determine the quadtratic that has the following square root (5/3, 7/3)

Larry cannot make exactly 23 cents using only 4-cent and/or 9-cent stamps, but he can make any amount of postage greater than or equal to 24 cents.

The problem of finding the largest number of cents that Larry cannot make exactly using only 4-cent and/or 9-cent stamps is a classic example of the Frobenius coin problem. This problem arises in many areas of mathematics, including number theory and combinatorics.

To solve the problem, we can use the coin-changing algorithm, which is a general method for finding the largest amount that cannot be formed from any combination of two coin denominations. The algorithm states that the largest amount N that cannot be formed using denominations a and b is given by:

N = ab - a - b

In this case, a = 4 cents and b = 9 cents, so we have:

N = 4 x 9 - 4 - 9 = 23

Therefore, the largest amount of postage that Larry cannot make exactly using only 4-cent and/or 9-cent stamps is 23 cents. This means that he can make any amount of postage greater than or equal to 24 cents using these stamps.

The Frobenius coin problem has many practical applications, such as in currency systems, vending machines, and computer algorithms for making change. It also has connections to other areas of mathematics, such as group theory and geometry.

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Answer:

9

Step-by-step explanation:

You take the amount of money that the gym membership cost, $55, and you divide that into, the amount of money he has, $495, and then that will leave you with 9 months.

Hope this helps :)))

The length of each side of the courtyard is 25 meters. Then 35.36 meters long is each walkway.

In the given question, a school has a square courtyard and wants to create diagonal walkways.

The length of each side of the courtyard is 25 meters.

We have to find how long is each walkway.

By dividing the square in half to form a right triangle, you can find the solution. The Pythagorean theorem can then be used to find the hypotenuse.

According the Pythagorean Theorem

\(a^2+b^2 = c^2\)

\((25)^2+(25)^2=c^2\)

Now solving,

625 + 625 = \(c^2\)

\(c^2\) = 1250

Taking square root on both side, we get

c = 35.36 meters.

Hence, 35.36 meters long is each walkway.

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Answer: 70%

Step-by-step explanation:

\(\measuredangle A\cong \measuredangle E\implies 112=16x\implies \cfrac{112}{16}=x\implies \boxed{7=x} \\\\[-0.35em] ~\dotfill\\\\ \overline{MS}\cong \overline{NR}\implies 41=3x+5y\implies 41=3(7)+5y\implies 41=21+5y \\\\\\ 20=5y\implies \cfrac{20}{5}=y\implies \boxed{4=y}\)

Answer:

88.23

Step-by-step explanation:

The equation for the first plan is:

9 + 0.17x

The equation for the second plan is

24

Then you set the two equations equal to each other

9 + 0.17x = 24

Subtract on both sides

0.17x = 15

Divide

x = 88.23

The joint probability mass function is determined to be p(x,y) = (2/3)xy, the conditional probability p(x > 1 | y = 1) is 1/2, E(X) is 10/3, and E(Y) is 2.

To find the value of k that makes the given function a probability mass function, we need to ensure that the sum of all probabilities over the entire sample space is equal to 1.

Let's calculate the sum of probabilities:

∑∑ p(x, y) = ∑∑ k(xy)

Since the function is defined as zero when x ≠ 1 and 2y ≠ 1, we only need to consider the cases where x = 1 and 2y = 1:

∑∑ p(x, y) = k(1 * y) + k(1 * (1/2))

To make this sum equal to 1, we need:

k(y + 1/2) = 1

Since this equation holds for all values of y, we can choose a value of y that satisfies the equation. Let's choose y = 1:

k(1 + 1/2) = 1

k(3/2) = 1

k = 2/3

So, the value of k that makes the function a probability mass function is 2/3.

Now let's find p(x > 1 | y = 1):

p(x > 1 | y = 1) = p(x = 2 | y = 1) / p(y = 1)

To calculate p(x = 2 | y = 1), we use the joint probability mass function:

p(x = 2 | y = 1) = k(2 * 1) = 2/3

To calculate p(y = 1), we sum the probabilities over all x values:

p(y = 1) = ∑ p(x, 1) = p(1, 1) + p(2, 1) = k(1 * 1) + k(2 * 1) = 2/3 + 2/3 = 4/3

Therefore, p(x > 1 | y = 1) = (2/3) / (4/3) = 1/2.

To find E(X), we need to calculate the expected value of X using the joint probability mass function:

E(X) = ∑∑ x * p(x, y)

= 1 * p(1, 1) + 2 * p(2, 1)

= 1 * (k * 1 * 1) + 2 * (k * 2 * 1)

= 1 * (2/3 * 1 * 1) + 2 * (2/3 * 2 * 1)

= 2/3 + 8/3

= 10/3

Therefore, E(X) = 10/3.

To find E(Y), we need to calculate the expected value of Y using the joint probability mass function:

E(Y) = ∑∑ y * p(x, y)

= 1 * p(1, 1) + 1 * p(1, 2)

= 1 * (k * 1 * 1) + 1 * (k * 1 * 2)

= 1 * (2/3 * 1 * 1) + 1 * (2/3 * 1 * 2)

= 2/3 + 4/3

= 6/3

Therefore, E(Y) = 2.

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We can solve this system of the linear equation as follows:

Substituting the value of x = 1/5 in the next equation, we have the value for y:

Then, we have that the solutions for this system are x = 1/5 and y = 6.

Answer:

$2

Step-by-step explanation:

If Player 1 gives $2 to player 2, then player 2 would have $2 and player 1 would have $8

Answer:

2r+10-4r+4=32

-2r+14=32

-2r= 32-14

-2r=18

R= -9

Step-by-step explanation:

Answer:

acute

Step-by-step explanation:

Hope this helps

Answer:

A you can always tell by the measurements of it

Answer:

A = 8

B = -4

Step-by-step explanation:

Answer:

Step-by-step explanation:

on the photo

Hope it makes sense. If you have any questions, feel free to ask them in the comment section below. I'll be happy to help. Have a wonderful day!

Since $3964 is greater than $3665, Account 1 will provide a greater amount in 10 years compared to Account 2. Thus, you should choose Account 1 to obtain the greater amount for college savings.To determine which account will provide the greater amount in 10 years, we can calculate the future value of each account using the given interest rates and compounding methods.

For Account 1, which pays 6% annual interest compounded quarterly, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the future value of the investment

P = the principal amount (initial investment)

r = annual interest rate (in decimal form)

n = number of times the interest is compounded per year

t = number of years

Plugging in the values for Account 1:

P = $2500

r = 0.06 (6% expressed as a decimal)

n = 4 (quarterly compounding)

t = 10

A = 2500(1 + 0.06/4)^(4*10)

A ≈ $3964

Therefore, Account 1 will have a balance of approximately $3964 after 10 years.

For Account 2, which pays 4% annual interest compounded continuously, we can use the formula for continuous compound interest:

A = P*e^(rt)

Where:

A = the future value of the investment

P = the principal amount (initial investment)

r = annual interest rate (in decimal form)

t = number of years

e = the base of the natural logarithm (approximately 2.71828)

Plugging in the values for Account 2:

P = $2500

r = 0.04 (4% expressed as a decimal)

t = 10

A = 2500*e^(0.04*10)

A ≈ $3665

Therefore, Account 2 will have a balance of approximately $3665 after 10 years.

Since $3964 is greater than $3665, Account 1 will provide a greater amount in 10 years compared to Account 2. Thus, you should choose Account 1 to obtain the greater amount for college savings.

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The correct answer is,

D. The second card is the better choice because the daily periodic interest on the first card is 0.041%, compared to 0.038% on the second card.

Since, We know that;

Our daily periodic rate is = APR / 365%

For the first card it can be represented as, ( daily periodic rate equaling )

= 14.99/365

= 0.041%.

And, For the second it can be represented as, ( daily periodic rate equaling ) 0.038%.

We know because it can be given.

Compare them; 0.041% > 0.038% ( by 0.003% )

Hence, Its Making Option D correct.

Thus the answer to your problem is,

D. The second card is the better choice because the daily periodic interest on the first card is 0.041%, compared to 0.038% on the second card.

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Answer:

8.30...

Step-by-step explanation:

Answer:

8.31

Step-by-step explanation:

13^2 - 10^2 = x^2

169 - 100 = x^2

x^2 = 69 <- lol

√69 = 8.3066

8.31

Answer:

4th answer is correct

Step-by-step explanation:

First, let us make x the subject.

\(\sf \frac{x+4}{4} =\frac{y+7}{7}\)

Use cross multiplication.

\(\sf 7(x+4)=4(y+7)\)

Solve the brackets.

\(\sf 7x+28=4y+28\)

Subtract 28 from both sides.

\(\sf 7x=4y+28-28\\\\\sf7x=4y\)

Divide both sides by 7.

\(\sf x=\frac{4y}{7}\)

Now let us find the value of x/4.

To find that, replace x with (4y/7).

Let us find it now.

\(\sf \frac{x}{4} =\frac{\frac{4y}{7} }{4} \\\\\sf \frac{x}{4} =\frac{4y}{7}*\frac{1}{4} \\\\\sf \frac{x}{4} =\frac{4y}{28}\\\\\sf \frac{x}{4} =\frac{y}{7}\)

Step-by-step explanation:

(2m + 4) / 8 = w

2m + 4 = 8w

2m = 8w - 4

m = 4w - 2

Step-by-step explanation:

option A is correct.

hope this answer helps you dear! take care

uh I don't think brainly can help with this

The probability that all four songs are liked will be 0.03418 and the probability of not liking the next four songs will be 0.99658.

The probability of an event occurring is defined by probability.

Probability is also called chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.

As per the given,

Total songs = 53

Like songs = 14

Probability of selecting and liking the first song = 14/53

Now since repetition is not allowed and one like the song has been chosen out of 14 thus, the remaining songs = 13, and total songs = 43 - 1 = 52

Probability of selecting liking the second song = 13/52

Probability of selecting liking the third song = 12/51

Probability of selecting liking the fourth song = 11/50

a)

The probability of liking all songs will be 14/53 x 13/52 x 12/51 x 11/50 = 0.03418.

b)

The probability of not liking the next four songs =1 - The probability of liking all songs

The probability of not liking the next four songs = 1 - 0.03418 = 0.96582.

Hence "The probability that all four songs are liked will be 0.03418 and the probability of not liking the next four songs will be 0.99658".

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To calculate the least radius of gyration and the slenderness ratio of a hollow rectangular section with given dimensions and material thickness, we need to follow the formulas and steps involved. The least radius of gyration is a measure of the distribution of material around the centroid of a section, while the slenderness ratio provides information about the stability of the section under axial loading.

1. To calculate the least radius of gyration, we use the formula:

 r_min = sqrt((I / A))

  where I is the moment of inertia of the section and A is the cross-sectional area. For a hollow rectangular section, the moment of inertia can be calculated using the formula:

  I = ((b1 * h1^3) - (b2 * h2^3)) / 12

  where b1 and b2 are the outer and inner dimensions of the section, and h1 and h2 are the outer and inner heights of the section. The cross-sectional area A can be calculated as:

  A = (b1 * h1) - (b2 * h2)

2. To calculate the slenderness ratio, we divide the effective length of the section by the least radius of gyration:

  Slenderness ratio = L / r_min

  Given that the effective length is 6m, and considering the dimensions provided in millimeters (30cm x 15cm), we convert 60mm to meters (0.06m).

By substituting the given values into the formulas and performing the calculations, we can find the least radius of gyration and the slenderness ratio for the hollow rectangular section.

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The following can be shown about the diagonals of parallelogram PQRS to compare the proof that diagonals of a parallelogram bisect each other: B. PR and SQ have the same midpoint.

In Mathematics and Geometry, a parallelogram is a geometrical figure (shape) and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that has two (2) equal and parallel opposite sides.

In order for any quadrilateral to be considered as a parallelogram, two pairs of its parallel opposite sides must be equal (congruent). This ultimately implies that, the diagonals of a parallelogram would bisect one another only when their midpoints are the same:

(Line segment PR)/2 = (Line segment SQ)/2

Line segment PR = Line segment SQ

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Answer:

Step-by-step explanation:

Sides of the prism:

Volume:

Answer:

A non-terminating, non-repeating decimal is a decimal number that continues endlessly, with no group of digits repeating endlessly. Decimals of this type cannot be represented as fractions, and as a result are irrational numbers. Pi is a non-terminating, non-repeating decimal.

A non-repeating, non-terminating decimal is classified as an irrational numbers.

A decimal is a number that consists of a whole and a fractional part.

Given is the following statement - A non-repeating, non-terminating decimal.

A non - repeating and non - terminating decimal means is a decimal number that has no end and has no specific group of digits repeating endlessly. We cannot write such numbers in the form of x/y. Hence, these numbers are called irrational numbers.

Therefore, a non-repeating, non-terminating decimal is classified as an irrational numbers.

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Answer:

Step-by-step explanation:

the answer is 152

The values of k for which the augmented matrix follows the consistent  linear system are all the real numbers except 2 i.e. R- {2}

The linear equations become consistent when it has unique or infinitely many solutions. We have to find k according to the linear system which is consistent.

Consider the given matrix,

\(\left[\begin{array}{ccc}1&k&-4\\4&8&2\end{array}\right]\)

After dividing R2 by 2,

\(\left[\begin{array}{ccc}1&k&-4\\2&4&1\end{array}\right]\)

Now the linear equations will be,

x+ky = -4

2x+4y = 1

For infinitely many solutions it should be coincident lines so a1/a2=b1/b2=c1/c2 which is not going to happen for any value of k.

Therefore it should follow the condition of a unique solution i.e.

a1/a2\(\neq\)b1/b2

1/2\(\neq\)k/4

k\(\neq\)2

Therefore the value of k other than 2  i.e R-{2} will satisfy the linear equations.

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Answer:

9 pints

Step-by-step explanation:

if you times 9 x 50 you get 450

Answer:

The top looks like a trapezoid and so does the bottom so it's a prism.

lets find the area of the base!

15(base 1) + 7(base2) = 22

22 x 5(height) = 110

110 divided by 2( x 1/2) = 55

Now we multiply by the actual height of the TOTAL prism which is 11.

55 x 11 = 605 cubic feet, is your answer.

Formula for AREA of a trapezoid:

B1(base 1) + B2(base 2) x H(height) x 1/2 (basically just dividing by 2)

Answer:

About 525 times.

Step-by-step explanation:

You have a 5 in 8 chance of getting a consonant originally. You should try to find an equal ratio except with 840 as the second number. As of now it's      5/8 = ?/840

8 is a factor of 840 and if you divide 840 by 8 you get 105. If you actually think about it 105/840 would be an equal ratio to 1/8 so you multiply 108 by 5 to get 525.