The ratio of students to teachers is 72 : 3. Which statement describes this relationship?
Responses
A There are 3 students for each teacher.There are 3 students for each teacher.
B There are 8 students for every 9 teachers.There are 8 students for every 9 teachers.
C There are 36 students for every 2 teachers.There are 36 students for every 2 teachers.
D There are 24 students for each teacher.

Answer:

Step-by-step explanation:

a

Answer:

ITS A

Step-by-step explanation:

The reason why is because that dude up there said the same thing so yeah..

Answer: $ 18.08

Step-by-step explanation:

Given: Money in wallet = $25.83

Given: Money spent = $7.75

To find: Money left in the wallet after lunch = money in the wallet - money spent

                                                                     = $(25.83-7.75)

                                                                     = $ 18.08

The possible set of inequalities are;

x = -3,

x = -1,

x = 1,

x = 3,

x = 5.

Inequalities are the comparison of mathematical expressions, whether one quantity is greater or smaller in comparison to another quantity.

We use these symbols to represent inequalities, '>' , '<', '≥', '≤'

The critical points of a rational inequality are the x-values at which the inequality changes direction (from "<" to ">" or vice versa). In this case, the critical points are -1, 3, and 4.

To find the complete solution to the inequality, we need to test points on either side of the critical points. For example, if we test a value less than -1, such as -2, and find that it satisfies the inequality, then all values less than -1 also satisfy the inequality. On the other hand, if a value less than -1 does not satisfy the inequality, then no values less than -1 satisfy the inequality.

Therefore, a complete solution to the inequality can be found by testing values around each critical point. A common set of points to test for this purpose is the critical points themselves, and values just less than and just greater than each critical point.

So, a possible set of points to test to find the complete solution to the inequality is:

x = -3,

x = -1,

x = 1,

x = 3,

x = 5.

These points bracket the critical values and allow us to determine which intervals of values satisfy the inequality.

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The composite figure consists of two rectangular pyramids, volume is 45 unit³.

Pyramids are three-dimensional structures having triangle faces and have an encompassing polygon shape at its base. If the base of a pyramid is rectangular, then it is called a rectangular pyramid.

Given,

Total height of two rectangular pyramids = 10 units

height of each pyramid is 5 unit.

Base lengths are 9units and 1.5 units.

Both are connected at their bases.

Dimensions are same of both pyramids

Composite figure consists of two rectangular pyramids.

Volume of the composite figure

= 2(length × width × height)/3

= 2(9×1.5×5)/3

= 2(13.5×5)/3

= 2(67.5)/3

= 135/3

= 45 unit³

Hence, 45 unit³ is volume of composite figure, that consists of two rectangular pyramids.

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Answer:A D

Step-by-step explanation:

Answer:

If the ratio of lemon disinfectant to water is 4 oz to one gallon, then we can say that for each gallon of water, we need 4 oz of lemon disinfectant. To find how much lemon disinfectant is needed for 6 gallons of water, we can multiply the amount needed for one gallon by the number of gallons:

4 oz/gallon * 6 gallons = 24 oz

Therefore, we need 24 oz of lemon disinfectant to be added to 6 gallons of water.

Step-by-step explanation:

Answer:

Given: x * 4 oz = 6 gallons.

First, multiply 4 oz and x:

4x = 6 gallons.

Then convert 6 gallons to oz:

4x = 768 oz.

Then divide both sides by 4:

x = 192.

Suppose that, Au=0 and Av=0. Then, we already have A(u+v)=Au+Av. Now, A(u + v) = Au + Av = 0 + 0 = 0.

Now, let c and d be scalars. Using both parts of Theorem 5, A(cu + dv) = A(cu) + A(dv) = cAu + dAv = c0 + d0 = 0.

A matrix, also known as matrices, is a rectangular array or table with numbers, symbols, or expressions that are arranged in rows and columns to represent a mathematical object or a property of that object. Matrix types are not all associated with linear algebra. In particular, this applies to incidence matrices and adjacency matrices in graph theory.

Unless otherwise stated, all matrices in this article, which focuses on matrices related to linear algebra, represent linear maps or can be viewed as such. The majority of mathematical and scientific disciplines use matrices, either directly or indirectly through the use of geometry and numerical analysis.

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Answer:

Hey bro, solving this would be relatively simple. If the Redwood tree is 6 meters tall, then the height of the carpool lane sign can be easily calculated using similar triangles. Using the lengths of their respective shadows, the carpool lane sign should be 3 meters tall, because the ratio between the height of the Redwood tree and the carpool lane sign, is the same ratio as between their respective shadows (8 to 4). The based way to solve this problem would be to measure the length of the shadows, and then use the ratio to calculate the height of the carpool lane sign.

Answer:

You need to set up the problem to solve for X. X = how tall is the tree? Set up your problem in this fashion. Set up the formula then arrange to solve for X. X/9 (shadow of the tree) = 15 (how tall the building is)/6 (shadow of building) X= 15/6 * 9 To get X alone, you need to move 9 to the other side of the equation. multiply by 9 on each side. For X side, this nullifies 9 and gets 9 to the other side. X= 2.5*9 You have divided 15 by 6, now multiply by 9 to get final answer for X X=22.5 meters The tree is 22.5 meters tall.

Step-by-step explanation:

If this is not.. right ill do another answer!!

Answer:

Step-by-step explanation:

1. measurement of length

2. measurement of area

3. measurement of volume

4. measurement of weight

5. measurement of length

6. measurement of weight

7.measurement of volume

8. measurement of area

A system of equations where n is the number of nickels and q is the number of quarters he has is represented by (C) 25q + 5n = 7, n = 2q.

The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions.

An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. as in 3x + 5 = 15, for example.

There are many different types of equations, including linear, quadratic, cubic, and others.

Let's learn more about math equations in this tutorial.

So, we know that nickels are double quarters.

And nickels are represented by n and quarters are represented by q.

Then, we can write as:
n = 2q

Then, the equation that represents the situation will be:

25q + 5n = 7

Therefore, a system of equations where n is the number of nickels and q is the number of quarters he has is represented by (C) 25q + 5n = 7, n = 2q.

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Answer: X axis , Y axis , y=-2

Step-by-step explanation:

Answer:

The average of all the data is calculated in statistics. 

However, statistics is a field that goes beyond average and is not a complete science of it. 

There are other additional statistical tools. 

which explains how statistics is an extension of mathematics.

the coach can form 4 teams of 9 boys and 9 girls each, and there will be 9 players left over who cannot form a complete team.

The GCD (Greatest Common Divisor), also known as the HCF (Highest Common Factor), is the largest positive integer that divides two or more integers without leaving a remainder.

For example, the GCD of 12 and 18 is 6, because 6 is the largest positive integer that divides both 12 and 18 without leaving a remainder.

Given by the question.

To form teams with an equal number of boys and girls, we need to find the greatest common divisor (GCD) of 36 and 45.

The prime factorization of 36 is 2^2 x 3^2, and the prime factorization of 45 is 3^2 x 5.

The common factors are 3^2 = 9. Therefore, the GCD of 36 and 45 is 9.

This means that the coach can form teams of 9 boys and 9 girls each.

To find out how many teams he can form, we need to divide the total number of boys and girls by the number of players on each team:

Number of teams = Total amount of players / Number of players per team

Number of teams = (36 + 45) / 18

Number of teams = 81 / 18

Number of teams = 4 with a remainder of 9

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The required solutions of the given system of equation are  x = 1 and y = 1.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

To find the values of x and y that satisfy the system, we need to solve the equations simultaneously:

y = -2x + 3 ... (1)

y = 5x - 4 ... (2)

Setting the right-hand sides of (1) and (2) equal to each other, we get:

-2x + 3 = 5x - 4

Simplifying this equation, we get:

7x = 7

Dividing both sides by 7, we get:

x = 1

Substituting x = 1 into either equation (1) or (2), we get:

y = -2(1) + 3 = 1

Therefore, the only solution that satisfies both equations is x = 1 and y = 1.

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The accumulated amount will be ​$133.

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

Given that;

A student invests ​$70 each month in an ordinary annuity with 3% interest compounded monthly.

We know that;

⇒ Simple interest = P × r × t

Where, P is principle amount , 'r' is rate and t is time.

Here, P = $70

r = 3%

n = 30 years

Substitute all the values, we get;

Hence, We get;

⇒ Interest = P × r × t

⇒ Interest = 70 × 0.03 × 30

⇒ Interest = $63

Hence, The accumulated amount will be ;

⇒ P + Interest

⇒ $70 + $63

⇒ $133

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The correct answers are: a reflection across the x-axis and a translation 1, unit right,  a rotation of 180° about the origin and a translation of 1 unit left.

To check for congruence, we need to verify that the two triangles have the same shape and size, which means that one triangle can be mapped onto the other using a sequence of transformations.

For the first sequence of transformations (a reflection across the x-axis and a translation 1 unit right), we can reflect triangle ABC across the x-axis, which will map (-6, 2) to (-6, -2), (-4, 6) to (-4, -6), and (-2, 2) to (-2, -2). We can then translate the reflected triangle 1 unit to the right, which will map (-6, -2) to (-5, -2), (-4, -6) to (-3, -6), and (-2, -2) to (-1, -2). This mapped triangle is triangle ADEF, and since it was obtained by a sequence of transformations, we can conclude that ABC is congruent to ADEF.

For the second sequence of transformations (a rotation of 180° about the origin and a translation of 1 unit left), we can rotate triangle ABC 180° about the origin, which will map (-6, 2) to (6, -2), (-4, 6) to (4, -6), and (-2, 2) to (2, -2). We can then translate the rotated triangle 1 unit to the left, which will map (6, -2) to (5, -2), (4, -6) to (3, -6), and (2, -2) to (1, -2). This mapped triangle is also ADEF, and since it was obtained by a sequence of transformations, we can conclude that ABC is congruent to ADEF.

Therefore, the correct answers are:

a reflection across the x-axis and a translation 1 unit right

a rotation of 180° about the origin and a translation of 1 unit left.

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Function to calculate amount of coffee in Dave's system after x hours

= y = 135(0.6)ˣ

An exponential function is a Mathematical function in the form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to.

Given,

Dave drinks 12-ounce cup of coffee each morning

One cup has 136 mg of caffeine

caffeine in his system decreases about 40% every hour
In x hours,

Amount of caffeine in his system

y = a(1 - 40/100)ˣ

or

y = 136(1-0.4)ˣ

y = 135(0.6)ˣ

Hence, y = 135(0.6)ˣ is the function to calculate amount of caffeine in system of Dave after x hours.

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Answer:

504

Step-by-step explanation:

3780÷7.5=504

504 mph because 504 x 7.5 = 3780

Please give good review. :)

Farid is able to produce 8 small pies.

Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.

here, we have,

Given: For the filling, Farid blends 1 pound of each blackberries, blueberries, and raspberries. Following that, he spoons 6 ounces of the filling into each tiny pie pan.

We need to find How many tiny pies can be made if he wants to use all of the filling.

Raspberries, blueberries, and blackberries, each weighing 1 pound, are combined by Faris for the filling.

3 pounds of filler total from 1+1+1= 3*16 ounces.

1 pound equals 16 ounces. = 48 ounces

Each little pie tin is filled with 6 ounces of filling by Faris.

48 ounces divided by 6 ounces equals 8 mini pies.

Hence, the Farid made 8 mini pies with 6 ounces.

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The additional piece of information needed to prove that ΔLKN ~ ΔKNM by the SAS similarity theorem is; MN/LK||MN.

The SAS (Side-Angle-Side) similarity theorem states that if two triangles have two pairs of corresponding sides that are in proportion, and the included angles are congruent, then the triangles are similar.

In this case, we are given that ΔLKN and ΔKNM share the angle at vertex K, and we know that LN/MN and LK/KN are in proportion.

However, we need to establish that MN/LK||MN, that means MN is parallel to LK and forms a transversal with LN.

This information is necessary to establish that the included corresponding sides are congruent, which is required for the triangles to be similar.

Therefore, the additional piece of information needed to prove that ΔLKN ~ ΔKNM by the SAS similarity theorem.

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Three equal payments of $1,468834.26 made today, in month 10, and in month 15, with 5% semiannual interest, will be sufficient to cover the debt of $4,000,000 that matures in month 7.

To replace the obligation of $4,000,000 that matures in month 7, we need to calculate the size of three equal payments that can be made today, in month 10, and in month 15, that will cover the debt with interest.

First, we need to determine the semiannual interest rate. The annual interest rate is 10%, so the semiannual interest rate is 5% (10%/2).

Next, we can use the present value formula to calculate the size of the equal payments:

PV = PMT * [(1 - (1 + r)^-n) / r]

where PV is the present value of the debt, PMT is the size of the equal payments, r is the semiannual interest rate, and n is the number of semiannual periods.

Since the debt matures in month 7, which is the end of the sixth month, and the payments will be made today (month 0), in month 10 (the end of the ninth month), and in month 15 (the end of the fourteenth month), we have three semiannual periods to consider.

Using the values we have, we can substitute them into the formula:

PV = $4,000,000

r = 5%

n = 3

$4,000,000 = PMT * [(1 - (1 + 5%)^-3) / 5%]

Solving for PMT, we get:PMT = $1,468834.26

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Translation:

Replace an obligation of $4,000,000 that matures in month 7, by three equal payments, one today, another in month 10 and the final one in month 15, considering an interest of 10% Cash Semiannual.

Answer:

√2

Step-by-step explanation:

√3 x√2/√3 =√2

Answer:

 [tex]\sqrt{2}[/tex]

explanation:

[tex]\frac{\sqrt{6} }{\sqrt{3} }[/tex]

= [tex]\sqrt{2}[/tex]

(Decimal: 1.414214)

The probability of randomly selecting a number between 1 and 1000 (including both ends) which is divisible by 3, 3 and 5, and 3 or 5 is 33.3%, 6.6%, and 46.7%, respectively.

To find the probability of randomly selecting a number between 1 and 1000 (including both ends), we can count the number of the desired outcomes and divide it by the total number of possible outcomes.

a. To find the probability of randomly selecting a number between 1 and 1000 (including both ends) which is divisible by 3, we can count the number of multiples of 3 between 1 and 1000, and divide by the total number of possible outcomes.

The first multiple of 3 is 3, and the last multiple of 3 that is less than or equal to 1000 is 999.

999/3 = 333

So there are 333 multiples of 3 between 1 and 1000.

probability = 333/1000 = 0.333 = 33.3%

b. To find the probability of randomly selecting a number between 1 and 1000 (including both ends) which is divisible by 3 and 5, we can count the number of multiples of 15 (the least common multiple of 3 and 5) between 1 and 1000, and divide by the total number of possible outcomes.

The first multiple of 15 is 15, and the last multiple of 15 that is less than or equal to 1000 is 990.

990/15 = 66

So there are 66 multiples of 15 between 1 and 1000.

probability = 66/1000 = 0.066 = 6.6%

c. To find the probability of randomly selecting a number between 1 and 1000 (including both ends) which is divisible by 3 or 5, we can count the number of multiples of 3 or 5 (or both) between 1 and 1000, and divide by the total number of possible outcomes.

To count the number of multiples of 3 or 5, we can add the number of multiples of 3 and the number of multiples of 5, and then subtract the number of multiples of 15 (to avoid double-counting).

The number of multiples of 3 between 1 and 1000 is 333, the number of multiples of 5 is 200, and the number of multiples of 15 is 66.

probability = (200 + 333 - 66)/1000 = 0.467 = 46.7%

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The total revenue function is 60x.

The total cost function is 35x + 450.

The profit function is 25x - 450.

Since we have a constant selling price of GH 60, a fixed cost of GH¢450 and a variable cost of GH¢35 an item.

Let x be the number of items

Total revenue function =  constant selling price * x

Total revenue function = 60x

Total Cost Function = Variable cost + Fixed cost

Total Cost Function = 35x + 450

Profit function = Total revenue function - Cost function

Profit function = 60x - (35x + 450)

Profit function = 60x - 35x - 450

Profit function = 25x - 450

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Answer:

The correct answer is C) The scale factor is multiplied by the scale figure's lengths.

When using a scale factor, you are typically working with a "scale figure," which is a smaller or larger version of the original figure. To determine the lengths of the original figure using a scale factor of 0.25, you would multiply each length of the scale figure by 0.25.

For example, if the scale figure has a length of 8 units, you would multiply 8 by 0.25 to get 2, which would be the corresponding length of the original figure. So if the original figure was four times larger than the scale figure, it would have a length of 32 units (4 times 8).

Therefore, when using a scale factor to determine the lengths of an original figure, you need to multiply each length of the scale figure by the scale factor to get the corresponding length of the original figure.

Step-by-step explanation:

Answer:70

Step-by-step explanation:

Given: <f and <c ratio 2:5

To find: <f and <c

Solution: 2x+5n=180' minus 110'

7n=70'

x=10'

<f= 2x10=20'

<e= 5x10=50'

The sum of <F and <E

= 20'+50'=70'

Answer:

100

Step-by-step explanation:

1.) Plug in the values of x and y into the equation

10(20/2)

2.) Divide 20 by 2

10(10)

3.) Multiply 10 by 10

100

First press button 9, then press the button on which the (^) sign is mentioned. Then button press 6. Then the value you get is 531,441.

At the point when the important parts and fundamental cycles of a mathematical technique are given qualities, the articulation's outcome is the consequence of the calculation it portrays.

The meaning of straightforwardness is simplifying something to accomplish or get a handle on while likewise making it somewhat less troublesome.

The expression is given below.

⇒ 9⁶

First press button 9, then press the button on which the (^) sign is mentioned. Then button press 6.

The value of the exponent numerical expression 9⁶ will be 531,441.

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The correct question is given below.

What is the correct sequence of steps for calculating 9⁶ on a scientific calculator?

Answer:

2,508 shoppers

Step-by-step explanation:

Ratio of female to male : 10:9

Let F be the number of female shoppers and M be the number of male shoppers

That can be expressed as
[tex]\dfrac{F}{M}= \dfrac{10}{9}[/tex]

Given M = 1188

[tex]\dfrac{F}{1188}= \dfrac{10}{9}[/tex]

Multiply both sides by 1188

[tex]\dfrac{F}{1188} \times 1188= \dfrac{10}{9} \times 1188\\\\F = 1,320[/tex]

Total number of shoppers = M + F
= 1188 + 1320
= 2,508 shoppers

The Taylor series expansion of f(h) = ln(3 - 2h) around h = 0 is given by:

f(h) = f(0) + f'(0)h + R(h)

where f(0) = ln(3), f'(0) = -2/3, and R(h) is the remainder term.

To find the remainder term, we need to take the higher-order derivatives of f(h) and evaluate them at h = 0. We have:

f''(h) = 4/(3(3 - 2h))^2, f'''(h) = -32/(3(3 - 2h))^3, and so on.

Evaluating these at h = 0, we get f''(0) = 4/9 and f'''(0) = -32/27.

Thus, the remainder term can be expressed as:

R(h) = (1/2)f''(xi)h^2 = (1/2)(4/9)(xi)^2h^2 = (2/9)(xi)^2h^2

where xi is some unknown constant between 0 and 4.

Therefore, the first two terms in the Taylor series expansion of f(h) are:

ln(3) - (2/3)h

and the remainder term involves the unknown constant xi, given by R(h) = (2/9)(xi)^2h^2.

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