Need help solving a percent mixture problem using linear equations

Answer:

12

Step-by-step explanation:

Pythag

According to the concept of algebraic expression and arithmetic, the correct answers are A) Number of adults = N - 25. B) Number of adults when N = 124: 124 - 25 = 99

A) Let's denote the number of children as N. Since there are 25 fewer adults than children, the number of adults can be expressed as N - 25.

B) If there are 124 children, we substitute N with 124 in the expression from part A. Thus, the number of adults would be 124 - 25 = 99.

To arrive at these answers, we used the given information that there are "N" children and 25 fewer adults than children. By substituting the value of N, we determined the number of adults in terms of N and then calculated the specific number of adults when N is equal to 124.

Note: The given question is incomplete. The complete question is:

Some adults and children are watching a musical. there are 'N' number of children. There are 25 fewer adults than children.

A) find the number of adults in terms of 'N'.

B) if there are 124 children how many adults are there?​

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Answer:

9

Step-by-step explanation:

Answer: b = 8

Step-by-step explanation:

From the equation, we can see that x = 0 is one of the solutions. This means that the remaining solutions must add up to 5.

Let's factor the equation and set each factor equal to zero:

x²(x+3)(x - b) = 0

x = 0 or x + 3 = 0 or x - b = 0

Solving for x in each case, we get:

x = 0 or x = -3 or x = b

Since the sum of the solutions is 5, we can write:

0 + (-3) + b = 5

Simplifying, we get:

b - 3 = 5

Adding 3 to both sides, we get:

b = 8

Therefore, the value of b is 8.

Answer:

$343.45

Step-by-step explanation:

$318.75 x 1.0775 = $343.45

or

$318.75 x 0.0775 = $24.70

$318.75 + $24.70 = $343.45

The selling price of the lawn mower is $343.45 if the customer purchased a lawn mower for a total purchase price of $318.75.

It is defined as the ratio of two numbers expressed in the fraction of 100 parts. It is the measure to compare two data, the % sign is used to express the percentage.

We have a customer purchased a lawn mower for a total purchase price of $318.75.

Sales tax rate = 7.75%

Sales tax amount = 7.75% of $318.75

Sales tax amount = $24.64 ≈ $24.70

Original price = 318.75 + $24.70 = $343.45

Thus, the selling price of the lawn mower is $343.45 if the customer purchased a lawn mower for a total purchase price of $318.75.

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Use the slope formula to find the slope of the line:

Replace for the given values

The slope of the line is 4.

You can use mental math to find the slope because as one of the points is (0,0), the formula is simplified to a simple division.

Answer:

h(0) = -5

Step-by-step explanation:

Given that,

→ x = 0

Then the value of h(0) will be,

→ h(x) = -x - 5

→ h(0) = -0 - 5

→ [ h(0) = -5 ]

Hence, the answer is -5.

Answer:

x=-5

Step-by-step explanation:

Well, if you put 0 in for h(0) you get 0=-x-5

-x=5

x=-5

The mass of the water is 7880.1 grams.

Specific heat capacity is the amount of heat energy required to raise the temperature of a substance per unit of mass.

Mathematically -

Q = mcΔT

where -

{Q} = heat energy

{m} = mass

{c} = specific heat capacity

{ΔT} =change in temperature

Given is the water in a container changes its temperature from 12°C to 38°C, when 205 calories are transferred to it.

Specific heat capacity of water = 4.186 J/g°C

205 calories = 857720 Joules

We can write -

Q = mcΔT

857720 = m x 4.186 x (38 - 12)

857720 = 108.836 x m

m = 857720/108.836

m = 7880.1 grams

Therefore, the mass of the water is 7880.1 grams.

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{QUESTION IN ENGLISH -

The water in a container changes its temperature from 12°C to 38°C, when 205 calories are transferred to it. What is the mass of water in the container?}

To maximize the volume, of the rectangular prism, the carton should have dimensions of approximately 10.74 inches (length), 10.74 inches (width), and 5.37 inches (height).

Assuming the height of the rectangular prism is h inches.

According to the given information, the length and width of the prism will be twice the height, which means the length is 2h inches and the width is also 2h inches.

The total surface area of the rectangular prism is given by the formula:

Surface Area = 2lw + 2lh + 2wh

Substituting the values, we have:

576 = 2(2h)(2h) + 2(2h)(h) + 2(2h)(h)

576 = 8h² + 4h² + 4h²

576 = 16h² + 4h²

576 = 20²

h² = 576/20

h² = 28.8

h = √28.8

h = 5.37

The height of the prism is approximately 5.37 inches.

The length and width will be twice the height, so the length is approximately 2 * 5.37 = 10.74 inches, and the width is also approximately 2 * 5.37 = 10.74 inches.

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Using Scale Factor, the value of x = 33.6.

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

Scale factor = Dimension of the new shape / Dimension of the original shape is the fundamental formula used to calculate it.

The formula is expressed as Scale factor = Larger figure dimensions Smaller figure dimensions in the event that the original figure is enlarged.

Dimension of the large triangle divided by the little triangle is the formula to utilize.

Based on the accompanying figure,

The little triangle's corresponding side length is 28, whereas the giant triangle's side length is x.

Scale factor = 6/5 Scale factor = 6/5 = 28

x = 33.6

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Complete Question -

If the figures below are similar with a scale factor of 6:5, find the value of x

Answer:

can I see a copy of the picture? I will edit answer once I can see the picture of the gingerbread man

The surface area of a cylinder is 284m² and it's volume is 366.9m³

To find the surface area and volume of a cylinder, we need to know the radius (r) and height (h) of the cylinder. The formulas for the surface area (A) and volume (V) of a cylinder are as follows:

From the given question, the data are;

a. The surface area of the cylinder is;

SA = 2π(4)² + 2π(4)(7.3)

SA = 283.999≈284m²

b. The volume of the cylinder is

v = πr²h

v = π(4)²(7.3)

v = 366.9m³

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Answer:

the answer is d

Step-by-step explanation:

i got it right on edge 2021

(x,y) → (x +4, y + 2) is the rule for the transformation shown in the figure that translates triangle ABC into triangle A'B'C'. Therefore, the correct option is option D.

A transformation in mathematics is a function f which projects a set X to it only, i.e., f: X X. This function typically has some geometrical foundation. Examples include geometric transformations, such as spatial transformations, affine transformations, including particular affine transformations like rotations, reflections, and translations, as well as linear transformations of vector spaces.

Although it is usual to refer to any function of a set within itself as a "transformation," particularly in phrases like "transformation semigroup" or related expressions, there is another type of terminological norm in which the word "transformation" is exclusively used to refer to bijections. (x,y) → (x +4, y + 2) is the rule for the transformation shown in the figure that translates triangle ABC into triangle A'B'C'.

Therefore, the correct option is option D.

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The person who gets to say the last number, 1000, will be Person 6.

Here, we have,

In this scenario, we have seven people sitting in a circle and counting clockwise. The goal is to determine which person will say the last number when they reach 1000. To solve this problem, we can use the concept of modular arithmetic.

When dividing 1000 by the total number of people (7), we get a quotient of 142 and a remainder of 6 (1000 = 142*7 + 6). This means that after completing 142 full rounds of counting, the group will have reached the number 994 (142*7). In the next round, they will continue counting from 995 to 1000.

Since the remainder is 6, it indicates that the last number (1000) will be spoken by the person sitting 6 positions after the first person in the circle (clockwise). In other words, Person 1 says numbers 1, 8, 15, and so on, while Person 6 will say 6, 13, 20, and so on.

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complete question:

10) Seven people sit in a circle and begin counting clockwise starting from 1.Each person in the group is keeping track of the numbers she is saying (e.g. 1,8, 15...) If they continue in this way, counting on and on, until they reach 1000, which person will get to say the last number

Answer: Statement 1 is false.

Step-by-step explanation: 1 is false because all natural numbers, whole numbers, and integers are rationals.

Let's begin by listing out the given information:

We will calculate for the slope:

We proceed to use the point-slope formula to calculate the equation of the line:

Answer:

the answer would be 7/5

Step-by-step explanation:

2 of them would already make a whole, and if you add another one, it's going to be more than just one pitcher of lemonade.

Using it's concept, it is found that the probability that a randomly selected student is in music/drama is:

P(Music/Drama) = 0.25.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, the number of students is given by:

N = 20 + 7 + 3 + 20 + 13 + 2 + 25 + 5 + 5 = 100.

Of those, the number involved in music/drama is:

D = 7 + 13 + 5 = 25.

Hence the probability is given by:

p = 25/100 = 0.25.

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The simplified expression of x(3x + 5)-5(2x - 1) is 3x² - 5x + 5

From the question, we have the following parameters that can be used in our computation:

x(3x + 5)-5(2x - 1)

Open the brackets

So, we have

3x² + 5x - 10x + 5

Evaluate the like terms

So, we have

3x² - 5x + 5

Hence, the simplified expression is 3x² - 5x + 5

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Remainder of question:

Find the probability distribution of x

Answer:

The random variable x is defined as: X = {0, 1, 2, 3, 4}

The probability distribution of X:

P(X = 0) = 0.656

P(X = 1) = 0.2916

P(X= 2) = 0.0486

P(X=3) = 0.0036

P(X = 4) = 0.0001

Step-by-step explanation:

Sample size, n = 4

Random variable, X = {0, 1, 2, 3, 4}

10% (0.1) of the homeowners are insured against earthquake, p = 0.1

Proportion of homeowners who are not insured against earthquake, q = 1 - 0.1

q = 0.9

Probability distribution of x,

\(P(X = r) = ^nC_r *p^r q^{n-r} \\\\P(X= 0) =(^4C_0 *p^1 q^4 )\\P(X=0) = (^4C_0 *0.1^0 0.9^4 ) = 0.656\\P(X= 1)= (^4C_1 *p^1 q^3 )\\P(X=1) = (^4C_1 *0.1^1 0.9^3 ) = 0.2916\\P(X= 2)=( ^4C_2 *p^2 q^2) \\P(X=2) = (^4C_2 *0.1^2 0.9^2 ) = 0.0486\\P(X= 3) = (^4C_3 *p^3 q^3) \\ P(X=3) = (^4C_3 *0.1^3 0.9^1 ) = 0.0036\\P(X= 4) = (^4C_4 *p^4 q^0 )\\ P(X=4) =(^4C_4 *0.1^4 0.9^0 ) = 0.0001\)

The solutions to the nearest tenth are x = -0.1 and x = 1.3

From the question, we have the following parameters that can be used in our computation:

5x² - 2x - 1 = 4x

Evaluate the like terms

So, we have

5x² - 6x - 1 = 0

Next, we solve using a graph

The graph of 5x² - 6x - 1 = 0 is added as an attachment

From the attached graph, we can see that the curve intersects with the x-axis at x = -0.1 and x = 1.3

This means that the solutions are x = -0.1 and x = 1.3

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Answer:

The solutions to the equation 5x^2-2x-1=4x to the nearest tenth are x ≈ 1.3 or x ≈ -0.4.

Step-by-step explanation:

To solve the equation 5x^2-2x-1=4x to the nearest tenth, we can start by moving all the terms to one side of the equation.

5x^2-2x-1=4x

5x^2-6x-1=0

Next, we can use the quadratic formula to solve for x:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 5, b = -6, and c = -1.

Plugging these values into the formula gives:

x = (-(-6) ± sqrt((-6)^2 - 4(5)(-1))) / 2(5)

x = (6 ± sqrt(56)) / 10

The values of x and y are 20 and 12.

The values of x and y are -3 and 2.

We have,

In a parallelogram,

- Opposite sides are congruent:

The opposite sides of a parallelogram have equal lengths.

- Opposite angles are congruent:

The opposite angles of a parallelogram have equal

Now,

a)

Opposite angles are congruent:

So,

5x + 29 = 7x - 11

29 + 11 = 7x - 5x

40 = 2x

2x = 40

x = 40/2

x = 20

And,

3y + 15 = 5y - 9

15 + 9 = 5y - 3y

24 = 2y

y = 24/2

y = 12

b)

Opposite sides are congruent:

So,

-6x = -4x + 6

-6x + 4x = 6

-2x = 6

x = -3

And,

7y + 3 = 12y - 7

12y - 7y = 3 + 7

5y = 10

y = 2

Thus,

The values of x and y are 20 and 12.

The values of x and y are -3 and 2.

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The required polynomial is given by x + 5.

What is a polynomial?

A polynomial is an equation made up of coefficients and indeterminates that uses only the addition, subtraction, multiplication, and powers of positive-integer variables.

Here, we have

Given: the quotient of (x⁴+5x³-3x-15) and (x³-3) is a polynomial.

we have given that

f(x) = x⁴+5x³-3x-15

and

q(x) = x³-3

Since we know that

Euclid's division lemma states that

f(x) = q(x) × g(x) + r(x)

Now,

x⁴+5x³-3x-15 =  x³-3 × g(x) + 0

So, our equation becomes

x⁴+5x³-3x-15/x³-3  = g(x)

x + 5 = g(x)

Hence, our required polynomial is given by x + 5.

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Answer:

Option A i.e. (1, 0) is correct.

Step-by-step explanation:

We know that graph of a Parabola illustrates a U-shaped curve.

The graph of Parabola has an important characteristic, it consists of an extreme point which is termed as 'vertex'.

When a parabola opens up, the vertex will be the lowest point on the Parabola graph.

When a parabola opens up, the vertex will be the lowest point on the Parabola graph. This lowest point is the minimum value of the parabola function.

Given the equation

y = x² - 2x + 1

From the given Parabola graph, it is clear that the parabola opens up.  

Thus, the vertex will be the lowest point on the Parabola graph which is also the minimum value.

It is clear that the vertex of the parabola is located at (1, 0).

Therefore, the point (1, 0) is the vertex of the function.

SECOND METHOD:

Given the equation

y = x² - 2x + 1

The vertex of an up-down facing parabola of the form y = ax² + bx + c is

\(x_v=-\frac{b}{2a}\)

\(a=1,\:b=-2,\:c=1\)

\(x_v=-\frac{\left(-2\right)}{2\cdot \:1}\)

\(x_v=1\)

Plug on \(x_v=1\) in the equation y = x² - 2x + 1 to find the \(y_v\) value

\(\:y_v\:=\:x^{2} \:-\:2x\:+\:1\)

\(\:y_v\:=\:\left(1\right)^2\:-\:2\left(1\right)\:+\:1\)

\(y_v\:=1-2+1\)

\(y_v\:=0\)

Therefore, the vertex is:

\(\left(x_v,\:\:y_v\right)=\left(1,\:0\right)\)

Hence, option A i.e. (1, 0) is correct.

Answer:

a) 7.5 meters b) 588.75

Step-by-step explanation:

To calculate the volume you need to multiply the 3 values together so

3x5x0.5 = 7.5

That is the volume

Then you got to multiply that by 78.50 to get the answer for b

78.50x7.5 =588.75

Answer:

r =3.4 mm

Step-by-step explanation:

circumference of a circle = 2πr

21.3 = 2*3.14*r

21.3 = 6.28*r

21.3 / 6.28 = r

3.39 = r

3.4 = r

Answer: $950

Step-by-step explanation:

he had 450 in his account after writing a check for 500. all you have to do is add 450 + 500.