Example
The product of 4 and (3 + x) is equal to 36. What is the value of x?
The equation 4(3 + x) = 36 models this statement.
Think: 4 times what number is 36?
Since 4.9 equals 36, that means (3 + x) equals 9.
Since 3 + x = 9, and 3 + 6 = 9, that means x equals 6.
The sum of twice a number, n, and 14 is 30. Write an equation that models this
statement. Then explain how you might use reasoning to find the value of n.

The solution of the expression in scientific notation is 1.5 * 10^-2

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

6.0 * 10^4 / 4.0 * 10^8

Divide 6 by 4

So, we have

6.0 * 10^4 / 4.0 * 10^8 = 1.5 * 10^4/10^8

Evaluate the final quotient

6.0 * 10^4 / 4.0 * 10^8 = 1.5 * 10^-2

Hence, the solution is 1.5 * 10^-2

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Solutions for the system of equations  2x −5y =1  , 4x −10y =3 has no solution as ( 2 /4 ) = (-5/-10) ≠ (1/3) .

Simplify the system of equations to get the solution of the system :

2x - 5y = 1

⇒ 2x = 1 + 5y

⇒ x = ( 1+ 5y ) / 2  __(1)

4x -10y = 3

⇒ 2 ( 2x - 5y ) = 3

⇒2x - 5y = 3/2  ___(2)

Standard form of the system of equations are :

a₁x + b₁y + c₁ = 0

a₂x + b₂y + c₂ = 0

Substitute the value of x from (1) into (2) we get,

2 ( 1 + 5y )/2  - 5y = 3/2

⇒1 + 5y -5y = 3/2

⇒1 = 3/2

⇒2 = 3 which is not true.

System of the equation has no solution.

Here, ( a₁ /a₂ ) = (b₁ /b₂) ≠ (c₁ /c₂ ) that is ( 2 /4 ) = (-5/-10) ≠ (1/3) .

Therefore, the system of equations has no solution.

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The C++ or Python code for the given problem is float ballRadius = ballHeight / 2.0;

To assign the value of ballRadius with ballHeight divided by 2.0, you can write the following code in a programming language such as C++ or Python:

float ballRadius;

float ballHeight = [some value];

ballRadius = ballHeight / 2.0;

This code uses the division operator (/) to divide ballHeight by 2.0, which results in a floating-point value. This value is then assigned to the variable ballRadius. By dividing ballHeight directly by 2.0, we are not using the fraction 1.0 / 2.0.

In detail, the operation ballHeight / 2.0 performs floating-point division, which means that the result will be a floating-point value with decimal places. The value of ballHeight is divided by 2.0, which is a floating-point constant. The result of this division is assigned to the variable ballRadius, which is also a floating-point value.

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Answer:

The answer is C. 32,568. Assuming that the gumballs are 1 inch in diameter and packed in a rectangular prism, each compartment can hold approximately 190% of the volume of the spheres. Therefore, each compartment can hold approximately 7,560 gumballs. Since there are 3 compartments per machine and 25 machines, the total number of gumballs that Raven ordered is 32,568.

Step-by-step explanation:

All the missing reasons are given below.

A parallelogram is a two-dimensional shape with four sides and opposite sides that are parallel and equal in length. It can be defined as a quadrilateral with two pairs of parallel sides. In other words, opposite sides of a parallelogram are parallel and equal in length. The opposite angles of a parallelogram are equal and its diagonals bisect each other. A rectangle and a rhombus are both examples of parallelograms. The properties of parallelograms are important in geometry, trigonometry, and linear algebra.

The missing reasons for steps 3 and 4 are:

So the complete proof would be:

Given: ABCD with diagonal BD

Prove: ABD = CDB

Statements:

Reasons:

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The population mean (μ) is estimated to be: μ = 18 minutes

In this problem, we are given a sample of 81 people who waited in line for a rollercoaster at an amusement park. We are also given the sample mean (18 minutes) and the sample standard deviation (0.5 minutes).

To estimate the population mean (μ), we use the sample mean (18 minutes). Since the sample mean is a good estimate of the population mean, the estimated population mean (μ) is 18 minutes.

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The expected population mean () is: = 18 minutes.

Additionally, the sample mean (18 minutes) and sample standard variation are provided (0.5 minutes).

We use the sample mean to determine the population mean (). (18 minutes). The expected population mean () is 18 minutes because the sample mean is a reliable indicator of the population mean.

From the line dot plot of 12 college students wages,

The Mean is $118.25

The Median is $118.

It is the average value of the set given.

It is calculated as:

Mean = Sum of all the values of the set given / Number of values in the set

We have,

From the dot plot.

Weekly wages = 112, 113, 116, 116, 116, 118, 118, 119, 119, 124, 124, 124.

Now,

Mean = Sum of all the values / Number of values

= (112 + 113 + 116 + 116 + 116 + 118 + 118 + 119 +119 + 124 +124 +124) / 12

= 118.25

Median = Mid value from the wages.

= 118

Thus,

The Mean is $118.25

The Median is $118.

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The radius, the arc length, and the central angle of the resulting circular sector is 13 cm

What is Radius?

A radius of a circle or sphere is any of the line segments connecting its center to its perimeter, and it is also their length in more recent usage. The term is derived from the Latin radius, which means both ray and spoke of a chariot wheel.

1) volume of the cone = 1/3[tex]\pi[/tex][tex]r^{2}[/tex]h

r = radius

h = height or depth

given, D = 10 cm

so r = 5 cm

v = 1/3*22/7*5*5*12

v = 100[tex]\pi[/tex]

2) for up to 6cm height

volume = ?

here in this triangle

triangle ΔAOC and ΔEDC are similar (have some shape as all three angle of both Δ are same

when two figure are similar the ratios of the length of their corresponding sides are equal

here,  ΔAOC and ΔEDC

so r = 2.5cm

so volume when cup is 6cm deep

v1 = 1/3[tex]\pi r^{2} h[/tex]

v1 = 1/3 *[tex]\pi[/tex]*2.5*2.5*6

v1 = 12.5[tex]\pi[/tex]

length = [tex]r^{2}+h^{2}[/tex] pythogonus theorem

length = 13cm

arc length = angle (in radius)*radius

2*[tex]\pi[/tex]*5

=10[tex]\pi[/tex]

centre angle = 10[tex]\pi[/tex]/13 radiance

= 10 * 180 Degree/13

=138.46 degree

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Over the 0.33 and 0.375 range of values for the "bill passing" will country C remain optimal.

a. To calculate the estimated costs for each country, we must divide the cost by the likelihood of the bill being approved or rejected. Each country's expected cost is computed as follows:

Country A: 0.4 * 260 + 0.6 * 210 = 244

Country B: 0.4 * 320 + 0.6 * 160 = 256

Country C: 0.4 * 240 + 0.6 * 240 = 240

Country D: 0.4 * 275 + 0.6 * 210 = 250

Since country C has the lowest expected cost of $240,000, East West should choose this country for manufacturing.

b. Part a solution will continue to stay optimal as long as the estimated cost for country C is less than the estimated cost for the other countries. This means that if the "bill passing" range is such that country C still has the lowest estimated cost, the solution will remain optimal. To evaluate this range, we can find the "break-even points," which are the points at which the expected costs for country C equal the expected costs for countries A and D. The following is how these break-even points are calculated:

BE (country A) = (210 - 240) / (260 - 210) = 0.375

BE (country D) = (210 - 240) / (275 - 210) = 0.33

This means that as long as the probability of the bill passing is between 0.33 and 0.375, the solution of choosing country C will remain optimal.

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The conversion of 150 pounds weight in kilograms 68.039.

What is meant by weight?

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Answer:

s=8

Step-by-step explanation:

The two angles are vertical angles and vertical angles are equal.

110 = 8s-2

Add 2 to each side.

110+2 = 8s-2+2

112 = 8s

Divide each side by 8

112/8=8s/8

14=s

Answer:

Step-by-step explanation:

Angle ABD plus angle DBC = 90. That's what that little square in the corner there means...a right angle which is 90 degrees. Using substitution,

3x + 15 + 2x = 90 and

5x + 15 = 90 and

5x = 75 so

x = 15. Now we need to plug in 15 for x in 2x to get 2(15) which is 30. Second choice down.

If the height of a square pyramid remains fixed while its sides of the base is multiplied by 3, then the volume of the new pyramid is 108 cm³ (option C)

The volume of a square pyramid is given by:

V = A . h = a² . h

Where;

A = the area of the base = a²

h = height of the pyramid

a = sides of the base

In this problem,

V = 12 cm³

a² . h = 12   .... (equation 1)

Now, the sides of the base are multiplied by 3. Hence, the new volume will be:

V = (3a)² . h

  = 9 a² . h

from equation 1 we know that a² . h = 12. Hence,

V = 9 x 12 = 108 cm³

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Answer:

150

Step-by-step explanation:

80% on time so 20% late, 30 late

30/20% = 150

The graph representing the inequality x ≥ 12 is with a closed and shaded circle to the left.

What is inequality ?

An inequality is an expression that shows the non-equal comparison of the two or more numbers and variables. A number line can be used to represent numbers put on regular intervals. A number line is sometimes   used to represent an inequality.

The height of the water slide is = 56 feet

The graph representing the inequality x ≥ 12 is shown on the number line begining from 12 with a closed and shaded circle.

Therefore, The graph representing the inequality x ≥ 12 is with a closed and shaded circle to the left.

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The measure of the angle X for the trigonometric ratio of sine X equal to 0.7547 is 49° to the nearest degree.

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

For the sine of X equal to 0.7547, we can make x the subject by finding the sine inverse of 0.7547 as follows:

sin X = 0.7547

X = sin⁻¹(0.7547)

X = 48.9992

Therefore, the measure of the angle X for the trigonometric ratio of sine X equal to 0.7547 is 49° to the nearest degree.

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On solving the provided question, we can say that by percentage the proportion of pupils who participate in either cricket or volleyball.

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions.

In a study conducted at a school, 300 students preferred volleyball, 250 preferred cricket, and 110 preferred playing both sports. Calculate the following using a Venn diagram: a. the number of pupils who play cricket exclusively.

b. the proportion of pupils who participate in either cricket or volleyball.

After their SEE, a survey found that 120 students desired to be both an engineer and a doctor, while 190 students wanted to be both. Draw a Venn-diagram and count the number of students who said they wanted to be neither of them if 300 students were surveyed.

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Answer:93000

—————————————-

Let's call the number of small stuffed animals sold "x" and the number of large stuffed animals sold "y".

We know that:

x + y = 27 (the total number of stuffed animals sold)

13x + 12y = 350 (the total amount of money Aya earned)

We can use these two equations to solve for x and y. To do this, we'll use substitution:

x + y = 27

x = 27 - y

Now, we'll substitute this expression for x into the second equation:

13(27 - y) + 12y = 350

351 - 13y + 12y = 350

351 = 350

This equation is true for all y, which means that we cannot solve for y using these two equations. We need more information to determine the number of small and large stuffed animals sold.

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x + y = 27 (the total amount of stuffed creatures sold) (the total number of stuffed animals sold)

These two formulae can be used to find the answers to x and y. We'll use replacement to accomplish this:

x + y = 27

x = 27 - y

We will now change x in the second equation to the following expression:

13(27 - y) + 12y = 350

351 - 13y + 12y = 350

351 = 350

The height of the juice container with a base area of 100cm² is 15 cm

Is the measure of the space occupied by a body bounded by an environment called perimeter, the same is expressed in units of squared side. Example: ft^2, m^2

The base area of a cylinder is given by:

base area = π*r²

base area = 100 cm^2

100 = π * r^2

r^2 = 100 / π

r = √(100 / π)

The volume of a cylinder is given by:

volume = π*r²*h

1500 = π * [√(100 / π)]^2 * h

1500 = π* (100 / π) * h

1500 = 100h

Clearing the variable (h) height we have:

h = 1500 / 100

h = 15 cm

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The total number of Cheeseburgers will be 263.

What is an Equations?

Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

Cheese burgers= x

Hamburgers= y

y-x= 62

x+y = 588

we add both the equations we get 2y = 650

y=650/2

y= 325

x = 588-325= 263

Hence, The total number of Cheeseburgers will be 263.

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If a fair coin is tossed 14 times then the probability that exactly three head occur is 0.023 .

The Binomial Probability formula is used to find the Probability of getting exactly 3 heads in 14 tosses of a fair coin .

The formula is:

⇒ P(X=k) = ⁿCₓ × pˣ ×  (1-p)ⁿ⁻ˣ  ;

where,

⇒ P(X=k) is the probability of getting exactly "x" heads in n tosses of coin ;

⇒ n (number of tosses) =  14

⇒ k (number of heads) = 3

⇒ p (probability of getting heads in a single toss) =  0.5 for a fair coin

Substituting  in the values, we get:

⇒ P(X = 3) = ¹⁴C₃ * (0.5)³ * (1 - 0.5)¹¹

⇒ P(X = 3) = ¹⁴C₃ * (0.5)³ * (0.5)¹¹

On simplifying further ,

we get ;

⇒ 0.02221679 ≈ 0.023 .

Therefore , the probability of getting exactly 3 heads 0.023 .

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All the given options are paradoxical, and it's not possible to determine their truth value as they depend on their own veracity.

The statement "Exactly one of these statements is false" can be referred to as the liar paradox. It is a classic example of self-referential statements, where the truth of the statement depends on its own veracity.

In this paradox, if the statement is true, then it must be false, and if the statement is false, then it must be true. Hence, this statement creates a paradox and it's impossible to determine its truth value.

In the case of options (b), (c), and (d), it's also not possible to determine their truth value as they too depend on the truth value of the other statements, which are paradoxical.

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Answer: citizen scientists are already providing large amounts of data for monitoring biodiversity, but they could do much more, according to a new study published in the journal Biological Conservation, which suggests that citizen science has the potential to contribute much more to regional and global assessments of biodiversity. Citizen scientists are regular people who provide data or input to science, for example by monitoring species in their community or examining satellite imagery for evidence of deforestation or land use change.

Step-by-step explanation:

Sales tax is added to the price.

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

The statement is about sales tax

As a general rule

sales tax are added to the price of the item that is being bought

So, the complete statement is Sales tax is added to the price.

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The limit of the function [tex]\lim_{x \to9}[/tex]  [( x² - 81 ) / ( x - 9 ) ] is equal to 18.

[tex]\lim_{x \to9}[/tex] [( x² - 81 ) / ( x - 9 ) ]

Substitute the limit x tends to 9 in the function we have,

= ( 9² - 81 ) / ( 9 - 9 )

= ( 81 - 81 ) / 0

= 0 /0

0 /0 form is not defined term.

Simplify the function before substituting the limit we have,

[tex]\lim_{x \to9}[/tex] [( x² - 81 ) / ( x - 9 ) ]

= [tex]\lim_{x \to9}[/tex] [ ( x ² - 9² ) / ( x - 9 ) ]

= [tex]\lim_{x \to9}[/tex] [ ( x - 9 ) ( x + 9 ) / ( x - 9 ) ]

= [tex]\lim_{x \to9}[/tex] ( x + 9 )

= 9 + 9

= 18

Therefore, the value of the limit for the function [tex]\lim_{x \to9}[/tex] [( x² - 81 ) /( x - 9) ] is equal to 18.

The given question is incomplete, I answer the question in general according to my knowledge:

Find the following limit or state that it does not exist.

[tex]\lim_{x \to9} \frac{(x^{2} - 81)}{(x - 9)}[/tex].

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The conditions that must be met for the results of an ANOVA test to be reliable are Independence , Random Sampling , Large Sample Size and Normality .

The ANOVA (Analysis of Variance) is defined as a statistical method that is used to determine if there are significant differences among the means of two or more groups.

For the results of an ANOVA test to be reliable, the conditions that must be met are :

(i) Independence: The observations within each group should be independent of each other.

(ii) Normality: The data within each group should be approximately normally distributed.

(iii) Random Sampling: The samples within each group should be selected randomly from the population.

(iv) Large Sample Size: The sample size within each group should be large enough to provide a robust estimate of the population mean.

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Population - - > Sampling Frame - - > Sample - - > Individual being surveyed is the order from largest to smallest.

The population is the largest as they include all units or subject of interest in a particular study or experiment.

Next is the sampling frame which is the list or compilation of all subjects which can form part of a sample. It is a compilation of all elements in the population from which the sample can be drawn.

The sample is a subset of the population of population, usually selected at random and it is representative of the population.

The individual surveyed represents a single subject or observation from the chosen sample.

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tangential acceleration a in the form without finding t and n is |a|= T+ t N

The tangential acceleration is a measure of the rate of change in the magnitude of the velocity vector, i.e. speed, and the normal acceleration are a measure of the rate of change of the direction of the velocity vector.

r(t)=(cost+ t sin t )i +(  sin t−t cost)j

first find the particle's velocity.

[tex]v=dr/dt\\=(−sint+sint+tcost)i^+(cost−cost+tsint)j^\\\\ \\=(tcost)i^+(tsint)j^[/tex]

find the speed.

|v|=[tex]\sqrt{t^{2} cos^{2}t+ t^{2} sin^{2}t }[/tex]

    = √t^2

    =t

When  t>0 ,  |t| simply becomes  t .

We know that  a T= [tex]\frac{d}{dt}[/tex]|v|

, which we can use to find that  [tex]\frac{d}{dt}[/tex](t)=1

Now that we know  a T , we can use it to find  a N

a=(cost−t sin t ) i+(sin t +t cos t)j

|a|^2=t^2+1

a N=√(t^2+1) -1

     = t

By substituting this back into the original definition, we find that

|a|=(1)T+(t)N=T+ t N

a in the form without finding t and n is |a|= T+ t N

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A piecewise function which is shown on the graph include the following: A. piecewise function A.

In Mathematics, a graph can be defined as a type of chart that is typically used for the graphical representation of ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis) respectively.

Based on the graph shown above, we can evaluate the piecewise function based on the following domains (input values or independent values);

For the domain x ≤ -2, the value of y (y-value) is equal to 5. Additionally, for the domain -2 < x < 1,we can logically deduce that the function is a polynomial, which implies that it must have this ordered pair (0, -5):

For -2 < x < 1, when x is equal to 0 and y is equal to -5;

y = x² ± 5

For the domain x ≥ 1, we know that, when y is equal to 0, x would lie between 3 and 4;

y = 2^{x - 2} - 3

When y = 0, the value of x is given by:

0 = 2^{x - 2} - 3

2^{x - 2} = 3

x = 3.584.

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