A 12 ounce Pepsi costs $1.44. A 16 ounce Pepsi costs $2.24. Which is the better buy?

The answer choices are:
A. 12 ounce; $0.15 per ounce.
B. 16 ounce; $0.14 per ounce.
C. 12 ounce; $0.12 per ounce.
D. 16 ounce; $0.09 per ounce.

Since W satisfies all three conditions, it is a subspace of R4. And since we have shown that W = Span{u, v}, we can choose answer (C): "Since u and v are in R4 and W = Span{u, v}, W is a subspace of R4."

What is sub space?

In mathematics, a subspace is a subset of a vector space that is itself a vector space under the same operations of vector addition and scalar multiplication as the original space.

To show that W is a subspace of R4, we need to show that it satisfies three conditions:

The zero vector is in W.

W is closed under vector addition.

W is closed under scalar multiplication.

First, let's find vectors u and v such that W = Span{u,v}. We are given that a vector B in W has the form:

B = (2s + 5s + 3t, 4s - 5t, 2t, 45-50)

We can rewrite this as:

B = (7s, 4s, 0, 45-50) + (3t, -5t, 2t, 0)

So, we can take u = (7, 4, 0, -5) and v = (3, -5, 2, 0) to span W.

Now, let's check the three conditions:

The zero vector is in W:

Setting s = t = 0 in the expression for B gives us the vector (0, 0, 0, -5). This vector is in W, so the zero vector is in W.

W is closed under vector addition:

Let B1 and B2 be two vectors in W. Then, we have:

B1 = su1 + tv1 = a1u + b1v

B2 = su2 + tv2 = a2u + b2v

where a1, b1, a2, b2 are scalars.

Then, B1 + B2 is given by:

B1 + B2 = su1 + tv1 + su2 + tv2

= (a1u + b1v) + (a2u + b2v)

= (a1 + a2)u + (b1 + b2)v

which is also in W, since it can be expressed as a linear combination of u and v.

W is closed under scalar multiplication:

Let B be a vector in W and let k be a scalar. Then, we have:

B = su + tv = au + bv

where a, b are scalars.

Then, kB is given by:

kB = k(su + tv)

= (ks)u + (kt)v

which is also in W, since it can be expressed as a linear combination of u and v.

Therefore, since W satisfies all three conditions, it is a subspace of R4. And since we have shown that W = Span{u, v}, we can choose answer (C): "Since u and v are in R4 and W = Span{u, v}, W is a subspace of R4."

To learn more about sub spaces from the give link:

https://brainly.com/question/30318872

#SPJ1

Answer:

your answer is 8

Step-by-step explanation:

If you divide  322.4 by the speed 40.3 you would get 8 the amount of hours traveling the given distance.

If you dont think the answer is correct you can simply mutiply 40.3 by 8 to ensure that 322.4 miles is in fact how far you will go in that time

hope this help. Have a good day!

\

Bye

Statement (c) is correct for a simple graph. Every trail is a path, and every path is a trail.

In graph theory, a simple graph is an undirected graph with no loops or multiple edges between the same pair of vertices. A path in a graph is a sequence of vertices where each consecutive pair is connected by an edge. A trail in a graph is a path that allows for repeated vertices and edges.

Statement (a) is not correct because not every path is a trail. A path does not allow for repeated vertices or edges, whereas a trail does.

Statement (b) is not correct because not every trail is necessarily a path. A trail may contain repeated vertices or edges, but a path does not.

Statement (d) is not correct because paths and trails do have a relation. A trail is a more general concept that encompasses paths by allowing for repetition of vertices and edges.

Therefore, statement (c) is the correct statement. In a simple graph, every trail is a path, and every path is a trail.

Learn more about vertices here : https://brainly.com/question/29154919

#SPJ11

45 billion Korean Won is equal to 45 million US Dollars.

The formula for  (USD) is USD = KRW / 1000. To calculate 45 billion won in USD, we must first convert KRW to USD. 45 billion KRW is equal to 45,000,000,000 KRW. Using the formula above, we can calculate the amount of USD:

USD = 45,000,000,000 KRW / 1000

USD = 45,000,000 USD

Therefore, 45 billion won is equal to 45 million US Dollars.

To better understand this conversion, it is important to remember that one US Dollar is equal to 1000 Korean Won. As an example, if you have 10,000 Korean Won, you can convert that to USD by dividing 10,000 by 1000, which equals 10 USD. The same concept applies when converting larger numbers. To convert 45 billion KRW to USD, we must divide 45,000,000,000 by 1000, which equals 45,000,000 USD.

In conclusion, 45 billion Korean Won is equal to 45 million US Dollars.

Learn more about conversion here:

https://brainly.com/question/28770698

#SPJ4

We need to see the "given system".

Answer:

Since parallel lines never cross, then there can be no intersection; that is, for a system of equations that graphs as parallel lines, there can be no solution. This is called an "inconsistent" system of equations, and it has no solution.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given the triangle MNO which is extended through point O to point P, we are given the followings;

Interior angles;

∠MNO=(3x+11)

∠OMN=(2x+20)

Exterior angle;

∠NOP=(8x−5)

To find x, we will use the theorem, "The sum of the interior angles is equal to the exterior"

Hence;

3x+11+2x+20 = 8x - 5

5x + 31 = 8x - 5

Collect like terms;

5x - 8x = -5-31

-3x = -36

x = -36/-3

x = 12

Hence the value of x is 12

Answer: x=12

Step-by-step explanation:

Answer: x=4

Step-by-step explanation:

6x + 10 = 5x + 14

x + 10 = 14

x = 4

Answer:

8x+6y

Step-by-step explanation:

multiplyy!!

Answer: count them up on each side

Step-by-step explanation:

Answer:

mmhhh

Step-by-step explanation:

(-9,8) look where it ends

An inequality representing c, the total number of 150-kilogram crates that can be loaded into the shipping container: c ≤ 98

We know that an inequality is a mathematical statement that represents the inequalities between two algebraic expressions with two variables .

It is an unequal relation between two algebraic expressions.

Here, the greatest weight that can be loaded into the container = 26,000 kilograms

the weight of each crate = 150 kilogram

and the weight of other shipment = 11300 kilograms

Let c be the total number of 150-kilogram crates that can be loaded.

So, we get an inequality:

150 c + 11300 ≤ 26,000

150 c ≤ 26,000 - 11300

150 c ≤ 14700

c ≤ 98

Learn more about an inequality here:

brainly.com/question/28816565

#SPJ4

\(\qquad\qquad\huge\underline{\boxed{\sf Answer}}\)

Let's evaluate ~

\(\qquad \sf  \dashrightarrow \: \dfrac{1}{3 {}^{ - 2} \times {x}^{ - 4} \times {y}^{2} } \)

plug in the values :

\(\qquad \sf  \dashrightarrow \: \dfrac{1}{3 {}^{ - 2} \times {3}^{ - 4} \times { - 1}^{2} } \)

\(\qquad \sf  \dashrightarrow \: \dfrac{1}{3 {}^{ - 6} {}^{ } {}^{} } \)

\(\qquad \sf  \dashrightarrow \: {3}^{6} \)

\(\qquad \sf  \dashrightarrow \:729\)

Therefore, B is the Correct choice ~

・ ．━━━━━━━†━━━━━━━━━．・

Answer:

729

Step-by-step explanation:

Given expression:

\(\sf \dfrac{1}{3^{-2}x^{-4}y^2}\)

Apply exponent rule \(\sf \dfrac{1}{a^{-b}}=a^b\)

\(\sf \implies \dfrac{3^2x^4}{y^2}\)

\(\sf \implies \dfrac{9x^4}{y^2}\)

Substituting x = 3 and y = -1:

\(\sf \implies \dfrac{9(3)^4}{(-1)^2}\)

\(\sf \implies \dfrac{9 \cdot 81}1}\)

\(\sf \implies 729\)

A right triangle with a 45 degree angle means the two short sides are the same, so y = 30

the hypotenuse is the length of the side x sqrt (2), so x =30sqrt(2)

answer: x = 30sqrt(2) and y = 30

Answer:

y=4x

Step-by-step explanation:

Direct Variation means y=kx where k is a Constant

since y=8 when x=2

y=kx -->  8=k*2  then k=4

Then y=4x

Answer: Yes. It will be amended

Step-by-step explanation:

Since 5/6 of the 52 states in a country must approve the amendment before the country's constitution is amended, then the number of states that must approve it will be:

= 5/6 × 52

= 43.33

= 43 approximately

Since 44 states approve an​ amendment, the constitution be​ amended since it's more than 5/6 of the 52 states.

Therefore, the probability of getting 2 Jacks in a hand of 12 cards is 0.190156, rounded to 6 decimal places.

Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1. Events that are certain to happen have a probability of 1, while events that are impossible have a probability of 0. Events that are more likely to happen have a higher probability value, while events that are less likely to happen have a lower probability value. The calculation of probability involves determining the number of ways an event can happen and dividing that by the total number of possible outcomes.

Here,

o find the probability of getting 2 Jacks in a hand of 12 cards from a standard 52-card deck, we can use the hypergeometric distribution.

The total number of ways to choose 12 cards from a deck of 52 is:

C(52, 12) = 52! / (12! * 40!)

= 5,311,735,669

The number of ways to choose 2 Jacks from 4 Jacks is:

C(4, 2) = 4! / (2! * 2!)

= 6

The number of ways to choose 10 non-Jack cards from 48 non-Jack cards is:

C(48, 10) = 48! / (10! * 38!)

= 17,296,959

So the total number of ways to get 2 Jacks and 10 non-Jack cards in a hand of 12 cards is:

6 * 17,296,959 = 103,781,754

Therefore, the probability of getting 2 Jacks in a hand of 12 cards is:

103,781,754 / 5,311,735,669 = 0.0195156

To know more about probability,

https://brainly.com/question/30034780

#SPJ1

L is the collection of all binary strings that contain the character "bob" and satisfy the requirement that the residue of 2n-i modulo 3 is 1, where n is the number of characters after the first instance of "bob."

The language L is defined as follows:

L = {w = bob1...bn : [2n-i]3 = 1; n > 0} U {0}

where b represents either 0 or 1, i is the position of the first occurrence of the letter b in w (i.e., the index of the first occurrence of "bob" in w), and [x]3 denotes the remainder of x when divided by 3 (i.e., the residue of x modulo 3).

In other words, L is the set of all binary strings that contain the substring "bob" and satisfy the condition that the residue of 2n-i modulo 3 is 1, where n is the number of characters after the first occurrence of "bob".

The language L also includes the string "0" as a special case.

For example, the following strings are in L: "bob1", "bob100", "1101bob010", "00101bob1000", "0".

The following strings are not in L: "0bob", "01bob0", "bob010", "0101bob0", "111".

Learn more about Language L

brainly.com/question/30548874

#SPJ11

The smallest positive value x is mathematically given as

\(x= \pi/B\)

Generally, the equation for is mathematically given as

d) for a displacement of the wave at t=0 is 30 sec

\($A \sin (B x-C(0))=0$\)

\(\begin{aligned}-A \sin B x &=0 \\\sin B x &=\sin n \pi \\B x &=m \pi\end{aligned}\)

Therefore, x=(n \pi)/ 8

Since n equals one for the smallest value, the equation that follows provides an answer for the smallest positive value of x that can be found.

\(\begin{aligned}x &=\frac{n \pi}{B} \\&=\frac{(1) \pi}{B} \\x &=\frac{\pi}{B}\end{aligned}\)

In conclusion, the smallest positive value x is

x= \pi/B

Read more about displacement

https://brainly.com/question/11934397

#SPJ4

Complete Question

The complete Question is attached below

Answer:

-2.5

Step-by-step explanation:

25/-10 = -2.5

20/-8 = 2.5

10/-4 = 2.5

-5/2 = 2.5

so the answer is -2.5

Can I pls have brainliest

Answer:

The diameter of the floor is 6 yards

Step-by-step explanation:

Here, we are to calculate the diameter of a circular floor that has a circumference of 18.84 yards

Mathematically,

C = π * D

where C is the circumference

Plugging the values of the circumference , we have ;

18.84 = 22/7 * D

7 * 18.84 = 22D

D = (7* 18.84)/22 = 5.99 which is approximately 6 yards

f(x) and g(x) are not closed under subtraction because when subtracted, the result will be a polynomial, the correct option is B.

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminate in mathematics. Majorly used polynomials are binomial and trinomial.

Given f(x) and  g(x) two polynomial functions in the standard form of the polynomial,

According to Closure Property, when something is closed, the output will be the same as the input.

The polynomials f(x) and g(x) can be seen in the image.

On subtracting the two polynomials, the output will be a polynomial and so it is closed under subtraction.

Therefore, The reason why f(x) and g(x) are not closed under subtraction is that the outcome of subtraction will be a polynomial, making option B the best choice.

Learn more about Polynomials here:

https://brainly.com/question/11536910

#SPJ1

Complete question:

The interest earned by Mrs Grey over the 7 years is R5670. The cost of the television set 5 years ago was R20,600.

4.1.1 To calculate the interest earned by Mrs Grey over 7 years, we use the formula for simple interest: Interest = Principal x Rate x Time. Mrs Grey's principal is R18,000 and the rate is 4.5% per annum. The time is 7 years. Using the formula, we can calculate the interest as follows:

Interest = R18,000 x 0.045 x 7 = R5670. Therefore, Mrs Grey has earned R5670 in interest over the 7 years.

4.1.2 To calculate the cost of the television set 5 years ago, we need to account for the inflation rate. The cost of the television set now is R27,660. The average rate of inflation over the last 5 years is 6.7% per annum. We can use the formula for compound interest to calculate the original cost of the television set:

Cost 5 years ago = Cost now / (1 + Inflation rate)^Time

Cost 5 years ago = R27,660 / (1 + 0.067)^5 = R20,600. Therefore, the cost of the television set 5 years ago was R20,600.

4.1.3 To determine the rate of simple interest Mrs Grey should have invested her money at 7 years ago, we can use the formula for interest: Interest = Principal x Rate x Time. We know the principal is R18,000, the time is 7 years, and the interest earned is R5670. Rearranging the formula, we can solve for the rate:

Rate = Interest / (Principal x Time)

Rate = R5670 / (R18,000 x 7) ≈ 0.0448 or 4.48% per annum. Therefore, Mrs Grey should have invested her money at a rate of approximately 4.48% per annum to have earned enough interest to purchase the television set using only her original investment and the interest earned over the 7 years.

Learn more about simple interest here:

brainly.com/question/30964674

#SPJ11

The rate of interest for 2nd year is 4.1%

From the given parameters;

Rate of interest for 1st year = 2.5

As we know the formula for Simple interest is given by

                         => I = (PTR)/100

We will use this formula in the following problem

Let 100 be Feri's investment

At the Rate of interest of 2.5  

Interest on 100 = [(100(1)(2.5)]/100 = 2.5

Total amount at end of 1st year = 100 + 2.5 = 102.5

Let x be the rate of interest for 2nd year

At the rate of interest of x

interest on 100 = [(100(1)(x)]/100 = x

Total amount at end of 2st year = 102.5 + x  

Given that, at end of the 2 years, the rate of interest becomes 6.6%  

Interest on 100 at the rate of 6.6%  

=>  [(100(1)(6.6)]/100 = 6.6

=> total amount = 100 + 6.6 = 106.6

As we know in both cases, the amount must be equal

=> 102.5 + x  = 106.6  

=> x = 4.1

Therefore, The rate of interest for 2nd year = 4.1

Learn more about interest rate at: https://brainly.com/question/2294792

#SPJ1

Answer:

m is the slope so plug in y=6x+b

and b is the y intercept so the equation is y=6x+5

Step-by-step explanation:

The solution for inequality 10 - 1/2x < -18 is 0 < x < 1/56.

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

The given inequality is -

10 - 1/2x < -18

Solve the inequality to get the value for x.

First collect all the like terms -

-1/2x < -18 + (-10)

Then use arithmetic operation of addition -

-1/2x < -28

Multiply (-1) to both the sides -

-1/2x × (-1) < -28 × (-1)

1/2x < 28

Then move the coefficient of variable to right hand side of the equation -

x < -1 / (2 × (-28))

Then use arithmetic operation of multiplication and division-

x < 1/56

Therefore, the inequality is 0 < x < 1/56.

To learn more about inequality from the given link

https://brainly.com/question/11234618

#SPJ1

Answer:

y=17

Step-by-step explanation:

We move all terms to the left:

23-(y+40.)=0

We add all the numbers together, and all the variables

-(y+40)+23=0

We get rid of parentheses

-y-40+23=0

We add all the numbers together, and all the variables

-1y-17=0

We move all terms containing y to the left, all other terms to the right

-y=17

y=17/-1

y=-17

Answer:

Step-by-step explanation:

Answer is 30

Answer:

n = 4

Step-by-step explanation:

simplify left side first:

(1/2) (-4 + 6n) = -2 + 3n.

now simplify right side:

(1/3)n + (2/3) (n + 9) = (1/3)n + (2/3)n + (2/3) (9) = (3/3)n + 6 = n + 6.

so, we now have -2 + 3n = n + 6.

subtract n from both sides and add 2 to both sides

-2 + 3n - n + 2 = n + 6 - n + 2

2n = 8

n = 4

Considering the given table, we have that:

a) The modal class is 24-26.

b) The estimate of the mean is of 23 years.

The modal class of a frequency table is the class that has the most observations. In this problem, the class is of 24-26, as it has 8 observations, being the largest number.

The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

From the frequency table, consisting of 20 observations, a discrete distribution can be built, considering the half-way point of each interval. Then:

Then the estimate of the mean is:

E(X) = 0.15 x 19 + 0.1 x 21 + 0.35 x 23 + 0.4 x 25 = 23 years.

More can be learned about the mean of a discrete distribution at https://brainly.com/question/24628525

#SPJ1

[1] H 2.4

    Let us turn the pictures into equations, using the key given. Then, we will solve.

x + x + \(\frac{1}{4}\)x + 1 + 1 + 1 = x + x + x + \(\frac{1}{2}\)x

2x + \(\frac{1}{4}\)x + 3 = 3x + \(\frac{1}{2}\)x

\(\frac{9}{4}\)x + 3 =  \(\frac{7}{2}\)x

3 = \(\frac{5}{4}\)x

x = 2.4

[2] J

    We can tell the first two options are incorrect because there was a change in size, not position.

    Option H would make the shape bigger, but it becomes larger. This means the answer is option J.