of course, quadratic equations don't always come with the coefficients labeled , , and . for example, assuming the solutions are real and , the larger solution of -bx^2 c^2x a^3

Each one of the given ratios should be expressed in its simplest form as follows:

In Mathematics, a ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

In this exercise, you are required to express each of the given ratios in its simplest form. Therefore, we would divide both sides of the ratio by highest common factor (HCF) as follows;

50:150 = 50/150 = 1/5 = 1:5. (divide both sides by 50).

25:40 = 25/40 = 5:8. (divide both sides by 5).

33:99 = 1:3. (divide both sides by 33).

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Complete Question:

Express each one of the following ratios in its simplest form.

(i) 50: 150

(ii) 25:40

(iii) 33 : 99​

The time that is taken to fall is  3.1 s.

In this case, we have been told that A rock is thrown upward with a velocity of 18 meters per second from the top of a 36 meter high cliff, and it misses the cliff on the way back down.

We have to know that the maximum height that the rock has attained by the use of the formula;

v^2 = u^2 - 2gh

v = final velocity

u = initial velocity

g = acceleration

h= distance

v = 0 m/s at the maximum height

h = u^2/2g

h = (18)^2/2 * 9.8

h = 324/19.6

h = 16.5 m

The height from the cliff upwards is; 16.5 m + 36 m = 52.5 m

The distance that is covered when falling is;  52.5 m - 4 m = 48.5 m

If it is falling then it is dropped from a height and u = 0 m/s

h = 1/2gt^2

48.5 = 0.5 * 9.8 * t^2

t = √48.5/0.5 * 9.8

t = 3.1 s

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The required roster form of the given sets are C ∩ (B’ ∪ A) = {p, q}.

The roster form of a set is defined as a set that can be represented mathematically in a precise way using a roster notation. In a roster notation, if the set has more than one element, a comma is used to denote the separation between every pair of elements.

The given sets are defined as follows:

U = {f, g, h, p, q, r, x, y, z}

A = {f, g, p, q}

B = {g, h, q, x, y}

C = {p, q, x, y, z}

The complement of set B is the set of all elements in the universal set U that are not in set B.

U = {f, g, h, p, q, r, x, y, z}

B = {g, h, q, x, y}

B’ = {f, p, r, z}

The union of set B' and A is the set of all elements that are in set B' or in set A.

A = {f, g, p, q}

B’ = {f, p, r, z}

B’ ∪ A = {f, g, p, q, r, z}

The intersection of set C and (B’ ∪ A) is the set of all elements that are in both set C and set (B’ ∪ A).

C = {p, q, x, y, z}

B’ ∪ A = {f, g, p, q, r, z}

C ∩ (B’ ∪ A) = {p, q}

So, C ∩ (B’ ∪ A) = {p, q}

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Answer:

9 234

Step-by-step explanation:

base area multiplied by height is volume

According to the information, the coach will buy 9 ice cream sandwches and 6 frozen juice pops.

To calculate how many sandwiches and frozen juices the coach bought we have to perform the following mathematical operation:

First we have to built a equation incluiding all the values of the problem.

Now, we have to include the price of each product

$2 * I + 2.50 * J = 33.00

Then we have to solve the equation.

According to the above the number of sanwiches is 9, and the number of juices is 6.

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Answer:

I'm not understanding can you say it in a similar way?

Answer:

Step-by-step explanation:

Opportunity cost and production possibilities

Shen is a talented artist who sells hand-crafted goods on his website. Shen currently crafts and sells both crochet hats and baskets. He spends 8 hours

a day working on crafts. The following table gives different daily output scenarios depending on how much of his time is spent on each good

Answer:I think it is 6

Step-by-step explanation:

Answer:

h(2) = 6

Step-by-step explanation:

This function is called h.

In function notation, it is h(x).

h(2) means the value of the y-coordinate of the point whose x-coordinate is 2.

Look up 2 on the y axis.

Now go up until you get to the blue line of the function.

What y value does that correspond to? Go left horizontally until you get to the y-axis. You intersect the y-axis at 6. That means that

h(2) = 6

The interpretation of the confidence interval is that "we can be 95% confident that the true population proportion of people who think climate change lies between 0.146 and 0.214".

Given :

A random sample of 1,175 people in a certain country was asked whether they thought climate change was a problem.

The sample proportion of those who think climate change is a problem was calculated, and a 95 percent confidence interval was constructed as (0.146, 0.214).

95% confidence interval means a person is 95% confident that true population lies in it.

95% confidence interval is given by (0.146,0.214).

So, the interpretation of the confidence interval is that "we can be 95% confident that the true population proportion of people who think climate change lies between 0.146 and 0.214".

Therefore, the correct option is C) We are 95 percent confident that the proportion of people in the sample who think climate change is a problem is between 0.146 and 0.214.

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The polynomial that represents the perimeter of the figure is 3x

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

Side length = x

Triangle type = equilateral triangle

See attachment for the figure

The perimeter of an equilateral triangle can be calculated as

P = 3 * side length

substitute the known values in the above equation, so, we have the following representation

P = 3 * x

So, we have the following representation

P =3x

Hence, the perimeter expression is 3x

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Answer:

Bottom model and has 60 toys in all

Step-by-step explanation:

The equation -1.5x = 4(x + 2.18) solved for x is -1.59. Option C

Algebraic expressions are described as expressions that are mainly composed of variables, terms, constants, coefficients and factors.

These expressions are also composed of arithmetic operations, such as;

From the information given, we have that;

-1.5x = 4(x + 2.18)

expand the bracket

-1. 5x = 4x + 8.72

Now, collect like terms, we get;

-1.5x - 4x = 8.72

subtract the like terms

-5.5x = 8.72

Divide both sides by the coefficient of x

x = -1.59

Hence, the correct option is Option C

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Complete question:

Solve the following equation for x. Round the answer to the nearest hundredth.

−1.5x= 4(x + 2.18)

A. 0.63

B. 3.49

C. -1.59

D. -0.40

(a) Any number could represent the amount of current flowing through the capacitor in decimal form. So that the electric capacitor is Continuous.

(b) There are exactly that many players. So On-line gaming system is Discrete.

(c) The number of flights or their proportion depend on the aircraft, which are expressed as whole numbers. So an airport is continuous.

In the question, we have to classify the systems as being either discrete or continuous:

Discrete data, often known as discrete values, is information that only accepts specific values. This type of data, which typically takes the form of whole numbers or integers, can be counted and has a finite set of possible values.

Data that can be measured is referred to as continuous data. There are an endless number of alternative possibilities for the values in this data, which are not fixed.

Nevertheless, the main distinction between discrete and continuous data is that the former has a finite value that can be counted while the latter has an infinite range of possible values that can be measured.

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A function that represents the amount of air that is f(r)=4/3π[3r²+3r+1]

Since a function is a rule that applies a specific output to a specific input, we can define a function in a variety of ways. This could involve a change in variables, for example, or defining a function that represents a rate of change.

The amount or volume of air required to inflate the spherical balloon from a radius of r inches to a radius of r+1 inches.

The formula for the volume of a sphere is V = 4/3 πr³

where V = volume and r = radius.

V= 4/3π[(r+1)³−r³]

V=4/3π[r³+3r²+3r+1−r³]

V =4/3π[3r²+3r+1]

 For r in inches and V(r) in inches cubed,

 f(r)=4/3π[3r²+3r+1].

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Based on the table, a statement which is true include the following: C. The table shows a linear relationship, but not a proportional relationship.

In Mathematics, a proportional relationship is a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the data points on this graph as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 6/2 ≠ 11/4 ≠ 34/9 ≠ 81/16

In this context, we can reasonably infer and logically deduce that the table shows a linear relationship because as the value of time (in hours) increases, the value of distance (miles) also increases. However, it does not show a proportional relationship.

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The number of weeks, it will take before it is up to 45 minutes of walking per day is, 9 weeks.

In the arithmetic sequence  the common difference remains constant between any two consecutive terms. In this sequence we can get the next term by adding one fixed value which is known as a common difference. It is also known as arithmetic progression(AP).

Formula for any nth term in AP,

T = a + nd

d = T₂-T₁

Where, a is first term , n is nth term and d is common difference

Given that,

The therapist suggests walking for 5 minutes each day for the first week

Increasing that time by 5 minutes per day each week

Number of weeks will it be before you are up to 45 minutes of walking per day = ?

At the end of first week, he will walk for 5 minute

in the beginning of second he started increasing time 5 minutes per day

So, before he reach up to 45 minutes weeks passed,

Before up to 45 minutes,

number of weeks =   ?

45 =  5 + 5n

n  =  8

Total number of weeks of walking = 1 + 8

                                                         =  9

Hence, the number of weeks is 9

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we conduct a one-sided test on the statistic one tail of a critical area of distribution.

The critical value for a two-tailed test of h0: β1 = 0 at α = .05 in a simple regression with 22 observations is 4.35.

What is a critical value?

A critical value can be calculated for different types of hypothesis tests. The critical value of a particular test can be interpreted from the distribution of the test statistic and the significance level.

Test of significance of linear regression between x and y.

Null hypothesis: There is no significant linear relationship between x and y.

Alternative hypothesis: There is a significant linear relationship between x and y.

Test statistic:

F0 = Mean square due to regression/  mean squared error ~ F(1, n-2)

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The polynomial equation with the given zeros is something like:

p(x) = a*(x - 1)²*(x + 2)²*(x - 5)²

Remember that for a polynomial of degree a with the zeros {x₁, x₂, ...} the polynomial can be written as:

p(x) = a*(x - x₁)*(x - x₂)*...

Here we don't know the leading coefficient, and we know that the zeros are:

{1, 1, -2, -2, 5, 5}

These appear twice because all have a multiplicity of 2.

Then the equation is:

p(x) = a*(x - 1)*(x - 1)*(x + 2)*(x + 2)*(x - 5)*(x - 5)

p(x) = a*(x - 1)²*(x + 2)²*(x - 5)²

Where a can be any real number different than zero.

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The angle measures for this problem are given as follows:

The sum of the measures of the internal angles of a polygon with n sides is given as follows:

S(n) = 180 x (n - 2).

Hence, for an hexagon, with six sides, the sum is given as follows:

S(6) = 180 x (6 - 2)

S(6) = 720º.

A regular hexagon has all angle measures equal, hence the measure of each angle is given as follows:

720/6 = 120º.

The segment FB is a bisection of the angle F of the hexagon, dividing it into two equal angles, hence the angle measures are given as follows:

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As per the given equation of the least squares regression line y=10+0.9x the score of Carla's final exam is 95.5.

As given in the question,

Given equation of the least squares regression line is :

y = 10 + 0.9x

Where 'y' shows the predicted final exam score

And 'x' represents the score of the first exam.

Carla's first exam score is equal to 95

Then predicted value 'y' of the Carla's final exam score is given by :

y = 10 + ( 0.9 ) × 95

⇒ y = 10 + 85.5

⇒ y = 95.5

Therefore, the predicted final score of Carla's as per the given least squares regression line is equal to 95.5.

The above question is incomplete, the complete question is :

In a statistics course a linear regression equation was computed to predict the final exam score from the score

on the first test. The equation of the least-squares regression line was y=10+0.9x where y represents the predicted final exam score and x is the score on the first exam.

Carla scored 95 on the first test. What is the predicted value of the Carla's score on the final exam?

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The change in y between x = 5 and x = 9 is 2572.

What is a function?

An assignment of a Y element to every X element constitutes a function from X to Y. Both the set X and the set Y are referred to as the function's domain and codomain, respectively.

Here, the function is given as y(x) = 4x ^ 3 + 3x ^ 2 - 3x.

we'll find the value of given function i.e. y when x = 5 and 9.

when x = 5,   y(5) = 4(5) ^ 3 + 3(5) ^ 2 - 3(5)

                            = 4(125) + 3(25) - 15

                            = 500 + 75 - 15

                            = 560.

when x = 9,   y(9) = 4(9) ^ 3 + 3(9) ^ 2 - 3(9)

                            = 4(729) + 3(81) - 27

                            = 2916 + 243 - 27

                            = 3132.

So, the change in y is  2572 (3132 - 560).

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The amount of tin was used to make the can of cylindrical can is 478 cm²

An equation is an expression that shows the relationship between numbers and variables.

Area is the amount of space occupied by a figure. Area is usually calculated for a two dimensional shape while volume is calculated for a three dimensional shape.

The surface area of cylindrical can = 2π(radius * height + radius²)

From the image:

radius = 9 cm/2 = 4.5 cm, height = 12.4 cm

Hence, substituting:

The surface area of cylindrical can = 2(3.14)(4.5 * 12.4 + 4.5²) = 478 cm²

The surface area of cylindrical can is 478 cm²

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The missing angle measure is of:

1. 25º.

The missing side length is of:

2. 12 cm.

Triangles ABC and ACD(3) are similar by the AAS theorem.

Similar triangles are triangles that share these following two features:

For this problem, we have that the segment SSC is the bisection of angle A, hence:

We have two similar angle measures, C and 25º, along with the opposite length, hence the AAS theorem is used.

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The rate of change In gallons of gas per year from 1995 to 1997 is: C. Δg/Δt = 4 gal/year.

In Geometry, the rate of change of the data in this table can be calculated by using this mathematical equation;

Rate of change (slope), m = (Change in y-axis, Δg)/(Change in x-axis, Δt)

Rate of change (slope), m = (y₂ - y₁)/(x₂ - x₁)

From the information provided in the graph above, we can logically deduce the following data points located on the line:

Substituting the given data points into the rate of change formula, we have the following;

Rate of change (slope), Δg/Δt = (y₂ - y₁)/(x₂ - x₁)

Rate of change (slope), Δg/Δt = (538 - 530)/(1997 - 1995)

Rate of change (slope), Δg/Δt = 8/2

Rate of change (slope), Δg/Δt = 4 gallon/year.

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The inverse of the function is f⁻¹(x)=3+√18+x, 3-√18+x

A relation is a function if it has only One y-value for each x-value.

Let us consider the function f(x)=(x-3)²

Where x belongs to [1, 2]

f(x)=x²+9-6x

y=x²+9-6x

Interchange the variables.

x=y²+9-6y

y=3+√18+x

y=3-√18+x

Relace y with f⁻¹(x)

f⁻¹(x)=3+√18+x, 3-√18+x

Hence, the inverse of the function is f⁻¹(x)=3+√18+x, 3-√18+x

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The symbol for sample deviation or standard deviation is "σ"(sigma).

The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. The standard deviation shows a "typical" variation from the mean. Because it uses the data set's original units of measurement, it is a well-liked measure of variability.

Because it is the square root of the means of the squared deviations from the arithmetic mean, the standard deviation is often referred to as root-mean-square deviation or sample deviation, sample standard deviation.

the standard deviation of sample deviation is denoted by σ(sigma).

Hence the symbol is "σ"(sigma).

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By  exponential expressions  3(5x + 3).(27)x as 3f(x)  this we get value 3.5x(27.3,x(x)f) + 3.3(27.3,x(x)f) .

Simply put, exponential expressions are a condensed approach to express powers. The base's frequency of use as a factor is indicated by the exponent.

f(x) = ax, where x is the input variable and is expressed as an exponent, is the formula for an exponential function.

In addition to being dependent on the exponential function, the exponential curve also depends on the value of x. Whenever a>0 and a1 are not equal.

Example :

3(5x + 3).(27)x as 3f(x) : 3.5x(27.3,x(x)f) +3 .3 (27 .3,x(x)f)

Steps

3(5x+3)(27x , 3f(x))

= 3(5x + 3)(27.3,x(x)f)

Apply the distributive law :

a(b + c) = ab + ac

a = 3(27x,3f(x)), b=5x,c = 3

=3(27x,3f(x)). 5x + 3(27x,3f(x)).3

=3.5x(27.3,x(x)f) + 3.3(27.3,x(x)f)

The Complete Question.

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Answer:

3c=3x+6

Step-by-step explanation:

-2+3c=2x+6+x

-2+3c=3x+6      First combine the x on the right side.

-2+3c=3x+6

+2            +2    Add 2 to both sides to eliminate 2 on the left side.

3c=3x+6

Here proof i.e. ∠1=∠3 is also given in the image for the given geometric shape.

What are geometric shapes?

In Mathematics, Geometric shapes are the figures which demonstrate the shape of the objects we see in our everyday life. In geometry, shapes are the forms of objects which have boundary lines, angles and surfaces. There are different types of 2d shapes and 3d shapes.

Shapes are also classified with respect to their regularity or uniformity. A regular shape is usually symmetrical such as a square, circle, etc. Irregular shapes are asymmetrical. They are also called freeform shapes or organic shapes. For example, the shape of a tree is irregular or organic.

In plane geometry, the two-dimensional shapes are flat shapes and closed figures such as circles, squares, rectangles, rhombus, etc.  In solid geometry, the three-dimensional shapes are cube, cuboid, cone, sphere and cylinder. We can observe all these shapes in our daily existence also. For example books (cuboid shape), glasses (cylindrical shape), traffic cones (conical shape) and so on.

Now

To prove   ∠1=∠3

Here as given ∠1+∠4=180°

and also ∠2+∠3=180°    (supplementary angles)

therefore,

∠1+∠4=∠2+∠3

and also ∠2=∠4  ( complementary angles)

Hence,

          ∠1=∠3

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The two supplementary angles are 155 and 25.

Two angels whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.

Given;

Two angles are supplementary

One is 150 degrees more than 1/5 of the others

Let one angle be x

Then the other angle will be x/5+150

Now,

x+ x/5+150=180

6x/5+150=180

6x/5=180-150

6x/5=30

x=150/6

x=25

Other angle= x/5+150=25/5+150

=155

Therefore, the angles will be 155 and 25.

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The spaceship's velocity modulus increased due to the firing of the brake rocket in order to transfer the spacecraft into a circular orbit of the Moon satellite.

When approaching the Moon, a spacecraft follows a parabolic trajectory which is almost tangent to the Moon's surface. At the moment of maximum approach, the brake rocket is fired for a short time interval. This causes a decrease in the spacecraft's velocity and an increase in its centripetal force. This, in turn, causes the spacecraft to move away from the Moon and into a circular orbit of a Moon satellite. The increased centripetal force causes the spacecraft to accelerate, and thus its velocity modulus increases. The magnitude of this increase in velocity modulus depends on the duration and power of the brake rocket. In conclusion, the velocity modulus of the spacecraft increases due to the firing of the brake rocket.

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