1. At Franklin High School, there are 480 male students, 320 female students, and 40
teachers. Find the following ratios and write them as a fraction in simplest form.
1A. Female students to male students
2. Teachers to male students

1. At Franklin High School, There Are 480 Male Students, 320 Female Students, And 40teachers. Find The

Answers

Answer 1
1. 2/3 is the ratio for female student to male students
2. 1/12 is the ratio for teachers to male students
3. 20/1 is the ratio for the total amount of students to teachers
4.3/5 is the ratio for male students to the total amount of students

Explanation:
1. To get the simplest ratio for 320/480 you need to divide both numbers by 160 and if solved correctly, you would get 2/3 and that number cannot be simplified any further so your answer will be 2/3.
2. To get the simplest ratio for 40/480 you need to divide both number by 49 and if solved correctly, you would get 1/12 and that number cannot be simplified any further so that would be your final answer
3. For this, you first need to find the total amount of students and this is easy by just adding 480 and 320. The answer will be 800 and to find the simplest fraction of 800/40, simply divide both numbers by 40 and you will get 20/1
4. Since we now know the total amount of students we just need to find the simplest answer for 480/800 and the greatest number you can divide both of these by is 160 and your answer would be 3/5 which is also the most simplest ratio.

Related Questions

Sally's class is raising money for charity with a goal of raising $2,000. They raise $997 at a bake sale and $961 at a car wash. Sally wants to see if they raised enough money to meet their goal. Complete the statements.

Answers

Sally's class haven't raised $2,000 as the amount made is $958. The estimated value is $1900. The amount needed is $42.

How to illustrate the value?

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

In this case, Sally's class is raising money for charity with a goal of raising $2,000. They raise $997 at a bake sale and $961 at a car wash. Sally wants to see if they raised enough money to meet their goal. The amount made will be:

= $997 + $961

= $1958

They have not made $2000. The amount left is:

= $2000 - $1958

= $42

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How many grams are in 3.29 X 10²5 molecules of water (H₂O)?

Answers

Water molecules with a mass of 3.34 * (10 )23 weigh 9.911 grams.

What is the mass in grams of 3.34 x 1023 molecules of H2O?

Firstly, you wish to transform the quantity of water molecules you have into the quantity of moles.

Undoubtedly, you are aware

Number of Particles = Mole Ratio x Avogadro's Constant

Avogadro's constant is equal to 3.34 * (10) 23 / 6.02  * (10) 23 when the number of moles is equal to the number of particles.

=0.55

so 0.55 moles

Consequently, mass/molar mass = number of moles.

Since we must determine the mass, we can use the formula Mass = Number of Moles x Molar Mass.

H 2 O's molar mass is calculated as H - 2(1.01) = 2.02 O- 16 18.02

Consequently, 18.02 g/mol is the molar mass.

We now possess the necessary values to determine the mass because of this.

Mass =  0.55 × 18.02

Mass = 9.911

As a result, the 3.34 mass

There are 9.911 grams in 3.34 * (10 )23 water molecules.

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Using the cosine rule calculate the magnitude of angle B when dide b=20.8cm c= 14.5cm and a= 9.3cm

Answers

Using the cosine rule calculate the magnitude of angle B when did the b=20.8cm c= 14.5cm and a= 9.3cm is [tex]\approx 37.02364^{\circ}[/tex]

What is cosine rule?c = [a2 + b2 - 2ab cos C] is the cosine formula to get the side of the triangle. a, b, and c are the triangle's three sides. When attempting to link all three sides of a triangle to a single angle, the cosine rule can be applied. You need to know the other two sides as well as the opposing angle in order to determine the length of a side. Your objective is to locate side a. With the aid of the sine rule, one can determine an angle from three sides and an angle or a side from three angles and a side.

Given,

b=20.8cm c= 14.5cm and a= 9.3cm

[tex]\gamma=\cos ^{-1}\left(\frac{a^2+b^2-c^2}{2 a b}\right)[/tex]

[tex]=\cos ^{-1}\left(\frac{9.3^2+20.8^2-14.5^2}{2 \cdot 9.3 \cdot 20.8}\right)[/tex]

[tex]\approx 37.02364^{\circ}[/tex]

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The volume of each cube is 1/64ins^3 Multiply the number of cubes needed to fill the prism by the volume of each cube to find the volume of the prism. Include units.


4. Instead of using cubes, Kaia uses the formula V = 1 x w × h. Fill in the spaces bel to complete her work. Include units.
V=lxwxh
V=
in3

Answers

Volume of a cube = a3

here a = 4

  then = a3 = 4^3 =64

The rectangular prism shows 12 cubes: 3 rows and 4 columns.

The volume of a prism is the area of the base times the height,

The volume of a rectangular prism is the length times width times height,

The volume of a cube is the length of one side cubed,

Volume of a rectangular prism = (length x width x height) cubic units.

V = (l x w x h) cubic units

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Triangles S, M, and L are scaled copies of one another. Determine the area of each triangle.

Answers

The area of each triangle is given as follows:

Triangle S: 4 units squared.Triangle M: 16 units squared.Triangle L: 36 units squared.

How to obtain the area of a triangle?

The area of a triangle is given by half the multiplication of the base and the height, as follows:

Area = 0.5 x base x height.

The dimensions for each triangle are given as follows:

Triangle S: base 2, height 4.Triangle M: base 4, height 8.Triangle L: base 6, height 12.

Hence the areas are:

Triangle S: 0.5 x 2 x 4 = 4.Triangle M: 0.5 x 4 x 8 = 16.Triangle L: 0.5 x 6 x 12 = 36.

Missing Information

The triangles are given by the image presented at the end of the answer.

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Determine the type of dilation shown and the scale factor used.

Enlargement with scale factor of 1.5
Enlargement with scale factor of 2.5
Reduction with scale factor of 1.5
Reduction with scale factor of 2.5

Answers

The type of dilation and scale factor in the figure shown is

Enlargement with scale factor of 2.5

How to find the type of dilation

Scale factors are used to increase or decrease image. The situation of increment is usually called magnifying or enlargement.

The given problem is enlargement since the preimage is smaller than the image. Also the scale factor will be greater than 1

Taking a point of reference say side 6 in the preimage and side 15 in the image and solve for the factor, assuming the factor is k

6k = 15

k = 15/6

k = 2.5

hence we say that the scale factor is 2.5

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Answer: Enlargement with scale factor of 2.5

Step-by-step explanation: I took the quiz so you don't have too!

How many images are formed If two plane mirror are position at an angle of 45â°?

Answers

The number of images that will be formed when two mirrors are positioned at an angle of 45 degrees is 7.

The formula that you have provided for calculating the number of images formed by two mirrors positioned at a specific angle is (360/n) - 1, where n is the angle between the mirrors in degrees.

When two mirrors are positioned at an angle of 45 degrees, n = 45. So, using the formula, the number of images formed would be: (360/45) -1 = 8 - 1= 7

It's important to note that this formula only gives you the approximate number of images that will be formed. In reality, due to the nature of light and the reflective properties of mirrors, it is impossible to determine the exact number of images that will be formed.

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Jon earns £90 one week. The next week, he receives a pay rise and earns £130. Write the amount of his pay rise as a fraction of his original pay. Give your answer in its simplest form.

PLEASE HELP I REALLY NEED IT FOR HOMEWORK

Answers

The fraction of Jon original pay is 4/10

How to calculate the fraction of Jon original pay?

Jon earns  £90  one week

The following week he earns  £130

His pay rise is

130-90

= 40

The fraction of his original pay is

= 40/100

= 4/10

Hence the fraction of Jon original pay is 4/10

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Molly jogged at a rate of 6 mph, what was her speed in feet per second?

Answers

Answer:

8.8 feet per second

Step-by-step explanation:

1 mile = 5280 feet

3600 seconds = 1 hour

6 mph = 5280(6)/3600 = 528/60 8.8 feet per second


Alex made a table to record how many trees were in his yard for each day that the landscapers were working. Which equation represents the data?

Answers

The answer would be C

please help im stuck like really stuck

Answers

Answer:

[tex]14v+7=7(2v+1)[/tex]

Step-by-step explanation:

break down the equation 14v +7

Answer:

7(2v+1)

Step-by-step explanation:

7 goes into 14 twice and into itself once so its factorised as 7(2v+1) you can do the multiplication to test it .

You are measuring the height of a spruce tree. You stand 45 feet from the base of the
tree. You measure the angle of elevation from the ground to the top of the tree to be
59. Find the height h of the tree to the nearest foot.

Answers

Provided the given distance and the angle of elevation, Using the trigonometry in the right angled triangle formed, The answer is 74.89 feet.

What is trigonometry?

Trigonometry is the branch of mathematics that deals with the relationships between the angles and sides of triangles, particularly right triangles. Trigonometry is used to study properties such as lengths, angles, and areas of triangles and the relationships between them. It is also used in many fields, including physics, engineering, and navigation. Trigonometry is based on the study of the ratios of the sides of a right triangle. The three main ratios are sine, cosine, and tangent. These ratios are defined using the right triangle's angles and are often abbreviated as sin, cos, and tan. In addition to these three main ratios, there are also several other trigonometric functions, including cosecant, secant, and cotangent. These functions are the reciprocals of the sine, cosine, and tangent functions, respectively.

What is a right triangle?

A right triangle is a type of triangle that has one angle that measures exactly 90 degrees. This angle is called the right angle and the two sides that form the angle are called the legs of the triangle. The side opposite the right angle is called the hypotenuse. A right triangle can also be defined as a triangle that has a 90-degree angle and two acute angles. The legs of the triangle are the sides that are opposite the acute angles, and the hypotenuse is the side that is opposite the right angle.

tan(A) = rise/run

tan(59) = height/45

height = tan(59)*45

=74.89 feet

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) Select the inequality that the number line represents. Use x as the variable.

Answers

The number line represents an inequality. The inequality is x  ≥ -3.

What is a number line?

A number line is a picture of a graduated straight line that serves as a visual representation of real numbers in primary mathematics. Every number line point is considered to correspond to a real number and every real number to a number line point.

If a number line contains a close circle, then the number includes in the inequality.

If a number line contains an open circle, then the number does not include in the inequality.

In the graph, there is a close circle on -3.

The line represents all real numbers greater than -3.

Since there is a close circle on -3, thus -3 include in the inequality.

The given variable is x.

The graph represents all real numbers greater than or equal to -3.

The inequality is x  ≥ -3.

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Y=x2+2x-2 graph each quadratic function

Answers

By evaluating the quadratic equation we can get some points, and with them we can estimate the graph.

The graph can be seen in the image at the end.

How to graph the quadratic equation?

Here we want to graph the function:

y = x^2 + 2x - 2

To do so, we can evaluate the quadratic equation in some values of x to get points, and then just connect the points with a general parabola.

when x = 0

y = 0^2 + 2*0 - 2 = -2

So the point is (0, -2)

when x = 1

y = 1^2 + 2*1 - 2 = 1 + 2 - 2 = 1

So the point is (1, 1)

when x = -1

y = (-1)^2 + 2*(-1) - 2

y = 1 - 2-  2 = -3

So the point is (-1, -3)

when x = -2

y = (-2)^2 + 2*(-2) - 2

y = 4 - 4 - 2 = -2

So we have the point (-2, -2)

And so on..., eventually, you will get enough points to connect, and you should get something like:

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How to prove 3 points are collinear in 3d using section formula?

Answers

The section formula provides a way to check if three points in 3D space are collinear by verifying that the equation (x2 - x1)(y3 - y1) - (x3 - x1)(y2 - y1) = 0 is satisfied when their coordinates are substituted.

To prove three points are collinear in 3D using the section formula, first determine the coordinates of the three points. Then, substitute the coordinates into the section formula equation, (x2 - x1)(y3 - y1) - (x3 - x1)(y2 - y1) = 0. Finally, calculate the equation and if it is equal to 0, the three points are collinear.

For example, if the coordinates of three points are (x1, y1, z1), (x2, y2, z2) and (x3, y3, z3), then the three points are collinear if the following equation is satisfied:

(x2 - x1)(y3 - y1) - (x3 - x1)(y2 - y1) = 0

If the equation is not equal to 0, the points are not collinear. To illustrate, if the coordinates of three points are

(x1, y1, z1), (x2, y2, z2) and (x3, y3, z3),

then the three points are collinear if the following equation is satisfied: (x2 - x1)(y3 - y1) - (x3 - x1)(y2 - y1) = 0.

If this equation is not equal to 0, then the three points are not collinear. To check if the points are collinear, one must calculate the equation and determine if the equation is equal to 0. If so, the three points are collinear.

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i need a solution and where its graphed please help

Answers

Case 1: The linear equations has infinite solutions.

Case 2: The linear equations has no solution.

How to find the solution of a system of linear equations graphically

In this problem we find two cases of systems of two linear equations with two variables, which are described by a system of the form:

a · x + b · y = c

d · x + e · y = f

Where:

a, b, d, e - Dependent variable.c, f - Independent variable.

The solution of this kind of systems can be found graphically on Cartesian plane, whose procedure is described briefly:

Determine x-intercept on each line.Determine y-intercept on each line.Mark the intercepts on Cartesian plane.Construct the resulting lines. Mark the point of intersection of the two lines.

Now we proceed to find the solution for each case:

Case 1

Line 1: y = 0.5 · x + 1

y-Intercept

y = 0.5 · 0 + 1

y = 1

(x, y) = (0, 1)

x-Intercept

0 = 0.5 · x + 1

0.5 · x = - 1

x = - 2

(x, y) = (- 2, 0)

Line 2: - 2 · x + 4 · y =  4

y-Intercept

- 2 · 0 + 4 · y = 4

4 · y = 4

y = 1

(x, y) = (0, 1)

x-Intercept

- 2 · x + 4 · 0 = 4

- 2 · x = 4

x = - 2

(x, y) = (- 2, 0)

Since the two lines have the same intercepts, then there are infinite solutions.

Case 2

Line 1: y = - x - 3

y-Intercept

y = - 0 - 3

y = - 3

(x, y) = (0, - 3)

x-Intercept

0 = - x - 3

x = - 3

(x, y) = (- 3, 0)

Line 2: y + x = 2

y-Intercept

y + 0 = 2

y = 2

(x, y) = (0, 2)

x-Intercept

0 + x = 2

x = 2

(x, y) = (2, 0)

The system of linear equations has no solution as both lines are parallel.

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4^(3x)= 16^(x-2)

Solve for x.

Answers

Answer:

x = -4

Step-by-step explanation:

4^(3x) = 16^(x-2)

First, we create equivalent expressions in the equation that all have equal bases.

4^3x = 4^2(x-2)

Since the bases are the same, two expressions are only equal if the exponents are also equal.

3x = 2(x − 2)

3x = 2x -4

x = -4

So, the answer is x = -4

What is the solution to the system of equations y equals one over 3x 10?

Answers

The solution to the given system of equations y = 1/3x - 10 and 2x + y = 4 is (6, -8).

y = 1/3x - 10 … (1)

2x + y = 4 … (2)

We can use the substitution method to determine the solution of the given system of linear equations.

Substituting (1) in (2), we get

⇒2x + (1/3 x - 10) = 4

⇒2x + 1/3 x - 10 = 4

⇒(6 + 1)/3 x = 14

⇒7/3 x = 14

⇒7x = 14 × 3

⇒7x = 42

Dividing both sides by 7

x = 6

Place the value of x in equation (1)

⇒y = 1/3 (6) - 10

⇒y = 2 - 10

⇒y = -8

--The given question is incomplete, the complete question is

"What is the solution to the system of equations y = 1/3x - 10 and 2x + y = 4?"--

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Is square root of 4 a polynomial?

Answers

Square root of 4 is not a polynomial. It is a quadratic function. Functions containing other operations like square root is not a polynomial.

A polynomial need not have any square root.  polynomial is a finite sequence form. it must contain no square roots of variables, no fractional or negative powers on the variables, and no variables in the denominators of any fractions. Polynomial are sums and differences of polynomial terms. For an expression to be a polynomial term, any variables in the expression must have whole number powers. It should not have any square root, cube root or any negative values. Quadratic function can have square root cube roots and fraction values.

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What value breaks 100 into 4 equal pieces?

Answers

Answer:

25 :)

Step-by-step explanation:

John i 7 year younger than jane. The um of their age i 10 year ago wa 55 year. How old are they now

Answers

John 38 years old and Jane 45 years old 10 years ago from the present age .

John: 48 years old

Jane: 55 years old

Jane is 55 years old and John is 7 years younger, so John is 55 - 7 = 48 years old.

John is 7 years younger than Jane, so if we subtract 7 years from Jane's age, we can find John's age. Jane is 55 years old, so if we subtract 7 years, we get 55 - 7 = 48. Therefore, John is 48 years old, and Jane is 55 years old. To find their age 10 years ago, we can subtract 10 years from each of their current ages. This would make John 38 years old and Jane 45 years old 10 years ago from the present age

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Which is the discriminant of the equation x2 =-- 4x 4?

Answers

Answer:  The discriminant of a quadratic equation ax² + bx + c = 0 is given by the formula:

b² - 4ac

Given the equation x^2 - 4x - 4 = 0, we can find the discriminant by substituting the values of a, b, and c into the formula:

b² - 4ac = (-4)² - 4(1)(-4) = 16 + 16 = 32

So, the discriminant of the equation x^2 - 4x - 4 = 0 is 32.

Step-by-step explanation:

What is the symmetric of -15??​

Answers

Answer:

The symmetric of -15 is 15.

Step by step explanation:

When we talk about symmetric, we must remember that it means the opposite of a number, that is, we take as a basis the number line where we have zero (0) as the central number, on one side the negative infinite numbers (-) and on the other, the positive infinite number (+), see the attached image.

In order to solve this type of exercise, just change the signs of the number in question, if it is negative it will become positive and vice versa.

[tex] \bold{- 15 = + 15}[/tex]

What is the symmetric of -15??
The symmetric of -15 is
Answer = 15

3. The Lovely Day Fruit company makes two varieties of fruit drink, Fruit Delight and Heavenly Punch. The chart below shows how much juice goes into each type and the profit per can of juice. Each week, the company receives a shipment of 9000 ounces of pineapple juice, 24000 ounces of orange juice, and 14000 ounces of apricot juice. Fill in the question marks appropriately and then use the linear programming process to find how many cans of each should be made each week to maximize profit.

Answers

The optimal solution is x = 2000 and y = 4000, meaning that 2000 cans of Fruit Delight and 4000 cans of Heavenly Punch should be made each week to maximize profit.

Fruit Delight:

Pineapple juice: 3 oz

Orange juice: 6 oz

Apricot juice: 2 oz

Profit: $1.50

Heavenly Punch:

Pineapple juice: 6 oz

Orange juice: 2 oz

Apricot juice: 4 oz

Profit: $2.00

Linear Programming Process:

We can use linear programming to solve this problem. We will create two variables, x and y, to represent the number of cans of Fruit Delight and Heavenly Punch respectively. The objective is to maximize profit, which can be expressed mathematically as:

Maximize: 1.50x + 2.00y

subject to:

3x + 6y ≤ 9000

2x + 4y ≤ 14000

6x + 2y ≤ 24000

x ≥ 0

y ≥ 0

Using linear programming software, we can solve this problem and find that the optimal solution is x = 2000 and y = 4000, meaning that 2000 cans of Fruit Delight and 4000 cans of Heavenly Punch should be made each week to maximize profit.

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Dante deposits $300 to open a savings account. He will earn 2% interest each year on his
money If he makes no deposits or withdrawals, how much money will Dante earn in interest
in 1 year? How much money will be in the account after 4 years?

Answers

Therefore , the solution to the given problem of  interest comes out to be $324.

What is meant by interest?

By dividing the original capital by the cost of borrowing, the time period, and other factors, simple interest is calculated. Simple return is calculated as follows: principal + interest + hours. This method of calculating interest is the simplest. The most typical method is to calculate it as a percent of the principal amount. For instance, if he took $100 from a buddy and promised to repay it with 5% interest, he would only be required to pay his proportion of the interest. $100 (0.05) = $5. When you make loans, you should pay interest, and you also need to when you lend money. Interest is often computed as a percentage of a loan.

Here,

Given: $300 is the principal amount

Time: 4 years,

2% interest rate

To discover the basic interest:

Using this formula

Simple interest equals

=> P*R*T/100,

=> 300*2*4/100

=> 24.

Total after four years equals 300 + 24 = 324

Therefore , the solution to the given problem of simple interest comes out to be $324.

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What is the measure of angle ACD?

Answers

Using the exterior angle theorem which involves the use of two interior angles in the polygon, the value of angle ACD in the triangle is 150 degrees

What is an Exterior Angle

An exterior angle of a polygon is an angle that is formed outside of the polygon by extending one of its sides. It is the supplementary angle of an interior angle.

Exterior angle theorem states that the sum of two interior angles is equal to one exterior angle.

Using that theorem in this problem;

∠ACD = 33 + 117

∠ACD = 150°

The value of angle ACD in the triangle is equal to 150 degrees

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Enter "100 divided by the sum of 22 and 3" as an expression.

Answers

Answer:

this question has 3 answers, according to improper fraction your answer can be 50 over 11(50/11).

According to decimal point your answer can be 4.55.

Step-by-step explanation:

According to mixed numbers your answer can be 4 as a whole number 6as numerator and 11 as denominator

Answer:

100÷(22+3)

Step-by-Step:

you cant leave it as 100÷22+3 because pemdas states that division would be first but according to the problem it needs to be the last part. parenthesis comes before any other operation so the only way to do addition first is to put it in parenthesis.

Which of the following is degree 2 polynomial y2 y3 +2y8?A. 2B. -1c. 3D. 8

Answers

Answer:

Step-by-step explanation: .

Can someone please solve this math problem? I can't use words, only numbers, infinity symbols, etc... The math problem is in the picture, Thanks!

Answers

Answer: 10

Step-by-step explanation:

Rewrite it in for y=a(1+r)^t

Answers

Answer:

I don't get it please elaborate!

Step by Step Explanation:

Thank you!

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