The statement, 81:135 = 36:60 is a proportion.
If a and b are non-zero numbers and c = 0, then a/c = b/c is a proportion.
State whether the following statements are proportions or not. If it is a proportion, then prove by the definition of proportion. If not, then solve the correct value of x. Be sure to show the complete steps in solving for x.

The small boy can use the mathematical reasoning of similar triangles and the concept of ratios to determine the height of the light post.

Similar triangles are triangles that have the same shape but can have different sizes. In this case, the shadow of the boy, the boy himself, and the light post form similar triangles.

Let h be the height of the light post, x be the distance between the boy and the light post, and s be the length of the shadow, we can use the following ratios -

(boy's height) / (boy's shadow) = (light post height) / (light post shadow)

i.e. (4 feet 6 inches) / (3 feet 4 inches) = (h) / (x)

Now, we can find the height of the light post by using the above equation and the given values of the boy's height and the shadow.

The small boy can measure the distance between him and the light post, and he can use this value in the above equation to determine the height of the light post. The equation is h/x = (4.5)/(3.33)

This is the ratio of the height of the light post and the distance between the boy and the light post, so h = (4.5 * x) / (3.33)

In this way, the small boy can use the mathematical reasoning of similar triangles and the concept of ratios to determine the height of the light post.

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To find the value of FG, FG is 11.

When there exist a triangle which has two of its sides to be equal in length, then it can be referred to as an isosceles triangle. Such that its two angles opposite the equal sides have equal measure.

Considering the given question, to find the value of FG;

since it has been given that <F ≅ <H, then;

GH ≅ FG  (properties of sides of an isosceles triangle)

Such that;

GH = 11, then

GH ≅ FG = 11

Thus the value of FG is 11.

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Answer:

a. The population is 100 college students.

b. The population is finite.

c. Two parameters and their values:

The total population size: 100

The sample size: 10

d. The sample is a group of 10 college students chosen from the population of 100.

e. Two corresponding statistics and their values:

The sample proportion: This is the proportion of individuals in the sample who have a certain characteristic (e.g. majoring in a certain subject). It is calculated by taking the number of individuals with the characteristic and dividing by the sample size. Its value would be different for each sample of size 10 taken.

The sample mean: This is the average of the measurements for the individuals in the sample. It is calculated by summing up the measurements and dividing by the sample size. Its value would be different for each sample of size 10 taken.

f. When another sample of size 10 is taken, the population and its size remains fixed but sample proportion and sample mean would change.

Step-by-step explanation:

Answer:

Okay so the answer would be 8 cups

Step-by-step explanation:

the reason this is is because if you combine the cups its 2 2/3 so then all you have to do is multiply it by 3 and then your answer is 8 cups of sugar

Answer:

Inequality Form:

x ≤ −5/12

Interval Notation:

(−∞, −5/12]

Step-by-step explanation:

The breaking apart numbers with addition help us to solve an addition more efficient than left-to-right addition.

Addition in math is a process of combining two or more numbers.

Given that, think about what you know about breaking apart numbers with addition.

Breaking apart an addend is a mental math strategy for addition. Some students may find this method more efficient than left-to-right addition.

This strategy involves breaking up one addend in an equation into more manageable parts.

1) 32 + 46 =

Breaking the second term 46 in 40 + 6

32 + 40 + 6

= 72 + 6

= 78

2) 89 + 73 =

Breaking the second term 73 into 70 + 3

89 + 70 + 3

= 159 + 3

= 162

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Answer:  1.25 or 1, 1/4

The least number of seats the manger could order to 270 seats

The information that the the seats are sold only in groups of 10 will help to know that the order will be in a multiple of 10.

The manager wants to order 267 seats and this is not a multiple of 10 the nearest multiple of 10 is 270.

This is because, 260 will be short of want the manager want however ordering for 270 will be in excess with three seats.

Hence the manager will order 270 and heave 3 extra seats

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Answer:

y=3x+5

Step-by-step explanation:

an equation is always

y= slope*x + intercept so y=3x+5

The solution of the system of equations:

-2x - 10y = -2

-4y = x

is the point (-4, 1).

Here we want to solve the system of equations below:

-2x - 10y = -2

-4y = x

By the substitution method, to do so, we need to isolate one of the variables in one of the equations and then replace that in the other equation.

We can see that x = -4y is already isolated on the second equation, then we can replace this on the first one to get:

-2*(-4y) - 10y = -2

We can solve this for y.

8y - 10y = -2

-2y = -2

y = -2/-2 = 1

And thus, the value of x is:

x = -4y

x = -4*1 = -4

The solution of the system is (-4, 1).

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The sum of the two given is 7.867.

When expressed in scientific notation, the number of significant figures equals the number of digits. Significant figures are the numbers that give any measurement meaning.

The decimal point is marked by leading zeros. They don't matter much. After the decimal point, a trailing zero is reliably known. It is important. In a whole number, every non-zero number has importance.

You must keep in mind these three guidelines in order to ascertain how many significant figures are present in a number.

If you add 4.667 g and 3.2 g,

the answer has 4 significant figures.

The sum of the two given is 7.867.

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The full question:

If you add 4.667 g and 3.2 g how many significant figures does the answer have

Create a table with the place values for the first and second factors down the left and the top and bottom, respectively.

What is the box method?

Multiplication using the box method: Create a table with the place values of the first and second factors down the left and the top and bottom, respectively. Second step: multiply the place values and add the results to the table. Step 3: Add up all of the table's rows. Step 4: Add the sums of these rows.

Placing the first word in the first box and the last term in the last box is the first step in utilizing the box technique to factor a trinomial. Multiply the first and last boxes after that. Identify the first and last boxes' products, which together make up the middle word. Put these words in the remaining spaces.

Here's how you can use the box method to distribute and simplify the expression:

( -5x - 2 ) ( 5x + 4 )

⇒-5x -2

⇒5x 4

⇒-25x^2 -10x + 20x - 8

⇒-25x^2 + 10x - 8

So the simplified expression is:

-25x^2 + 10x - 8.

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The length of the segment MP is 38 units

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

The triangle

On the triangle, we have

9x - 34 = 3x + 14

Evaluate the like terms

6x = 48

Divide by 6

x = 8

Given that

MP = 9x - 34

We have

MP = 9 * 8 - 34

Evaluate

MP = 38

Hence, the length of MP is 38 units

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The set of natural numbers between 11 and 155 is {12, 13, 14, 15, ..., 154}.

A natural number is a positive integer, also known as a counting number. The set of natural numbers is represented by the symbol {1, 2, 3, 4, ...}.

The set of natural numbers between 11 and 155 includes all the natural numbers that are greater than or equal to 12 and less than or equal to 154.

This set is represented by {12, 13, 14, 15, ..., 154}. This set is infinite, meaning it contains an infinite number of elements. The dots indicate that the set goes on infinitely in both directions, but in this case, we are only concerned with the numbers between 11 and 155.

It is important to note that the answer "A" is incorrect because it only contains 2 elements, while the correct answer B is infinite set of numbers between 11 and 155 inclusive.

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"No, the flowers were not put into groups first and then randomly assigned the two additives.

Now, According to the question:

Any well-defined method that yields an observable outcome that cannot be precisely predicted in advance is referred to as a random experiment. To avoid any ambiguity or surprise, a random experiment must be properly defined.

"Information available from the question"

The florist selects 20 flowers of different

And puts in each vase with same amount of water.

10 flowers have been assigned to receive the new additive.

The remaining 10 flowers receive the original additive.

Based on the data, this is not a randomized block design for the experiment because the flowers were not put into groups first and then randomly assigned the two additives.

Therefore,  "No, the flowers were not put into groups first and then randomly assigned the two additives.

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The probability of choosing a perfect cube is [tex]\frac{7}{502}[/tex] .

According to the question,

Suppose a number is chosen at random from the set {0,1,2,3,...,501}.

Cube of 1=1

Cube of 2=8

Cube of 3=27

Cube of 4=64

Cube of 5=125

Cube of 6 = 216

Cube of 7 = 343

Cube of 8 = 512

So in a set of members {0,1,2,3,... 501}, only 7 numbers are a cube of a natural number: 1,8,27,64,125,216,343.

The probability of selecting cubes in a set of members {0,1,2,3,... 501} is

= [tex]\frac{7}{502}[/tex]

So, the probability is [tex]\frac{7}{502}[/tex] .

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The solution to the expression when x = 3 is 26

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

8x + x * 2/3

Also, we have

x = 3

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

8 * 3 + 3 * 2/3

Evaluate the product

24 + 2

Evaluate the sum

26

Hence, the solution is 26

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Complete question

Given that 8x + x * 2/3, calculate the expression when x = 3

The algebraic expression 8x + 2x/3 is simplified to a simple fraction as 26x/3

We shall first find the lowest common multiple (LCM) of the denominators of both terms to have a single fraction and then we simplify as follows;

The denominator of 8x is 1 and 2x/3 is 3

LCM of 1 and 3 is 3

we simplify to a single fraction;

multiply the term 8x by the LCM 3

(3 × 8x + 2x)/3

multiply the term 8x by the LCM 3

(24x + 2x)/3

add the algebraic terms 24x and 2x together

26x/3

Therefore, the algebraic expression 8x + 2x/3 is simplified to a simple fraction as 26x/3.

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The translation rule that defines a translation 5 units right and 2 units up is given as follows:

(x,y) -> (x + 5, y + 2).

A translation is a movement to a graph or figure in which only the position of the figure changes, either left, right, up or down, keeping the inclination, orientation and congruence.

The translations are represented as follows:

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The system of equations is:

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

Total amount invested = $110000

Using the fiollowing variable representations:

We have

a + b + c = 200000

Using the total interest earned of 7145, we have:

10.9% * a + 2.9% * b + 5% * c  = 11165

So, we have

0.109a + 0.029b + 0.05%c  = 11165

Country day invests $20000 more in bonds than in CDs.

So, we have

b = c + 20000

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To add or subtract mixed numbers, first add or subtract the integer (whole number) portions of the mixed numbers, then add or subtract the fractional portions of the mixed numbers. Reduce the fractional portion of the answer to its lowest terms and combine it with the integer portion of the answer to get the final answer.

1. To add mixed numbers, first add the integer (whole number) portions of the two mixed numbers together. The result is the integer portion of your answer.

2. Next, add the fractional portions of the two mixed numbers together. If the fractional parts of the two mixed numbers have different denominators, you'll need to convert them to have the same denominator.

3. Reduce the fractional portion of your answer to its lowest terms. This is the fractional portion of your answer.

4. Combine the integer portion of your answer with the fractional portion of your answer to get the final answer.

5. To subtract mixed numbers, first convert the fractional portion of the subtrahend (the number being subtracted) to an equivalent fraction with the same denominator as the minuend (the number being subtracted from).

6. Subtract the integer portions of the two mixed numbers. The result is the integer portion of your answer.

7. Subtract the fractional portions of the two mixed numbers. Reduce the fractional portion of your answer to its lowest terms. This is the fractional portion of your answer.

8. Combine the integer portion of your answer with the fractional portion of your answer to get the final answer.

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Adam has gathered 232.32 g of trace elements, which are contained in a cylindrical container with a radius of 8.4 cm and a height of 10.8 cm.

Radius of the cylinder 8.4 cm

Height of the cylinder = 10.8 cm

Volume of the cylinder = π r² h

When we change the values in the formula, we obtain:

V = π (8.4 cm)² (10.8 cm)

V = 22 / 7 (70.56 cm²) ( 10.8 cm)

V = 2395.008 cm³

Presence of particle = 0.097 g for every cm³

The element's trace for 2395.008 cm3 will be:

= 2395.008 × 0.097 g

= 232.315776 g

As a result, Adam has gathered 232.32 g of trace elements in the cylindrical container with a radius of 8.8 cm and a height of 15.9 cm.

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The correct answer for equivalent interest rate and no. of times will the money be compounded is C) 1.5% and 16 times respectively.

The annual interest rate of 6% is equivalent to a quarterly interest rate of 6% / 4 = 1.5%. The money will be compounded quarterly, so it will be compounded 16 times in total over 4 years.

Compound interest is computed as interest on the initial principal plus any accrued interest from prior periods. Money multiplies more quickly thanks to compounding, and the more compounding periods there are, the higher the compound interest will be.

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Based on a survey of 2718​ people, a research center concluded that​ 32% of Americans​ "always" make a special effort to sort and recycle​ glass, cans,​ plastic, or​ papers. Participation bias is there in this case.

The bias would have no effect on a reader's perception of the assertion because no group of persons is much more likely to respond to the poll than any other.

When comparisons are performed between groups of patients who differ in outcome determinants and the differences are connected to the result, participation bias emerges.

1. Participation bias is inherent in studies that involve participant enrollment.

2 Because selective participation might jeopardize study external validity, determining the magnitude of participation bias is critical for optimizing inference from these investigations.

Few community studies have looked into the impact of participation bias. Nonparticipants in one population-based study of myocardial infarction (MI) were older, had more comorbidity, and had a lower survival rate than participants.

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The ratio of the number of empty tables to the total number of tables 13:21.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that 8 of the tables at Joy's Italian Restaurant are full

13 tables are empty

The total number of tables in the restaurant are 8+13=21

We have to find  ratio of the number of empty tables to the total number of tables

Empty tables = 13

Total number of tables=21

Ratio of the number of empty tables to the total number of tables 13:21

Hence, the ratio of the number of empty tables to the total number of tables 13:21.

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Sari-sari store must sell 20 pieces of type (a) detergent and 26 pieces of type (b) detergent to raise at least php 180.00.

Determine the number of pieces of type (a) detergent.

9.00 x x = 180.00

Divide both sides by 9.00:

x = 20 pieces

Determine the number of pieces of type (b) detergent.

7.00 x y = 180.00

Divide both sides by 7.00:

y = 25.71

Since we cannot sell partial pieces, the number of pieces of type (b) detergent must be rounded up to 26 pieces.

Therefore, the sari-sari store must sell 20 pieces of type (a) detergent and 26 pieces of type (b) detergent to raise at least php 180.00.

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Answer:

D) two solutions

Step-by-step explanation:

because the first one is: x = 5y + 4

and the second one is: -2x+10y=8

and the equals in the first one is just how to get the value of x and it doesn't count as a third solution

All the expressions which are equivalent to -5/2z-5/6 are given below.

Expressions that are equivalent to the same thing, even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).

Given:

An expression,

-(5/2)z - 5/6

Simplifying,

-(5/2)z - 5/6,

= -5(z/2 + 1/6) is an equivalent expression.

= -5/2 (z + 1/3) is an equivalent expression.

Therefore,  -5(z/2 + 1/6)  and -5/2 (z + 1/3) are the equivalent expressions

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The total amount of oil he would have if he pours them both in a can is 2.7 liters.

In order to determine the amount of oil he would have, add both numbers together. In order to add the numbers, both numbers have to be in the same form. One of the numbers is a decimal and the other is a fraction.

In order to convert the fraction to a decimal, divide the numerator by the denominator.

1/5 = 0.2

Total number of oil = 0.2 + 2.5 = 2.7 liters

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Answer:

Step-by-step explanation:

Total number = 260

Ratio would be 1 : 3

So, the first part is given by

[tex]\frac{1}{4}[/tex] x 260

=[tex]\frac{260}{4}[/tex]

=65

And the second part is given by

[tex]\frac{3}{4}[/tex] x 260

=[tex]\frac{780}{4}[/tex]

=195

Hence, the first and second part are 65 and 195 respectively.

This problem can be solved used linear equations. Here there are two variables, number of students and number of adults. After calculations we get the number of students attended the play is 50.

Lets consider the number of students is x and number of adults is y.

Total tickets sold = 300

    x + y = 300  ------------ equation 1

The amount of total tickets sold is 3000.

Amount sold to students = 5x

Amount sold to adults = 11y

  So, 5x+11y =3000 ----------- equation 2

Equating the x term for equation 1

 Multiplying both sides with 5

 5 (x+y) = 5 × 300

 5x + 5y = 1500 ---------- equation 3

Subtracting equation 3 from equation 2

   5x + 11y = 3000

-  ( 5x + 5y = 1500)

    6y = 1500

    y = 1500/6 = 250

Number of adult attended = 250

From equation 1, x+y = 300

Substituting the value of y

                x + 250 = 300

                    x    = 300-250 = 50

So number of students attended is 50

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Answer: 50

Step-by-step explanation: i got it right on my quiz

Take care to properly set up your equations. The $3,000 is the sum of total money from student tickets and total money from the adult tickets.