There are 14 boys and 12 girls in Mateo's homework class. Which ratio correctly describes the students in the class?
A) The ratio of boys to girls is 7:6
B) The ratio of girls to boys is 6:8
C) The ratio of boys to all students is 14:28
D) The ratio of girls to all students is 6:7

Answer:

C

Step-by-step explanation:

Answer:

6 chaperones on 80 students.

Step-by-step explanation:

Here is the complete question: School guideline required that there must be 2 chaperones for every 25 students on a school trip. how many chaperones must there be for 80 students?

Given: There must be 2 chaperones on every 25 students.

Now, we will use unitary method to solve.

We know 2 chaperones = 25 students

∴ one student required [tex]\frac{2}{25}\ chaperones[/tex]

Next for 80 students, we require= [tex]\frac{2}{25} \times 80 = \frac{160}{25}[/tex]

∴ For 80 students, we require [tex]6.4 \ chaperones[/tex], however, we cannot use decimal for number of person, so we can round off the number to 6 chaperones on every 80 students.

Using the cross product property on this proportion gives us the following equation:

6 (3x + 3) = 7 (x + 16)

Use the distributive property

18x + 18 = 7x + 112

Subtract both sides by 7x

11x + 18 = 112

Subtract both sides by 18

11x = 94

Divide both sides by 11

x = 94/11

This fraction is already fully simplified and cannot be simplified further. This should be your answer.

Let me know if you need any clarifications, thanks!

Answer:

Step-by-step explanation:

6(3x+3) = 7(x+16)

18x+18=7x+112

-7 on both sides

11x+18=112

-18 on both sides

11x/11 = 94/11

x=8.5

Answer:

Step-by-step explanation:

3y + 8 +(-7y) + 9 =

3y + 8 - 7y + 9 =

-4y + 17

The equation of the line is y = 2x+ 5.

1. Identify the slope:

Lines are considered parallel if they have the same slope.

To find the slope of the given line, we can rearrange the equation 4x-2y=8 to slope-intercept form (y = mx + b) by isolating y: y = 2x - 4.

Therefore, the slope of both the given line and the parallel line we want to find is 2.

2. Use the point-slope form:

We can use the point-slope form of the equation to create the equation of the new line: y - y₁ = m(x - x₁)

Substituting the known point (-2, 1) and the slope (2): y - 1 = 2(x - (-2))

Simplifying the equation: y - 1 = 2x - 4

Combining like terms: y = 2x + 5

Therefore, the equation of the line that passes through (-2, 1) and is parallel to the line 4x-2y=8 is y = 2x + 5.

To find a parallel line to 4x-2y=8 that passes through (-2, 1), we determine the slope of the given line (which is 2) and use point-slope form to write the equation of the new line, resulting in y = 2x + 5.

The student is asking for the equation of a line that passes through a specified point and is parallel to a given line. The equation of the existing line is 4x-2y=8. To find a parallel line, we must have the same slope. First, let's find the slope of the given line by rewriting its equation in slope-intercept form (y=mx+b), where m is the slope and b is the y-intercept. The original equation is 4x - 2y = 8, which can be rewritten as y=2x-4. Thus, the slope is 2.

Since the new line must be parallel, it will also have a slope of 2. Using the point-slope form of a line, which is y - y1 = m(x - x1), where (x1,y1) is the point the line passes through, we substitute the point (-2,1) and the slope of 2 to get the equation y - 1 = 2(x + 2). Simplifying this, we get y = 2x + 5 as the equation for the line that is parallel to 4x-2y=8 and passes through the point (-2, 1).

The domain of the function f(x) = (2/5) * sqrt(x) is all real numbers x ≥ 0, or in interval notation, [0, ∞). This is because square roots are only defined for non-negative real numbers.

The domain of a function refers to all possible values that can be input into the function, usually represented by 'x'. For the given function f(x) =  \frac{2}{5} \sqrt{x}, we need to determine the set of x-values for which the function is defined. Since we cannot take the square root of a negative number in the set of real numbers, the smallest value for 'x' must be 0. Thus, the domain of the function f(x) = \frac{2}{5} \sqrt{x} includes all real numbers greater than or equal to 0.

This is written mathematically as “x ≥ 0” or in interval notation as [0, ∞). It's important to note that, for real numbers, square roots are only defined for non-negative values, which is why the domain starts at 0 and continues to positive infinity.

Answer:

Matt bought 7 packages of hot dogs and 5 packages of hamburger.

Step-by-step explanation:

We are given the following in the question

Let x represent the number of packages of hot dogs.

Cost of one packet of hot dog = $2.75

Let y represent the number of packages of hamburgers

Cost of one packet of hamburgers = $3.20

Then, we can write the following equations:

[tex]x + y = 12\\2.75x + 3.2y = 35.25[/tex]

Solving the two equations,

[tex]2.75x + 2.75y = 33\\2.75x + 3.2y = 35.25\\\Rightarrow 0.45y = 2.25\\y = 5\\x = 7[/tex]

Thus, Matt bought 7 packages of hot dogs and 5 packages of hamburger.

The solution is viable.

Constraints to the system of equation:

[tex]x,y \geq 0 \\x + y = 12\\2.75x + 3.2y = 35.25[/tex]

Answer:

d=5

Step-by-step explanation:

-5d+10=2d-25

-5d-2d=-25-10

-7d=-35

7d=35

d=35/7

d=5

Answer:

[tex]p =\{\text{all even numbers that are less than or equal to 20}\}\\\\p=\{n|n=2k\ \wedge\ n\leq20\ \wedge\ k\in\mathbb{N}\}=\{0,\ 2,\ 4,\ 6,\ 8,\ 10,\ 12,\ 14,\ 16,\ 18,\ 20\}[/tex]

Final answer:

The area of triangle ABC with vertices A(-1, -1), B(3, -1), and C(-1, 2) is calculated using the determinant method and results in 6 square units.

Explanation:

To find the area of a triangle with vertices on a coordinate plane, you can use the formula that requires knowing the coordinates of all three vertices.

For triangle ABC with vertices A(-1, -1), B(3, -1), and C(-1, 2), we can use the determinant method:

The area of triangle ABC is ½ |x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)|. Substituting our given coordinates into this formula, we get:

Area = ½ |(-1)(-1 - 2) + 3(2 - (-1)) + (-1)((-1) - (-1))|

Area = ½ |(-1)(-3) + 3(3) + (-1)(0)|

Area = ½ |3 + 9 + 0|

Area = ½ × 12

Area = 6 square units

The area of triangle ABC is therefore 6 square units.

In the beginning, 362 meters below sea level, or -362 meters (if we consider sea level as 0).

Because the Dead Sea is 71 meters below where she was, the equation to solve this would be

-362 - 71 = -433

The answer is -433.

Hope this helps!

Since Zoey is 362 meters below sea level while visiting a part of Israel and she descends 71 meters to visit the Dead Sea, the integer that represents the elevation, in meters, of the Dead Sea is a) -433.

We can use the mathematical operation of subtraction to determine the elevation of the Dead Sea as follows:

The present elevation of Zoey = -362 meters

The descent that she makes to visit the Dead Sea = -71 meters

The elevation of the Dead Sea = -433 (-362 - 71).

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Complete Question:

Zoey is 362 meters below sea level while visiting a part of Israel. She descends 71 meters to visit the Dead Sea. Which integer represents the elevation, in meters, of the Dead Sea?

a) -433

b) -391

c) -311

d) -291

Answer:

The first picture is a function and the second picture is not.

Step-by-step explanation:

Reason - In the first picture, there is no repeating value of x. In other words, every x value has a y value. However, in the second picture, the x value, 2 goes to 2 and -3.

Answer:

The number of years in which saving gets double is 8 years .

Step-by-step explanation:

Given as :

The principal amount saved into the account = p = $8,000

The rate of interest applied = r = 9%

The Amount gets double in n years = $A  

Or, $A = 2 × p = $8,000 × 2 = $16,000

Let the number of years in which saving gets double = n years

Now, From Compound Interest method

Amount = Principal × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]

Or, 2 × p = p × [tex](1+\dfrac{\textrm r}{100})^{\textrm n}[/tex]

Or, $16,000 = $8,000 × [tex](1+\dfrac{\textrm 9}{100})^{\textrm n}[/tex]

Or, [tex]\dfrac{16,000}{8,000}[/tex] = [tex](1.09)^{n}[/tex]

Or, 2 = [tex](1.09)^{n}[/tex]

Now, Taking Log both side

[tex]Log_{10}[/tex]2 = [tex]Log_{10}[/tex] [tex](1.09)^{n}[/tex]

Or, 0.3010 = n × [tex]Log_{10}[/tex]1.09

Or, 0.3010 = n × 0.0374

∴ n = [tex]\dfrac{0.3010}{0.0374}[/tex]

I.e n = 8.04 ≈ 8

So, The number of years = n = 8

Hence, The number of years in which saving gets double is 8 years . Answer

Answer:

  110

Step-by-step explanation:

You want the remainder from the division ...

  [tex]\dfrac{4x^3+2x^2-18x+38}{x-3}[/tex]

The remainder theorem tells you the remainder of ...

  f(x)/(x -a)

is f(a).

We can compute f(a) directly, or we can do it using synthetic division. The attachment shows the synthetic division approach.

If we want to evaluate f(x), it is convenient to write it in Horner Form:

  f(x) = 4x³ +2x² -18x +38 = ((4x +2)x -18)x +38

Then, for x = 3, this is ...

  ((4·3 +2)·3 -18)·3 +38 = (14·3 -18)·3 +38 = 24·3 +38 = 110

The remainder from the division is 110.

Answer:

Step-by-step explanation:

The basic concept for both is the same, except with grouping you have more than 3 terms and after factoring out what is common in each group, you are left with identical terms in a set of parenthesis that can then also be factored out.  For example, this would be factoring by grouping (then I will show you a factoring by GCF to better illustrate the idea):

If our polynomial is

[tex]x^3-x^2+3x-3=0[/tex]

we could group those terms into groups of 2 (without changing their order at all) to get:

[tex](x^3-x^2)+(3x-3)=0[/tex]

and we factor out what's common in each group to get:

[tex]x^2(x-1)+3(x-1)=0[/tex]

You can see that the (x - 1) is common now and can be factored out, leaving us with

[tex](x-1)(x^2+3)[/tex] (the secod term now can be factored if you need the complete linear factorization, but it will lead to imaginary numbers).  

An example of factoring out the GCF is to factor out what's common in all the terms.  It HAS TO BE COMMON IN ALL THE TERMS to do it this way.  For example, in the polynomial

[tex]6x^3-4x^2+2x-8=0[/tex] the GCF for all the terms is a 2, so that's all we can factor out.  It has to factor out of every term every time, no exceptions:

[tex]2(3x^3-2x^2+x-4)=0[/tex]

The method of GCF factoring often just serves to simplify the polynomial down a bit, but sometimes will still require factoring.

Final answer:

Factoring by grouping is used for polynomials with four or more terms, arranging them into groups with common factors, while factoring by GCF involves finding the largest common factor for all terms in an expression.

Explanation:

Factoring by grouping and factoring by the Greatest Common Factor (GCF) are two methods used in algebra to simplify expressions or solve equations.

Factoring by GCF involves finding the largest factor that is common to all terms in an expression.

For example, in the expression 4x + 8, the GCF is 4, so we can factor it as 4(x + 2).

Factoring by grouping, on the other hand, is used when an expression has four or more terms.

The method involves grouping terms so that each group has a common factor that can be factored out.

For instance, with the polynomial x^3 + 3x^2 + 4x + 12, we group the terms into (x^3 + 3x^2) + (4x + 12).

We then factor out the GCF from each group, yielding x^2(x + 3) + 4(x + 3).

Recognizing that (x + 3) is common between the groups, we can then factor further to get (x^2 + 4)(x + 3).

Answer:

6.4 meters per second

Step-by-step explanation:

Rate of Change

If two variables x and t are to be related as the rate x changes when t changes, it can be expressed as:

[tex]\displaystyle v=\frac{x}{t}[/tex]

Hans takes a ride in the elevator down from the 86th floor to the first floor, a distance of x=320 meters in t=50 seconds. The rate of descent is

[tex]\displaystyle v=\frac{320}{50}[/tex]

[tex]v=6.4\ m/s[/tex]

Answer:

Step-by-step explanation:

1) Given figure is a parallelogram

Area = 144 cm²

base  * altitude = 144

16 * x = 144

x =144/16

x = 9 cm

2)2) Trapezium

Area = [tex]\frac{a+b}{2}*h[/tex]      ; {a and b are parallel sides of trapezium}

( 37 +27 /2) * x  = 480 cm²

64/2 * h = 480

32 *  h = 480

h = 480/32

h = 15 cm

Triangle with sides RS=19, SQ = 20, AND QR = 18 must have unequal angles as triangles with unequal sides have unequal angles.

A triangle with unequal sides is known as the Scalene triangle. As mentioned in the question triangle QRS has unequal sides of length RS = 19, SQ = 20, and QR = 18.

Then we can say that triangle Δ QRS is a Scalene triangle.

A scalene triangle has unequal angles. It has no line of symmetry present in a  scalene triangle.

In a scalene triangle, the angle opposite to the longest side is the greatest.

Hence, we can say that the angles of  Δ QRS are unequal.

For more details about Triangles,

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The correct statement is that at least two angles of ΔQRS are equal, and one angle is different.

Here,

In a triangle, the sum of the measures of the three interior angles is always 180 degrees.

This is known as the triangle angle sum property.

Therefore, if we know the lengths of two sides of a triangle, you can determine the measure of the third angle using the Law of Cosines or the Law of Sines.

In the case of ΔQRS, we can use the Law of Cosines to find the measure of angle ∠Q:

Cos(∠Q) = (RS² + QR² - SQ²) / (2 * RS * QR)

Cos(∠Q) = (19² + 18² - 20²) / (2 * 19 * 18)

Cos(∠Q) = (361 + 324 - 400) / (2 * 19 * 18)

Cos(∠Q) = 285 / 684

Cos(∠Q) ≈ 0.416667

Now, to find the measure of ∠Q, we take the inverse cosine (arccos) of 0.416667:

∠Q ≈ arccos(0.416667) ≈ 65.392°

Now that we know the measure of ∠Q, we can find the measures of the other angles:

∠R = 180° - ∠Q - ∠S

∠R = 180° - 65.392° - ∠S

And

∠S = 180° - ∠Q - ∠R

∠S = 180° - 65.392° - (180° - 65.392° - ∠S)

∠S = 180° - 65.392° - 180° + 65.392° + ∠S

∠S = 2 * 65.392° - ∠S

2 * ∠S = 2 * 65.392°

∠S = 65.392°

So, the measures of the angles in ΔQRS are approximately:

∠Q ≈ 65.392°

∠R ≈ 49.608°

∠S ≈ 65.392°

As we can see, two of the angles (∠Q and ∠S) are equal, while the third angle (∠R) is different.

Therefore, the correct statement is that at least two angles of ΔQRS are equal, and one angle is different.

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Answer:

8 1/4

Step-by-step explanation:

20 2/4

-

12 3/4

__________

8 1/4

7 1/4

You subtract 20 and 2/4 by 12 3/4 and you get 8 1/4

Answer:

We know that

P(X) = Dividor × Quotient

So dividor = x-1

Quotient = x2 + 7 + 5/x-1

So,

P(x) = x3 - x2 + 7x -2

Step-by-step explanation:

Taking LCM of quotient we will get

(x3 - x2 + 7x - 2)/(x-1)

Now by multiplying the above equation with x-1,

Only thing remaining will be

x3 - x2 + 7x - 2

This is P(x).

The polynomial p(x) in standard form, when given the quotient formed from dividing p(x) by (x - 1), is x^3 - x^2 + 7x - 2.

The function p(x) can be expressed in standard form by multiplying divisor (x - 1) by the quotient, (x^2 + 7 + 5/(x - 1)) according to polynomial division rules. To get p(x), you multiply the quotient by the divisor and add the remainder. However, since there is no remainder mentioned, we assume it's zero and ignore it.

Therefore, p(x) is (x - 1)(x^2 + 7 + 5/(x - 1)). To simplify further, distribute (x - 1) across each term in the parenthesis:

So, the polynomial p(x) is x^3 - x^2 + 7x - 7 + 5 or, simplified further, x^3 - x^2 + 7x - 2.

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The sides are 7 inches and 5 inches. To get the perimeter, it's 7 +7 +5 + 5, which equals 24, and then 7 x 5 = 35 for the area.

(24 + 2y) + (7y)

(24 +  8) + 28

32 + 28

60

Answer:

60

Step-by-step explanation:

(24 + 2y) + (7y)

(24 + 2 x 4) + (7 x 4)

(24 + 8) + (28)

32 + 28 = 60

Answer:

18,000

Step-by-step explanation:

because its closer to 18,000 then 19,000.

Answer:

2i: 169.71

2ii: 0.17L

3a: 4×10⁻⁵

3b: 110011

Step-by-step explanation:

2i. The surface of the top and bottom of the tin is two times (top and bottom) π·r² = 2·π·3² = 18π cm².

The circumference of the circle is 2·π·r = 6π cm².

The area of the material connecting top and bottom is a rectangle of the tin height times the circumference: 6·6π = 36π cm².

This gives a total of  18π + 36π = 54π  cm².

With π approximated by 22/7 the total surface area is 54*22/7 ≈ 169.71.

Notice how the calculation is simple by waiting until the very last moment to substitute π.

2ii. The volume is the area π·r² of the circle times the height of the tin: 9π*6 = 54π cm³ ≈ 169.71 cm³.

Since 1L = 1000 cm³ the volume is 0.16971 litres, which should be rounded to 0.17 L.

3a: If we rewrite P as 36 x 10⁻⁴ and realize that 36/2.25 = 16, then the fraction can be written as

16 x 10⁻⁴⁻⁶ = 16 x 10⁻¹⁰.

The square root of that is taking it to the power of 1/2, so (16x10⁻¹⁰)^0.5 = 4x10⁻⁵ = 0.00004

3b: 1111 1111 is 255 in decimal. 101 is 5 in decimal. 255/5 is 51 in decimal. 51 in binary is 110011.

Answer:

-1/2

Step-by-step explanation:

Add 12 to both sides 8b=-4

Divide by 8 on both sides b=-4/8

Simplify b=-1/2

Answer:

B=-1/2

Step-by-step explanation:

8b-12=-16

fit’s you wanna try and get the variable on its own

8b-12=-16

8b=-4

b=-1/2

Answer:

The value of x is 4, 3rd point.

Step-by-step explanation:

Move all the variables to one side & move unknown value to the other side :

4x - 3 = 2x + 5

4x - 2x = 5 + 3

2x = 8

Then solve it :

2x = 8

x = 8/2

x= 4

Answer:

C. x = 4

Step-by-step explanation:

4x - 3 = 2x + 5

4x - 2x - 3 = 2x - 2x + 5

2x - 3 = 5

2x - 3 + 3 = 5 + 3

2x = 8

(1/2) 2x = 8 (1/2)

x = 4

Answer: OPTION D.

Step-by-step explanation:

For this exercise it is important to remember that:

1.  Direct proportion equations have the following form:

[tex]y=kx[/tex]

Where "k" is the constant of proportionality.

2. The graph of Direct proportions is an straight line that passes through the origin.

Observe the picture attached.

If you join the points G, C and A, you get a straight line that passes through the origin,

If you join the points F, G and H, you also get a straight line that passes through the origin,

Therefore, the sets of points show "x" in Direct proportion to "y", are:

[tex]\{F, G, H\}[/tex] and   [tex]\{{G, C, A}\}[/tex]

Answer:D){F, G, H} and {G, C, A} only

Step-by-step explanation:

Answer:

Step-by-step explanation:

We need to find the option for which the value of the function will be increasing, with the increasing variable.

Vertical line means the value of the x is constant, for any y. Hence, it is not the answer.

Horizontal line represents constant functions. Hence option B can not be the answer.

The data having a positive slope represents a increasing function with the increasing variable. Vice-versa for the data having a negative slope.

That is why option D will be the answer.

The correct option is d, which is the data canvas be modeled by a line with a negative slope.

A scatter plot is also known as a scatter chart, a scatter graph that uses dots to represent values for two different numeric variables. Each dot on the graph represents a particular on both the axis.

the Y values are decreasing as the x-values are increasing

As we can see in the graph below with the decreasing value of y and increasing value of x, therefore, it will be a negative slope.

Hence, the correct option is d, which is the data canvas be modeled by a line with a negative slope.

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Answer: The numbers are 10 and 23

Step-by-step explanation:

Let the smaller number be x

And the larger number be y

Ist sentence;

1. The sum of two numbers is 33.

X + y= 33 .........eqn 1

2. second sentence

the larger number is 3 more than two times the smaller number.

Y = 3 +2x

Put y into eqn 1

X+ 3 +2x = 33

3x= 33- 3

3x= 30

X = 30/3

X= 10 and y= 3+ 2x

Y= 3+ 2(10)

Y = 3+ 20

Y= 23

Therefore the two numbers are 10 and 23