ana opened a bank account with $1000 that earns interest, compounded continuously, at an annual rate of r

a. probability of neither a math major nor an engineering major is: 0.1783

b. probability is only an engineering major: 0.5167

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

Given that,

n(S) = 60

n(math) = n(M) = 183 ⇒ P(M) = n(M)/ n(S) = 183/600

n(engineering) = n(E) = 366 ⇒ P(E) = n(E)/ n(S) = 366/600

n(M∩E) = 56

P (M∩E) = n(M∩E) / n(S) = 56/600

a) probability of neither a math major nor an engineering major is:

P (M' ∩ E') = P (M∪E)'

P (M' ∩ E') = 1 - P (M∪E)

P (M' ∩ E') = 1 - [P(M) + P(E) - P(M∩E)]

P (M' ∩ E') = 1 - [183/600 + 366/600 - 56/600]

P (M' ∩ E') = 0.1783

b)

probability is only an engineering major:

P(E - M) = P(E) - P(M∩E)

P(E - M) = 366/600 - 56/600

P(E - M) = 0.5167

To know m ore about probability refer to:

https://brainly.com/question/24756209

#SPJ4

Answer: The value of sin(2x) can be found using the identity:

sin(2x) = 2sin(x)cos(x)

Since tan(x) = -1/5, we can use the tangent definition to find the sine and cosine values:

tan(x) = sin(x) / cos(x) = -1/5

Cross multiplying and solving for sin(x), we get:

sin(x) = -5 / sqrt(26)

And using the Pythagorean identity:

cos^2(x) + sin^2(x) = 1

We can find cos(x):

cos(x) = sqrt(1 - sin^2(x)) = sqrt(1 - (-5/sqrt(26))^2) = sqrt(26) / sqrt(26) = sqrt(26) / sqrt(26) = sqrt(26) / 5

Finally, substituting the values of sin(x) and cos(x) into the formula for sin(2x), we get:

sin(2x) = 2sin(x)cos(x) = 2 * (-5 / sqrt(26)) * (sqrt(26) / 5) = -2 sqrt(26) / 5 = -2 sqrt(26) / 5 = -2 sqrt(26) / 5

So the exact value of sin(2x) is -2 sqrt(26) / 5.

Step-by-step explanation:

For the given condition the correct inequality is,

⇒ x ≥ 20

Where, x represent the number of questions.

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

A student decides to solve at least 20 math problems every day to better their grade if they self and math problems every day.

Let number of questions done by a student = x

So, The inequality for the given condition is,

⇒ x ≥ 20

Learn more about the inequality visit:

https://brainly.com/question/25944814

#SPJ1

The bar diagram could describe the following real-world problem:

"Peter has an amount of $12 in a piggy bank. If he spends two-thirds of his piggy bank, what does he have now?"

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

We have to give that;

A bar diagram is shown in the figure.

Now, We can make a real-world problem that could represent the bar diagram.

So, We get;

"Peter has an amount of $12 in a piggy bank. If he spends two-thirds of his piggy bank, what does he have now?"

Hence, the above question represents the bar diagram shown.

Learn more about the algebraic expression here :

brainly.com/question/21751419

#SPJ1

The question seems incomplete, the missing graph has been attached below.

a)  v(t) = -32t + 80 feet/second  and a(t)= -32 feet/second²

b. t = 3 seconds.

c. 24 feet/second > 0).

d.  the time at which the rock reaches its highest height is 2.5 seconds and 80 feet respectively.

e. the acceleration is given by a(2.5) = -32 feet/second²

The velocity, v(t), of the rock is given by the derivative of the position function s(t) with respect to time,

v(t) = ds(t)/dt = -32t + 80 feet/second.

The acceleration, a(t) = dv(t)/dt = -32 feet/second²

b) v(3) = -32*3 + 80 = 24 feet/second.

This quantity represents the velocity of the rock at t = 3 seconds.

c) At t = 3 seconds, the rock is rising up because the velocity is positive (v(3) = 24 feet/second > 0).

d) the time at which the rock reaches its highest height,

v(t) = 0, we get -32t + 80 = 0, so t = 80/32 = 2.5 seconds.

The height of the rock will be found using the position function s(t), so s(2.5) = -16(2.5)^2 + 80(2.5) = 80 feet.

e) At the highest height, the velocity of the rock is 0, so the acceleration is given by a(2.5) = -32 feet/second².

Learn more about acceleration at: https://brainly.com/question/605631

#SPJ1

There is not enough information to determine the rates of change which is therefore denoted as option C in the table and graph given.

This is referred to as a pictorial representation or a diagram that represents data or values in an organized manner.

In the graph and table there was no clear representation of the variables in the x and y coordinates which is therefore the reason why there won't be enough information to determine the rate of change which is therefore the correct choice.

Read more about Graph here https://brainly.com/question/25184007

#SPJ1

The full question:

Compare the rates of change of the following table and graph. x y 1 -4 2 -8 3 -12 4 -16 A. The rate of change of the table is greater than the rate of change of the graph. B. There is not enough information to determine the rates of change. C. The rate of change of the table is equal to the rate of change of the graph. D. The rate of change of the graph is greater than the rate of change of the table.

Answer: The outlier of the data is 65! Hope this helps you!

The mean of the data set is $ 611 and the median of the set is $ 47

The median is the value that's exactly in the middle of a data set when it is ordered. It's a measure of central tendency that separates the lowest 50% from the highest 50% of values. The steps for finding the median differ depending on whether you have an odd or an even number of data points

Arrange the data points from smallest to largest.

If the number of data points is odd, the median is the middle data point in the list.

If the number of data points is even, the median is the average of the two middle data points in the list.

Given data ,

Let the mean of the data set be A = $ 611

The number of college freshmen = 5

Now , the equation will be

Let the number of freshmen be represented as N = { a , b , c , d , e }

So , the mean is A = ( a + b + c + d + e ) / 5

On simplifying the equation , we get

( a + b + c + d + e ) = $ 3,055   be equation (1)

And , the median of the data set is M = $ 47

So , the median is the middle data point in the list.

Let the list be represented as = { a , b , $ 47 , d , e }

Let the value of a = $ 27

Let the value of b = $ 30

Let the value of d = $ 1,000

Let the value of e = $ 1,951

So , the mean of the set is A = ( 27 + 30 + 47 + 1000 + 1951 ) / 5

On simplifying the equation , we get

The mean of the set is A = 3055 / 5

The mean of the set is A = $ 611

Hence , the median is $ 47

To learn more about median click :

https://brainly.com/question/28687994

#SPJ1

This function is not one-to-one because different ages can have the same height.

This function f(t) is not one-to-one because different ages can have the same height. For example, two people at age 20 could have the same height, even though one is 20 years old and the other is not. Additionally, two people of different ages can have the same height, such as a 5 year old and a 25 year old with the same height. One-to-one functions require that for every input there is only one output, which is not the case for this function. This is because height is not necessarily determined solely by age, and can be influenced by genetics and other environmental factors. Therefore, for any given age, there could be multiple possible heights, and this function does not satisfy the definition of a one-to-one function.

Learn more about function here

https://brainly.com/question/29633660

#SPJ4

The value of  80% of 150 is 120

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

80% of 150

The table of value is not given

However, the expression can be evaluated without the table

Using the above as a guide, we have the following:

80% of 150 =  80% * 150

Evaluate the product

80% of 150 = 120

Hence, the value is 120

Read more about percentage at

https://brainly.com/question/11360390

#SPJ1

A car is through internet is better to buy.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

In the fall of 2014,

1 U.S. dollar =  1.10 Canadian dollars.

Here, An automobile in Toronto sells for 26,000 Canadian dollars.

And, The same car on sale for 23,000 U.S. dollars on the internet.

Thus, The cost of car on internet is,

⇒ 23,000 U.S. dollars

⇒ 23,000 × 1.10 Canadian dollars.

⇒ 25,300 Canadian dollars.

Thus, A car is buy through internet is better to buy.

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

Answer:

Yards:2497.66667-Rounded up to 2498 yds. Miles: 1.41912879- or 1.4-miles Feet literally 7493 as its feet

Step-by-step explanation:

convert 7493 ft to miles, yards and feet​?

Alright, first, let's get rid of feet. 7,493 ft is feet, so all we need is to find miles and yards.

To convert feet to miles, divide feet by 5,280. So 7,493/5,280, which is 1.41912878788 miles.

To convert feet to yards, divide feet by 3. So 7,493/3, which is 2497.66666667 yards.

Hope this helped!

Answer:

5x linear monomial



-7 constant monomial

x^2+4 quadratic binomial

x^2-3x+11 quadratic trinomial

2x-9 linear binomial

Step-by-step explanation:

Linear indicates a line, the power of x in the equation is 1 (which we never write the power one, so it looks like just x)



Quadratics have an x to the power of 2

A constant is a plain number with no variable.

The prefixes mono-, bi-, and tri- can help you with these. Mono- means one. Monomials have one term, such as 5x or -7

Bi- means two. Binomials have two terms such as x^2+4 or 2x-9.

Tri- means three. Trinomials have three terms such as x^2-3x+11.

The question is:

How many Syrian citizens choose to leave the country every year for better opportunities?

A survey that is collected through the facts and numbers from the data is a quantitative survey.

We have to write a quantitative survey or simulation question(s)?

For that,

we will form the variable and target group.

The question:

How many Syrian citizens choose to leave the country every year for better opportunities?

Variable: Number of citizens looking for better opportunities

Target Group: Syrian citizens.

Hence, the question is given above.

To learn more about the quantitative survey;

https://brainly.com/question/25491466

#SPJ1

Answer:

the answer is

54

Step-by-step explanation:

substitute the inch (9) and wide (6) into formula and 9 x 6 = 54

Answer:

54

Step-by-step explanation:

length x width

9x6=54

Answer:

∠ Y = 60° , WY = 7 in

Step-by-step explanation:

the sides WX and YX are congruent then the triangle is isosceles with base angles congruent, that is

∠ Y = ∠ W = (180 - 60)° ÷ 2 = 120° ÷ 2 = 60°

Since all 3 angles in the triangle are congruent , all 60° then the triangle is equilateral with 3 congruent sides, then

WY = 7 in

The rate of change of the function y=3x+3 is 3

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

y = 3x + 3

The above function is a linear function

A linear function is represented as

y = mx + c

Where

m = slope = rate of change

Using the above as a guide, we have the following:

rate of change = 3

Hence, the rate of change is 3

Read ore about slope at

https://brainly.com/question/16949303

#SPJ1

Answer:

So, about 2.28% of men in the country are no more than 64 inches tall.

Step-by-step explanation:

First, we need to standardize the value of 64 inches to a z-score:

z = (64 - 68) / 2 = -2

We can use a standard normal distribution table or a calculator to find the percentage of men who are no more than 64 inches tall:

P(Z ≤ -2) = 0.0228

7 men should be able to dig 21 wells in approximately 4.7 days.

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

We can use the formula:

Number of days = (number of wells * number of days per well) / number of men.

So, we have

Number of days per well for 2 men:

11 days / 7 wells = 1.5714 days per well.

Using the above as a guide, we have the following:

the number of days for 7 men to dig 21 wells:

21 wells * 1.5714 days per well / 7 men = 4.7142days.

Hence, the number of days is 4.7 days.

Read more about rates at

https://brainly.com/question/24178013

#SPJ1

The graph of the linear function 2x + 3y = 1470 is given by the image presented at the end of the answer.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The function for this problem is defined as follows:

2x + 3y = 1470.

In slope-intercept format, it is given as follows:

3y = -2x + 1470

y = -0.67x + 490.

Hence the function is graphed considering that:

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

Answer:

Step-by-step explanation:

I took your points looooser hahahaha

Answer:

36.3%

Step-by-step explanation:

If a square is inscribed in a circle, the diagonals of the square must pass through the center of the circle and be equal to the diameter

Radius of circle = 72

Diameter of circle = 72 x 2 = 144

Therefore the diagonal of the square:

d = 144

If the side of a square is a, the diagonal is given by the formula

d = a√2

Plugging in the known value of d = 144 we get
a√2 = 144

a = 144/√2

Area of the square = a² = (144/√2)² = 144²/2 = 10,368

Area of the circle = πr² = (72)²  x π = 16,286 rounded to nearest integer

Area of region outside the square = 16,286  - 10, 368 = 5,918

P(point outside square) = Area of region outside square/area of circle

= 5,918/16,286

= 0.3634

= 36.34 %

= 36.3 % rounded to the nearest tenth

Answer:

If the angle between two unit vectors u and v is 3.14/3, then using the law of cosines, ||u + v||^2 = 2 + 2cos(3.14/3) = 2 + 2(0.5) = 3. Hence ||u + v|| = sqrt(3).

To find the value of k such that the system has a unique solution, no solution, or an infinite number of solutions, we can use the determinant of the coefficient matrix. If the determinant is nonzero, then the system has a unique solution. If the determinant is zero and the system of equations is inconsistent, then the system has no solution. If the determinant is zero and the system of equations is consistent, then the system has an infinite number of solutions. In this case, the determinant of the coefficient matrix is zero, which implies that the system has an infinite number of solutions.

The eigen values and eigen vectors of the matrix can be found by solving the characteristic equation, which is obtained by det(A - λI) = 0, where A is the matrix and I is the identity matrix.

For the matrix

2 1 -1

3 2 -3

3 1 -2

the characteristic equation is

(2 - λ)(3 - λ) - 3 = 0

which gives us λ = 1 and λ = 3 as the eigen values.

The corresponding eigen vectors can be found by solving the system of equations (A - λI)x = 0, where x is the eigen vector.

For λ = 1, the eigen vector is (1, -1, 1).

For λ = 3, the eigen vector is (-1, 2, 1).

If f(x) is a polynomial of degree 4 with roots 1, 2, 3, 4 and leading coefficient 1, and g(x) is a polynomial of degree 4 with roots 1, 1/2, 1/3, 1/4 and leading coefficient 1, then the limit of 1/f(x)/g(x) as x approaches infinity does not exist. This can be seen by noting that f(x) and g(x) both grow without bound as x grows without bound, so the ratio of the two polynomials also grows without bound.

Answer:

Step-by-step explanation:

To solve the equation, we can simplify the expression on the right side of the equation first:

9(7+9) = 9(16) = 144

Then, we can rewrite the equation as:

x + 81 = 144

To solve for x, we can subtract 81 from both sides:

x + 81 - 81 = 144 - 81

x = 63

Therefore, the completed equation is:

63 + 81 = 9(7+9)

Answer:

63

Step-by-step explanation:

First solve the right side of the equation by expanding the parenthesis using the BODMAS and Distributive Law:

9(7 + 9) = 9(16)

             = 144

Now equate the above answer to the left side of the equation:

—- + 81 = 144
—- = 144 - 81

   = 63

The answers both as whole numbers and fractions are given below:

In mathematics, the limit of a function is the value that the function approaches as its input (independent variable) gets arbitrarily close to a certain value, often denoted as a.

More precisely, given a function f(x), the limit of f(x) as x approaches a, written as "lim x → a f(x)", is the value that f(x) approaches as x gets arbitrarily close to a, but not necessarily equal to a.

If the limit exists and is equal to L, then we can write it as:

lim x → a f(x) = L

To solve this,

using the graph of y = f(x)

[tex]\lim_{x \to 4^+\} \frac{f(x) - 4}{f(x+3)}[/tex] = 3-4/6 = -1/6

[tex]\lim_{x \to 1^-\}{f(fx) +4) = f(4 +4) = f(8)[/tex] = 5

[tex]\lim_{h \to 0\} \frac{f(2+h) - f(2)}{h}[/tex] = f^1(2) = 1

Read more about functions here:

https://brainly.com/question/25638609

#SPJ1

Answer:

y = 1/2x +3

Step-by-step explanation:

Since they are parallel lines the slope will remain the same

now we need to find the y intercept and we will have the equation

Lucky we know that our y intercept is three

y = (slope)*x + (y intercept)

y = 1/2 x +3

more information needed. no graphs to choose.

no multiple choice given..

Answer:489

Step-by-step explanation:just divide 42,543 by 87

Answer489 I hope this helps

Step-by-step explanation:

The answer is 489 use a calculator

Answer:

p = 1,400

Step-by-step explanation:

In the simple interest rate formula, each year the same amount of interest is applied, as it's based off the initial amount invested and the interest rate.

[tex]I=P*r*t[/tex]

Where "r" is the interest rate, "t" is time, and "p" is the principle amount, or initial amount invested.

We're given the following values:

Now the only thing is generally speaking, interest is applied annually rather than monthly. So we would need to convert the 3 months into years, which we can do by dividing by 12, giving us: 0.25 years

So we actually have: t = 0.25 years

Now from here we can plug in known values, and leave anything we don't know alone. So we start with our initial formula of:

[tex]I=P*r*t[/tex]

Now from here we plug in i = 21, t = 0.25, r = 0.06 and leave "P" as "P"

[tex]21=P*0.25*0.06[/tex]

Now let's simplify the multiplication on the right side:

[tex]21 = 0.015P[/tex]

Divide both sides by 0.015:

[tex]1,400=P[/tex]

And now we have our missing value!

Answer:

no real factors

Step-by-step explanation:

-2x² - 11x - 20

try use the first 3 answers as factor, you'll see non works.