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

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

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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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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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.

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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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]

​

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

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.

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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Answer:

I don't get it please elaborate!

Step by Step Explanation:

Thank you!

The fraction of Jon original pay is 4/10

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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Answer:

25 :)

Step-by-step explanation:

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

The area of each triangle is given as follows:

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:

Hence the areas are:

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

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Case 1: The linear equations has infinite solutions.

Case 2: The linear equations has no solution.

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:

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

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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Answer: 10

Step-by-step explanation:

The symmetric of -15 is 15.

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]

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

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!

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

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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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:

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

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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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 .

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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Answer:

Step-by-step explanation: .

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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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

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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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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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.

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

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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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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