there are 17 mathematics majors and 325 computer science majors in a college. in how many ways can one representative be picked who is either a mathematics major or a computer science major?

The probabilities for each case are.

a) P =  9/64

b) P =  3/28

All the marbles have the same probability of being randomly selected, then the probability of getting a red marble is given by the quotient between the number of red marbles and the total number of marbles.

p = 3/8

Now we put the red marble back and we take one again, again with the same probability:

q = 3/8

The probability of these two events happening in sequence is given by the product of the two probabilities:

P = (3/8)*(3/8) = 9/64

b) Now we don't replace the red marble, then the probability of getting a second one is 2/7, because we didn't replace the first one we took.

Then the joint probability is:

p = (3/8)*(2/7) = 3/28

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Answer:

a lot

Step-by-step explanation:

If baseball team scored 5 more runs in its second game than its first. The team scored twice as many runs as the first game in the third game. The total number of runs in all three games was 29.Then 11 runs were scored in the second game

Two or more expressions with an Equal sign is called as Equation.

Let the runs scored by team in first game be x.

The team scored 5 more runs in its second game than its first.

x+5

The team scored twice as many runs as the first game in the third game.

2x

The total number of runs in all three games was 29

This we can write as x+x+5+2x=29

Add x variable terms

4x+5=29

Subtract 5 on both sides

4x=24

x=6

So the score in the second game will be x+5=6+5=11

Hence, 11 runs were scored in the second game

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(p+s)*3

(6.50+4.00)*3= 31.5 dollars

1) so if they spent p and s for each person then you need to times it by 3 bc there were 3 people

eg: if popcorn was 1 dollar and a drink was 2 dollars then 1 +2 dollars= 3 and thats how much one person spent but because there are three ppl, we times by 3 to get 9 dollrs use the same method for questions number 1

2) and q2 is the same kinda strategy as i explained so, 6.50+4.00= 10.5 and bc there are 3 ppl then times by 3= 31.50 dollars

make sure to add a zero at the end bc we are talking about money

Hope this helps!! x

Answer:

the answer is 20 .put the 5 in place of x                                                                          

and u always remember that f(5) =f(x)

Step-by-step explanation:

To determine if vector u belongs to the null space of matrix A, we need to perform matrix-vector multiplication between A and u. The null space of a matrix consists of all vectors that, when multiplied by the matrix, result in the zero vector. If A * u = 0, where 0 is the zero vector, then u belongs to the null space of matrix A.

To answer your question, we first need to understand what the null space of a matrix is. The null space of a matrix A, denoted as null(A), is the set of all vectors x such that Ax = 0. In other words, the null space of a matrix is the set of solutions to the homogeneous equation Ax = 0.
Now, if we want to know whether a vector u belongs to the null space of a matrix A, we need to check whether Au = 0. If Au = 0, then u belongs to the null space of A.
So, to answer your question, we need to check whether Au = 0. If it does, then u belongs to the null space of A. If it doesn't, then u does not belong to the null space of A.
The null space of a matrix is an important concept in linear algebra because it helps us understand the behavior of linear transformations and the properties of matrices. The null space is also closely related to the rank of a matrix, which is the dimension of the column space of the matrix. The rank-nullity theorem states that the rank of a matrix plus the dimension of its null space equals the number of columns in the matrix. This theorem is a fundamental result in linear algebra and has many important applications in fields such as engineering, physics, and computer science.

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Answer:

1

Step-by-step explanation:

-f + 2 + 4f = 8 - 3

3f = 6 - 3

3f = 3

f = 1

Answer:

f=1

Step-by-step explanation:

-f+2+4f=8-3

First what you want to do i that you want to simplify as best as you can.

-f+2+4f=8-3 becomes 3f+2=8-3 because you add the 4f to the -1f.

Then, just subtract 2 from both sides to get 3f=8-5

Now, simplify even more

3f=8-5 becomes 3f=3

It should be easy now, but if you still need help, divide

f=1

Step-by-step explanation:

volume= y×9×10=2700

90y=2700

y= 2700/90

y= 30 cm

Answer:

3.4166666666667

Step-by-step explanation:

Answer:

w= -12

Step-by-step explanation:

okay I understood it now. Here you go.

You’re welcome :)

Answer:

w= -12

Step-by-step explanation:

x both sides by 24

4w + 15 + -33

move the constant to the right  and change its sign

4w= -33 -15

calculate the difference ...

4w = -48

divide both sides by 4

w= -12

The statement, When two events are disjoint, they are also independent is false.

In a sample space, we can use probability laws to determine the probabilities of these events and how they relate to each other. Disjoint Events: Two events are non-overlapping or mutually exclusive if they have no common outcome. Mathematically, this can be written as, P(B ∩ A) = 0 --(1)

Independent Events: Events are independent when they do not "affect" the probability of another event occurring. Mathematically written as:

P(B/A) = P(B) P(A and B)

=> P(B ∩ A) = P(B) × P(A) --(2)

(1) ) and (2) events cannot be independent unless they overlap. That is, if events do not overlap, they are also dependent. Hence, disjoint events are not independent that means the above statement is false.

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Answer:

Find the slope of the original line and use the point-slope formula y−y1=m(x−x1)to find the line parallel to y=4x.

y=4x+4

Step-by-step explanation:

Answer:  10

Step-by-step explanation:

As shown below, ∠ABD = ∠DAC = x.

That means tan(x) = 5 by AD and that tan(x) = AD by 20

You can set those two equations equal to each other to find the length of AD:

5 by AD = AD by 20

5 = AD square by 20

100 = AD square

AD = Square root 100 = 10

Answer:

12

Step-by-step explanation:

let a = AB b=AD c=AC

from the pythagorean theorem:

(1)a² + c² = (16+9)² = 625

(2) b² +16² = a²

(3) 81+ b² = c²

by substitution into (1):

(b²+16²) + (81+b²) = 625

2b² = 625-81-256 = 288

b² = 144

b = 12

Answer:

Explanation:

Given the expression:

First, rewrite the fraction by separating the constants, and variables a and b.

Next, apply the division rule of exponents:

So, we have:

The simplified form of the expression without any negative exponent is:

Answer:

No, because a triangle will have to add up to 180 degrees. And if the two angles are already set for both triangles, there is only one answer that will make these triangles equal 180 degrees. So no there is no way possible.

Step-by-step explanation:

If the man had put $17 in the bank at 3% interest compounded continuously, then the formula for finding the final amount is A = Pe^(rt),   Therefore, the $17 would have been worth $396.44 in 2005 if it was put in the bank at 3% interest compounded continuously.

where A is the final amount, P is the initial amount, e is the mathematical constant, r is the interest rate, and t is the time in years.
Using this formula, we can calculate the value of $17 after 341 years (2005-1664). Plugging in the values, we get:
A = 17e^(0.03*341)
A = $396.44
Therefore, the $17 would have been worth $396.44 in 2005 if it was put in the bank at 3% interest compounded continuously.
In 2005, the $17 investment in 1664 at a 3% interest rate compounded continuously would be worth $D. To calculate this, we can use the formula for continuous compounding:
A = P * e^(rt)
Where:
A = the future value of the investment
P = the principal amount ($17)
e = the base of the natural logarithm (approximately 2.718)
r = the annual interest rate (0.03)
t = the number of years (2005 - 1664 = 341 years)
A = 17 * e^(0.03 * 341)
A ≈ 17 * e^10.23
A ≈ 17 * 27769.3
After rounding to the nearest dollar, the value of the investment in 2005 would be approximately $472,178.

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(A) The equation for the population p in terms of time t in minutes is:

                  \(P = 250 * 3^{t/16}\)

(B) The population after one hour is 267.5

According to the Question,

Given that,

(B) Tyrell is working in a lab testing bacteria populations. After starting out with a population of 250 bacteria, he observes the change in population and notices that the population triples every 15 minutes.

Therefore, the equation for the population P in terms of time t in minutes is

   \(P = 250 * 3^{t/16}\)

(B) The population after one hour.

   \(P = 250 * 3^{t/16}\\P = 250* 3^{1/16} \\P = 250*3^{0.0625}\)    P

Or, P = 250 × 1.07

Or, P = 267.5

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Answer:

7

Step-by-step explanation:

42/6=7

Step-by-step explanation:

By Pythagoras' Theorem, the sum of squares of the side lengths of a right-angled triangle is the square of its hypotenuse.

In Question 11, 2^2 + 1^2 = a^2. a = √5.

In Question 12, 2^2 - 1^2 = b^2. b = √3.

Answer:

Because 4 divided by 11 does not have an exact answer, it just keeps going on.

Step-by-step explanation:

Math in Focus, it's important to first understand the key components of the program, which include problem-solving strategies, critical thinking skills, and the use of real-world examples to reinforce concepts.

Math in Focus is a comprehensive math program designed to help students develop a deep understanding of mathematical concepts.

To get help with  One way to get help with Math in Focus is to work with a tutor or teacher who is knowledgeable about the program and can provide personalized instruction and support.

Additionally, students can use online resources, such as practice problems and video tutorials, to reinforce their learning and gain additional practice. Finally,

it's important for students to stay organized and keep up with the pace of the curriculum, as Math in Focus builds on concepts throughout the school year. With these strategies in place, students can excel in Math in Focus and build a strong foundation in math.

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Answer:

y = 18

Step-by-step explanation:

3.23(y – 18) - 19.17 = -19.17

3.23y - 18 x 3.23 = -19.17 + 19.17

3.23y - 58.14 = 0

3.23y = 58.14

3.23y/3.23 = 58.14/3.23

y = 18

Answer:

the answer is 864 in3

Step-by-step explanation:

Jerome photographed an aquarium that measured 12 inches by 18 inches by 24 inches.

So V=LxWxH....

12 x 18 x 24= 5,184

Then...

Lim photographed an aquarium that was 12 inches by 30 inches by 12 inches.

So= V=LxWxH

12 x 30 x 12=4,320

And they need to see who has more so 5,184-4,320=864in3

I hope this helps also Into Math said it was correct :)

Answer: (0,10)

Step-by-step explanation:

Answer:

4 m

Step-by-step explanation:

Let h represent the height reached by the tip of the rod on the wall.  The bottom tip of the rod is 3 m from the base of the wall.  Now a right triangle with horizontal leg 3 m and vertical leg h is formed with a hypotenuse of 5 m.  The Pythagorean Theorem applies here and enables us to find the value of h:

h^2 + (3 m)^2 = 5^2, or:

h^2 = 25 - 9 = 16

The top of the rod is h = √16, or 4 m, above the ground.

To answer this question, I'll need to provide a detailed explanation of the given piecewise function:

Cost = $20 for the first 2 lines, $5 for each additional line up to 10 lines, and $3 for each additional line over 10.

1) How much does each extra line cost?
Each extra line after the first two lines costs $5 up to 10 lines and $3 for each additional line over 10.

2.) Find the cost of a 4-line ad.
Since the first two lines cost $20 and each additional line costs $5, a 4-line ad would cost $20 + ($5 x 2) = $30.

3.) Find the cost of a 6-line ad.
Similarly, a 6-line ad would cost $20 + ($5 x 4) = $40.

4.) Find the cost of a 17-line ad.
For a 17-line ad, the cost would be $20 for the first two lines, $5 x 8 (for lines 3-10), and $3 x 7 (for lines 11-17). This gives us a total cost of $20 + ($5 x 8) + ($3 x 7) = $71.

In conclusion, each extra line costs $5 up to 10 lines and $3 for each additional line over 10. The cost of a 4-line ad is $30, a 6-line ad is $40, and a 17-line ad is $71.

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Answer:

<--------o           o------------->

         -4           2

Step-by-step explanation:

Because the sign in the inequalities is only greater than/ less than (not equal to), we know that there is an open dot on x=-4 and on x=2.

From there, we shade the area on the graph that is true to the function.  So, we can test points.

First we will test x=-5

-5<-4  --> this is true, so we will shade to the left of x=-4

Now test x=0

0<-4  --> this is false

0>2  --> this is also false, so the area between the two open dots will not be shaded

Now test x=3

3>2  --> this is true, so we will shade to the right of x=3

There are 4,320 ways to select six of the letters of the word algorithm and write them in a row if the first letter must be "a".

There are 7 letters in the word "algorithm", and we need to select 6 of them and arrange them in a row such that the first letter is "a". We can first choose the remaining 5 letters from the remaining 6 letters (excluding "a") in 6 choose 5 ways

⁶C₅ = 6!/5! = 6

Once we have chosen the 5 letters, we can arrange the 6 selected letters (including "a") in a row in 6! ways. Therefore, the total number of ways to select 6 letters and arrange them in a row with the first letter being "a" is

⁶C₅ × 6! = 6 × 720 = 4,320

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Answer:

8

Step-by-step explanation:

Kari has 2 choices for jackets and 4 choices for jumpsuits. We'll multiply those together to find the number of options she has.

Since the numbers are very small, we can grind out this same number (but be organized):

Jean/white

Jean/tan

Jean/green

Jean/black

Leather/white

Leather/tan

Leather/green

Leather/black

These are the eight choices.

One product/service that is currently in the decline stage is DVD rentals. The decline can be attributed to the rapid rise of digital streaming platforms and the decreasing popularity of physical media. Companies competing in a declining market have strategic options such as harvesting and divesting. Harvesting involves maximizing profits from the declining product/service by reducing costs and maintaining a loyal customer base, while divesting involves exiting the market and reallocating resources to more profitable ventures.

DVD rentals are in the decline stage of the product lifecycle due to several factors. The advent of digital streaming platforms like Netflix, Hulu, and Amazon Prime Video has revolutionized the way people consume media. The convenience and vast content libraries offered by these platforms have led to a significant decline in DVD rentals. Moreover, the proliferation of high-speed internet connections and the increasing availability of streaming devices have made it easier for consumers to access digital content.

In a declining market, companies have strategic options to consider. One option is harvesting, which involves maximizing profits from the declining product/service. Companies can achieve this by reducing costs associated with production, distribution, and marketing, as the demand for the product/service diminishes. They may also focus on retaining their loyal customer base by providing incentives, discounts, or exclusive offers. For example, DVD rental companies may lower rental fees, offer bundle deals, or introduce loyalty programs to retain their remaining customers.

Another strategic option is divesting, which involves exiting the declining market altogether. Companies may choose to reallocate their resources to more profitable ventures or invest in emerging technologies or industries. In the case of DVD rentals, companies could divest by shutting down physical rental stores and selling off their DVD inventory. They could then shift their focus to digital streaming services or invest in other areas with growth potential, such as content production or streaming device manufacturing.

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