease from 64°F to 32°F.

To know more about temperature:

https://brainly.com/question/7510619

#SPJ4

Answer:

that's angle side angle so ASA

Answer:

d -x=y the awnssr may not be correct but I tried so

Answer:

3x+12/10 simplified is =3x+ 6 /5

Step-by-step explanation:

x+2 /x^2 +6x +8=  7x3+8x2+2 x2

Answer:

The answer to this is: 17 but it does not have a remainder.

Step-by-step explanation:

and can i have brainliest please?

Answer:

11

Step-by-step explanation:

m - 8 (less than or equal to) 2

= m(less than or equal to) 10

So anything before 10 not after

Answer:

It is E. past me

Step-by-step explanation:

m-8+8=2+8

m≤ 10

So m has to be 10 or smaller so 11 is not a solution

Answer:

There are 15 calories in one serving.

Step-by-step explanation:

To find out how many calories are in one serving, you simply have to divide the number of calories by the number of servings.

75 / 5 = 15

The correct answer is 5! × 2! × 4! ways = 5760 ways.

Given that Professor Chang has nine different language books lined up on a bookshelf: two Arabic, three German, and four Spanish. The problem requires us to find out how many ways there are to arrange the nine books on the shelf while keeping the Arabic books together and keeping the Spanish books together.

The number of ways that the nine books can be arranged on the shelf keeping the Arabic books together and keeping the Spanish books together is as follows:

First, we group the Arabic books and the Spanish books. The Arabic books consist of two books, and the Spanish books consist of four books. These two groups will be treated as a single book, so there are 5 books on the shelf instead of 6.

The 5 books can be arranged among each other in 5! ways. The Arabic books can be arranged among each other in 2! ways and the Spanish books can be arranged among each other in 4! ways.

Therefore, the total number of ways to arrange the nine books on the shelf while keeping the Arabic books together and keeping the Spanish books together is 5! × 2! × 4! = 5760 ways.

Hence, the correct answer is 5! × 2! × 4! ways = 5760 ways.

Know more about Permutation and Combination here:

https://brainly.com/question/28720645

#SPJ11

(a) The family of all solutions to Ax - b can be represented as x = x' + N(A). (b) A solution to Ax = b in part (a) with x = 5 is Ax = 0.

To find the family of all solutions to the equation Ax - b and a specific solution with x = 5.

(a) We know that Ax - b has the given solution x' = [10, 10, 0, 0]. This solution is also referred to as a particular solution. To find the family of all solutions, we need to find the general solution by adding the particular solution to the null space of matrix A. The null space contains all the solutions to the equation Ax = 0. Let's denote the null space vectors as N(A).

After finding the appropriate combination of null space vectors, add it to the particular solution x' to obtain the required solution with x = 5.

(b) To find a solution with x = 5, we need to find a suitable combination of vectors in the null space N(A) that, when added to the particular solution x', results in a new vector whose first component is 5. Keep in mind that the null space vectors are obtained from the equation Ax = 0, and their linear combinations represent the possible transformations of the particular solution.

Please note that without the specific matrix A and vector b, it's impossible to provide exact solutions. However, the method described above should guide you in solving this type of problem.

You can learn more about  null space at: /brainly.com/question/17215829

#SPJ11

Answer:

yes (i think im not for sure)

Step-by-step explanation:

Answer:

20. is B (second one)

21. is A (first one)

Step-by-step explanation:

Answer:

46=p x 98 because 46 is the product of multiplying the percentage(p) to 98

156+97 because subtracting a negative number is the same as adding

Answer:

B (0, -2)

Step-by-step explanation:

Since the line intercepts at -2 on the y-axis, -2 is the y-intercept.

The product of the expression is determined using rules of exponent as 5⁻¹⁸.

The product of the expression is calculated by applying the rules of exponent as shown below;

5⁵⁶ x 5²² x 5⁻⁹⁶

Based on rules of exponent;

multiplication sign = implies addition

So we are going to add all the powers of 5 as follows;

5⁵⁶ x 5²² x 5⁻⁹⁶ = 5⁵⁶ ⁺ ²² ⁻ ⁹⁶

= 5⁵⁶ ⁺ ²² ⁻ ⁹⁶

= 5⁻¹⁸

Learn more about exponents here: https://brainly.com/question/11975096

#SPJ1

Answer:

x = 120

Step-by-step explanation:

Assuming you require to find the value of x

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 6 , then

sum = 180° × 4 = 720°

Sum the interior angles and equate to 720

140 + 150 + 90 + x + 130 + 90 = 720 , that is

x + 600 = 720 ( subtract 600 from both sides )

x = 120

Answer:

24t^2 + 11

Step-by-step explanation:

There is a lot left out of this question. If you are allowed rational numbers, a common factor could be 24.

24(t^2 + 11/24) is one possibility.

I think what you mean is there an integer that is a common factor. There is not.

So the answer is 24t^2 + 11

There is one more thing that needs to be clarified. Can you give t a value? If you can, then t = 11

the common factor would be

11(24 * 11 + 1)

I doubt very much that this is what is meant, but the question really should make it clear.

Answer:

1(24f²+11) is your answer

Step-by-step explanation:

24f2+11

taking common

1(24f²+11)