Sammy opened a college savings account. She opened the account with $85, and then

deposited $45 each month. Which equation best models the relationship between m, the

number of monthly deposits Sammy made, and S, the total amount in Sammy's college savings

account?

A. s= 85m - 45

B. s=45m - 85

C. s= 85m + 45

D. s= 45m + 85

Answer:

6:40pm

Step-by-step explanation:

60-41 = 19

46-19=27 ---> finished playing basketball at 3:27pm

60-27=33

54-33=21 ----> finished swimming at 5:21pm

21+19=40 ----> finished dinner at 6:40pm

Answer:

6:40

Step-by-step explanation:

You need to add the minutes each time separately, starting at the result of the last addition problem.

Answer:

$25 = $6.50d

Step-by-step explanation:

Since d represents the amount of boxes of donuts, you would need to multiply d in the equation by 6.5 or $6.50 since the problem states that 1 dozen donuts costs $6.50 (assuming 1 box contains 1 dozen donuts). $6.50d would have to equate or equal to $25 because the equation 25 = 6.5d shows the most amount of boxes of donuts Tucker could purchase with $25.

If you were wondering, Tucker could purchase up to 3 boxes donuts with $25.

Answer:

cost of 1 box = $6.50

total money =$25

he want $26 to buy 4 boxes

The function T(n) in terms of the number of operations is:

T(n) = 2n^3 + 3n^2 + 2n + 1 and the asymptotic complexity of the matrix multiplication algorithm is O(n^3).

To analyze the provided pseudo code for matrix multiplication and determine the function T(n) in terms of the number of operations, we need to examine the code and count the number of operations performed.

The pseudo code for matrix multiplication may look something like this:

```

MatrixMultiplication(A, B):

   n = size of matrix A

   C = empty matrix of size n x n

   for i = 1 to n do:

       for j = 1 to n do:

           sum = 0

           for k = 1 to n do:

               sum = sum + A[i][k] * B[k][j]

           C[i][j] = sum

   return C

```

Let's break down the number of operations step by step:

1. Assigning the size of matrix A to variable n: 1 operation

2. Initializing an empty matrix C of size n x n: n^2 operations (for creating n x n elements)

3. Outer loop: for i = 1 to n

- Incrementing i: n operations  

- Inner loop: for j = 1 to n

- Incrementing j: n^2 operations (since it is nested inside the outer loop)

- Initializing sum to 0: n^2 operations

- Innermost loop: for k = 1 to n

- Incrementing k: n^3 operations (since it is nested inside both the outer and inner loops)

- Performing the multiplication and addition: n^3 operations

- Assigning the result to C[i][j]: n^2 operations

- Assigning the value of sum to C[i][j]: n^2 operations

Total operations:

1 + n^2 + n + n^2 + n^3 + n^3 + n^2 + n^2 = 2n^3 + 3n^2 + 2n + 1

Therefore, the function T(n) in terms of the number of operations is:

T(n) = 2n^3 + 3n^2 + 2n + 1

To determine the asymptotic (big O) complexity of the algorithm, we focus on the dominant term as n approaches infinity.

In this case, the dominant term is 2n^3. Hence, the asymptotic complexity of the matrix multiplication algorithm is O(n^3).

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The statement is not always true.

The statement is only sometimes true.

We have,

Part A:

The statement "the product of two negative rational numbers is greater than either factor" is never true.

Let a = -1/2 and b = -1/3.

Then ab = (-1/2)(-1/3) = 1/6, which is less than both a and b.

Let c = -1/4 and d = -2/3.

Then cd = (-1/4)(-2/3) = 1/6, which is also less than both c and d.

Both of these examples demonstrate that the product of two negative rational numbers can be less than either factor and therefore the statement is not always true.

Part B:

The statement "the product of two positive rational numbers is greater than either factor" is sometimes true, but not always. To see why, consider the following examples:

Let e = 1/2 and f = 1/3.

Then ef = (1/2)(1/3) = 1/6, which is less than both e and f.

Let g = 2/3 and h = 3/4.

Then gh = (2/3)(3/4) = 1/2, which is greater than both g and h.

These examples demonstrate that the product of two positive rational numbers can be less than either factor (in the first example) or greater than both factors (in the second example).

Therefore, the statement is only sometimes true.

Thus,

The statement is not always true.

The statement is only sometimes true.

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The ratio of 2 meters to 76 centimetres is 50: 19.

In mathematics, a ratio is a comparison of two or more numbers that indicates their sizes in relation to each other.

In simpler terms, a ratio compares values.

Let's find the ratio of 2 meters to 76 centimetres as follows:

We have to first convert the units so they will be same.

Hence,

1 cm = 0.01 m

76 cm = ?

cross multiply

length in metres = 76 × 0.01

length in metres = 0.76 metres

Therefore, let's multiply the 2 units by 100.

0.76 × 100 = 76 metres

2 × 100 = 200 metres

In ratio, 200 : 76 will be simplified as 50 : 19

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Answer: (a^2 - 4)/(x^2 - 9) + (a^2 - 2a + (2-y))/(xy + 3y) - (x-3)

Step-by-step explanation: First, you need to simplify the fraction in the first term:

(a^2 - 4)/(x^2 - 9)

Next, you simplify the fraction in the second term:

(a^2 - 2a + (2-y))/(xy + 3y)

Then you subtract (x-3) from the fractions obtained in step 1 and 2:

(a^2 - 4)/(x^2 - 9) + (a^2 - 2a + (2-y))/(xy + 3y) - (x-3)

This is the final result of the operation.

It is important to note that the answer is a simplified fraction and only valid if x does not equal 3. If x=3, the denominator x-3 would be equal to zero, which is not allowed in mathematics.

If the school now has 1,378 students enrolled, last year, the number of students enrolled was B. 1,300.

Using the mathematical operations of addition, subtraction, division, and multiplication, we can determine the number of students.

Mathematical operations help us to determine unknown values, given a known domain.

Increase in school enrollment over last year's = 6%

Enrollment for the current year = 1,378

Let last year's enrollment = 100%

And the current year's = 1.06 (100 + 6)

Therefore, the enrollment last year = 1,300 (1,378/1.06)

Thus, the enrollment (number) last school year was B. 1,300.

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To calculate John's BMI, we need to use the formula BMI = weight (kg) / height (m)^2. When we calculate this, we get a BMI of 36.1.

First, we need to convert John's height and weight to the metric system. His height is 1.75 meters and his weight is 110.5 kilograms.
Next, we can plug those values into the formula: BMI = 110.5 / (1.75)^2.
According to the Centers for Disease Control and Prevention, a BMI of 30 or above is considered obese. Therefore, John falls into the obese category based on his BMI.
It's important to note that BMI is just one measure of health and does not take into account muscle mass or other factors that can affect weight. It's always best to speak with a healthcare professional to determine a healthy weight and lifestyle plan.

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Answer:

a) Arc  length (l) = 36 inches

b)

The nearest angle in degrees θ = 103.18°

Step-by-step explanation:

Step(i):-

An arc has a central angle of 1.8 radians and a radius of 20  inches.

Given arc has a central angle of 1.8 radians and

radius of circle = 20 inches

Given arc has a central angle (θ ) = 1.8 radians

Arc  length (l) = r θ

                 l = 20 × 1.8 radians

              l  = 36

The length of arc = 36 inches

b)

we will convert radians to degree

1.8 × 180° / π =  324° / π ≅ 103.18°

The nearest angle in degrees θ = 103.18°

The Total surface area of each given figure are:

g) 165 in²

h) 869 in²

i) 1146.57 ft²

j) 400 m²

g) The area of a triangle is given by the formula:

Area = ¹/₂ * base * height

Area of left triangle = ¹/₂ * 10 * 8 = 40 in²

Area of right triangle = ¹/₂ * 10 * 25 = 125 in²

Total surface area = 40 in² + 125 in²

Total surface area = 165 in²

h) This will be a total of the trapezium area and triangle area to get:

Total surface area = (¹/₂ * 22 * 19) + (¹/₂(22 + 38) * 22)

Total surface area = 209 + 660

Total surface area = 869 in²

i) Total surface area is:

T.S.A = (50 * 30) - ¹/₂(π * 15²)

T.S.A = 1146.57 ft²

j) Total surface area is:

TSA = 20 * 20 (This is because the removed semi circle is equal to the additional one and when we add it back to the square, it becomes a complete square)

TSA = 400 m²

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The laser starts at vertex $a$ and fires a laser beam towards point $x$ on side $\overline{bc}$ of the square $abcd$.

Let's consider the path of the laser beam. It will bounce off the sides of the square at a $45^\circ$ angle since the square has equal sides. Each time the laser beam hits a side, it reflects and changes direction by $90^\circ$.

We are given that the laser beam bounces off the sides $1998$ times before hitting point $x$. This means that it will hit each side $1999$ times (the initial hit plus $1998$ reflections). Since there are four sides to the square, the laser beam will make a total of $4 \times 1999 = 7996$ hits on the sides of the square.

Now, let's find the distance between vertex $a$ and point $x$.

Since the laser beam hits each side $1999$ times, the total distance it travels along the sides of the square is $1999$ times the perimeter of the square. The perimeter of the square is $4$ units, so the total distance is $1999 \times 4 = 7996$ units.

Since the side length of the square is $1$, the distance between vertex $a$ and point $x$ is $7996$ times the length of one side, which is $7996 \times 1 = 7996$ units.

Therefore, the distance between vertex $a$ and point $x$ is $7996$ units.

The distance between vertex $a$ and point $x$ is $7996$ units.

This means that the laser beam will hit point $x$ after traveling a distance of $7996$ units along the sides of the square.

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Answer:

it is a rational number

Step-by-step explanation:

hope dis helps ;D

Answer:

irrational

Step-by-step explanation:

A rational number is one that can be written as the ratio of two integers. For example 3=3/1, −17, and 2/3 are rational numbers.So in that case 2/3 is irrational.

The number of adult tickets that were sold would be = 435 tickets.

A ticket is an official document that gives an individual access to an event.

The cost of adult tickets = $8

The cost for student tickets = $4

The number of students tickets sold = X

The number of adults tickets sold = X +30

The told number of tickets sold = 840

To find X;

X + X + 30 = 840

2x + 30 = 840

2x = 840-30

2x = 810

X = 810/2

X = 405

Therefore, the number of tickets sold for adults = 405 +30 = 435 tickets.

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Answer:

-0.89

Hope I helped

Answer:

pllllc

13 Ib, 35 Ib ,resultant force 30 Ib,no;20

The concept of consecutive integers is explained as follows:

Consecutive numbers, or consecutive integers, are integers that follow each other in order. The difference between any two consecutive numbers is always 1. For example, the consecutive numbers starting from 1 would be 1, 2, 3, 4, 5, and so on. Similarly, the consecutive numbers starting from -3 would be -3, -2, -1, 0, 1, 2, and so on.

It is important to note that if we have a consecutive sequence of integers, one number will be even, and the next number will be odd. This is because the parity (evenness or oddness) alternates as we move through consecutive integers.

Furthermore, the sum of two consecutive numbers (and, in fact, the sum of any number of consecutive numbers) is always an odd number. This is because when we add an even number to an odd number, the result is always an odd number.

To generate a sequence of consecutive integers, we can start with any integer n and then use n, n+1, n+2, and so on to obtain consecutive integers. For example, if n is an integer, then n, n+1, and n+2 will be consecutive integers.

Here are some examples of consecutive integers:

- Starting from 1: 1, 2, 3, 4, 5, ...

- Starting from -3: -3, -2, -1, 0, 1, 2, ...

- Starting from 1004: 1004, 1005, 1006, 1007, ...

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Different logs measure different physical properties of the formation that are related to porosity, and the relationship between the log measurement and porosity can be expressed through equations.

The different logs used to obtain porosity and their principles of measurement, quantities measured, and relation to porosity.
There are three main types of logs used to obtain porosity: neutron logs, density logs, and sonic logs.
Neutron logs: These logs measure the hydrogen content in a formation, which is directly related to porosity. The tool emits neutrons that interact with hydrogen atoms, and the resulting gamma rays are measured. The count rate decreases with increasing porosity. The neutron log can be expressed as:
Porosity = (neutron log reading - matrix reading) / (fluid reading - matrix reading)
Density logs: Density logs measure the bulk density of a formation, which can be related to porosity. The tool emits gamma rays that interact with the formation, and the scattered gamma rays are measured. The bulk density decreases with increasing porosity. The density log can be expressed as:
Porosity = (matrix density - bulk density) / (matrix density - fluid density)
Sonic logs: Sonic logs measure the travel time of sound waves through a formation, which can be related to porosity. The tool sends an acoustic wave and measures the time it takes to travel a specific distance. The travel time increases with increasing porosity. The sonic log can be expressed using Wyllie's time-average equation:
Porosity = (sonic log reading - matrix reading) / (fluid reading - matrix reading)
In summary, neutron logs measure hydrogen content, density logs measure bulk density, and sonic logs measure travel time of sound waves. These measurements can be used to calculate porosity using the respective equations provided.

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Answer:

your friend is wrong

Step-by-step explanation:

There is a theorem in geometry called the Exterior Angle Theorem which was developed by Euclid (Greek mathematician that lived in Alexandria around 300 B.C.) that states that the exterior angle of a triangle will always equal the sum of the 2 nonadjacent interior angles.

If you look at the attached image, °d = °a + °c

To solve for t2 in the equation t2/t1=(p2/p1)^(n-1/n), we can cross-multiply to get t2=(p2/p1)^(n-1/n) * t1.


In the given equation, t2/t1 represents the ratio of two temperatures, while (p2/p1)^(n-1/n) is a ratio of pressures raised to a power. The exponent of (n-1/n) in the equation represents the ratio of specific heats, which is a constant value for a given gas. Thus, we can rewrite the equation as t2/t1= (p2/p1)^k, where k = (n-1/n).

To solve for t2, we can multiply both sides of the equation by t1, which gives us t2= (p2/p1)^k * t1.


Therefore, the equation to solve for t2 is t2= (p2/p1)^(n-1/n) * t1.

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To determine which set of data most likely has a mean closest to 29.5, we need to analyze the shape and position of the histograms in relation to the value 29.5.

Looking at the histograms described:

The first histogram ranges from 9 to 48, and the upward trend starts from 1 and ends at 33, followed by a downward trend. This histogram suggests that there may be values lower than 29.5, which would bring the mean below 29.5.

The second histogram ranges from 15 to 48, with an upward trend from 1 to 30 and then a downward trend. Similar to the first histogram, it suggests the possibility of values lower than 29.5, indicating a mean below 29.5.

The third histogram ranges from 12 to 56, and the upward trend starts from 1 and ends at 32, followed by a downward trend. This histogram covers a wider range but still suggests the possibility of values below 29.5, indicating a mean below 29.5.

The fourth histogram ranges from 15 to 54 and exhibits multiple trends. While it has fluctuations, it covers a wider range and includes both upward and downward trends. This histogram suggests the possibility of values above and below 29.5, potentially resulting in a mean closer to 29.5.

Based on the descriptions, the fourth histogram, with its more varied trends and wider range, is most likely to have a mean closest to 29.5.

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Simplified form of the expression 8 ( 3 + 4 ) using the Distributive Property of Multiplication over Addition is 56

To apply the Distributive Property of Multiplication over Addition, you need to multiply the number outside the parentheses by each term inside the parentheses and then add the products together.

In this case, the number outside the parentheses is 8, and the terms inside the parentheses are 3 and 4. So, you can apply the distributive property as follows:

8 ( 3 + 4 ) = 8 × 3 + 8 × 4

Multiply the numbers

= 24 + 32

Add the numbers

= 56

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Answer:

10 feet

Step-by-step explanation: 2+2=4  3+3=6   4+6=10

Step-by-step explanation:

50 +29+3022+378+2920

120+333839+2828

r

A complex number by its conjugate, we multiply the real parts and the imaginary parts separately. Finally, the result is: 85

The given complex number is 7 + 6i.

The conjugate of 7 + 6i is 7 - 6i.

Now, let's multiply them:

(7 + 6i)(7 - 6i)

Using the FOIL method (First, Outer, Inner, Last), we get:

(7)(7) + (7)(-6i) + (6i)(7) + (6i)(-6i)

Simplifying each term:

49 - 42i + 42i - 36i^2

Notice that i^2 represents -1, so we can simplify further:

49 - 36(-1)

49 + 36

Finally, the result is: 85

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The base of an exponent is a number that is increased to a definite power. So, the base of an exponent defines the number that is multiplied by itself.

The exponent means how many times the base number is multiplied.

The power can be expressed as the number obtained by increasing the base number to the exponent.

So, in the power \(a^{n}\), the letter “a” is the base. The letter n is the exponent.

It says, a is multiplied by itself n number of times.

Example - (-5) ² = (-5) × (-5) = 25

Example: (-5)³ = (-5) × (-5)× (-5) = -125

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Subtract 4 from both sides of the equation, then subtract f from both sides and divide both sides by -7/2 to solve for f.

In order to solve for f, the equation must be manipulated to isolate it on one side of the equation. To do this, the equation must be manipulated algebraically. First, subtract 4 from both sides of the equation. This will move the constant part to the other side of the equation, leaving only the f on the left side. Then, subtract f from both sides, which will move the f to the other side and leave only the constant on the left side. Finally, divide both sides of the equation by -7/2. This will move the coefficient of f to the other side and will leave only f on one side of the equation, thus isolating it. The resulting answer is f=1. This process of manipulating the equation algebraically is called solving the equation for f.

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Answer:

B.  16

Step-by-step explanation:

x² − 8x = 10

x² − 8x + (-4)² = 10 + (-4)²

x² − 8x + 16 = 10 + 16 --------- added 16 to both sides.

to finish the equation..

x² − 8x + 16 = 26

(x - 4)² = 26

\(\sqrt(x - 4)^2 = \sqrt{26}\)

x = \(\sqrt{26} + 4\)

x = \(4 - \sqrt{26}\)

Answer:

\(\Huge \boxed{\mathrm{B. \ 16}}\)

\(\rule[225]{225}{2}\)

Step-by-step explanation:

\(x^2-8x=10\)

The equation is in the form ax² + bx = -c. The value of b in the equation is -8.

To complete the square, we need to add (b/2)² = (-8/2)² =  -4² = 16 to both sides.

\(x^2-8x+16=26\)

Factoring left side of the equation.

\((x-4)^2 =26\)

Taking the square root of both sides.

\(x-4=\pm\sqrt{26}\)

Adding 4 to both sides.

\(x=4\pm\sqrt{26}\)

\(\rule[225]{225}{2}\)

A sample has a mean of m = 86. if one new person is added to the sample, the sample mean will increase.

There are various mean types in mathematics, particularly in statistics. Each mean helps to summarize a certain set of data, frequently to help determine the overall significance of a specific data set.

Imply a quantity that falls somewhere between the values of the extreme members of a set in mathematics. There are different types of means, and how they are calculated relies on the relationship that is known about or is regarded as governing the other members.

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Answer:

x=All real numbers

Step-by-step explanation:

2x+x+5=7x-4x+5

3x+5=3x+5

3x=3x

0=0

Any value of x will make the equation a true statement, so it has an infinite number of solutions.