Complete the following ratio table so that each pair represents the same rate.
1
5
2
10
3
15
4
20
5
25

Answer:

One-fourth equals three-twelfths

Step-by-step explanation:

From the above question:

The fractions

One-fourth

: A fraction bar divided into 4 parts. 1 is shaded.

One-half

A fraction bar divided into 2 parts. 1 is shaded

Three-twelfths:

A fraction bar divided into 12 parts. 3 are shaded.

Which is a correct comparison of these fractions?

Comparing the options

a) One-fourth equals three-twelfths

= 1/4 = 3/12

Divide numerator and denominator by 3

= 3 ÷ 3 /12 ÷ 3

= 1/4

Option a is correct

b) One-half is less than three-twelfths

1/2 < 3/12

This statement above is wrong.

One half is greater than three twelfths

1/2 is > 3/12

1/2 > 1/4

c) One-fourth is greater than one-half

1/4> 1/2

This statement above is wrong.

1/2 is greater than 1/4

d) Three-twelfths is greater than one-fourth

This is statement is wrong. Three -twelfths is equal to one - fourths

The correct comparison of these fractions is One-fourth equals three-twelfths.

If you save $2,015.82 every year at an interest rate of 8%, you can retire in 30 years and live another 25 years while still having enough money to spend $80,000 per year.

To calculate the amount you need to save per year for the next 30 years, we can use the future value of an ordinary annuity formula.

The future value of an ordinary annuity formula is:

\(FV = P \cdot \left(\frac{(1 + r)^n - 1}{r}\right)\)

Where:

FV = Future value of the annuity

P = Payment amount per period

r = Interest rate per period

n = Number of periods

In this case:

P = Amount you need to save per year

r = 8% = 0.08 (annual interest rate)

n = 30 (number of years)

We want the future value (FV) to be equal to the amount needed to spend per year during retirement, which is $80,000.

Using the formula, we can calculate the amount you need to save per year:

\(\$80,000 = P \cdot \left[\left(1 + 0.08\right)^{30} - 1\right] / 0.08\$\)

Simplifying the equation:

\($80000 = P \cdot [1.08^{30} - 1] / 0.08$\)

$80,000 * 0.08 = P * [1.08³⁰ - 1]

$6,400 = P * [1.08³⁰ - 1]

Dividing both sides by [1.08³⁰ - 1]:

\($P = \dfrac{\$6400}{1.08^{30} - 1}$\)

Calculating [1.08³⁰ - 1]:

[1.08³⁰ - 1] ≈ 3.172024

Dividing $6,400 by 3.172024:

P ≈ \($\frac{6,400}{3.172024} \approx$ $2,015.82\) (rounded to the nearest cent)

Therefore, you need to save approximately $2,015.82 per year into your investment account at the end of each year for the next 30 years.

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Answer:

Heyyy. Glad to see someone from malaysia taking add maths hete. Hope this helps

The density of the metal sculpture is 6.32 grams per cm³

Density can be defined as the quotient between mass and volume so we can just use the simple formula:

Density = mass/volume

And here we know the two values that we need to use as inputs in the formula above, these values are:

mass = 7.9kg

volume = 1250 cm³

We want the density in grams, then we can rewrite the mass as:

mass = 7.9kg = 7,900 g

Now just take the quotient between the two given quantities, we will get:

Density = 7,900g/1250 cm³ = 6.32 g/cm³

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The Fundamental Theorem of Algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. This theorem is important as it provides a way to prove the existence of solutions to polynomial equations and provides an analytical tool to find the exact location of the solutions.

This theorem is also known as the algebraic version of the Intermediate Value Theorem as it states that if a polynomial is continuous on a closed interval, then it must take on all values between its maximum and minimum.

The theorem can be easily proven by considering a single-variable polynomial of degree n and transforming it into a polynomial of degree n−1 with the same roots. By repeating this process, the polynomial can be reduced to a constant and hence, it must have at least one root.

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To find the consumer's and producer's surplus, we need more information about the demand and supply functions or the market equilibrium.

You provided the demand function D(x) = 25, but we require additional details to proceed with the calculations. The consumer's surplus is the difference between the maximum price consumers are willing to pay and the price they actually pay. It represents the benefit or surplus gained by consumers in a market transaction.

The producer's surplus is the difference between the minimum price producers are willing to accept and the price they actually receive. It represents the benefit or surplus gained by producers in a market transaction.

To calculate these surpluses, we typically need information about the supply function, equilibrium price, and equilibrium quantity. These values help determine the areas of the consumer's and producer's surpluses on the supply-demand graph.

Please provide the necessary information about the supply function, equilibrium price, or any other relevant details so that I can assist you in calculating the consumer's and producer's surplus accurately.

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Minimum value is 50, maximum value is 66, median is 59, Q1 is 53.5 and Q3 is 65. Box-and-whisker plot:

A box plot, often referred to as a whisker plot, shows the distribution of a continuous variable along with details like the median, quartiles, and outliers. A set of data's variety is shown graphically in this way. The plot, often known as a five-number summary, presents five bits of information. The fundamental benefit of box whisker plots is that the overlap between the distributions of various qualities may be calculated by comparing them side by side.

You must determine the minimum value, maximum value, median, and quartiles in order to create a box-and-whisker plot of the provided data.

The base number is fifty.

The highest number is 66.

You must sort the data from smallest to largest in order to determine the median. The listed data are:

50, 51, 51, 52, 53, 53, 54, 55, 58, 58, 58, 60, 61, 62, 63, 65, 65, 66, 66

The middle value of the ordered data is the median. Finding the average of the two middle values is necessary since the data set (18 values) contains an even number of values:

(58 + 60) ÷ 2 = 59

Divide the ordered data into four equal sections before calculating the quartiles. The median of the lower half of the data set is the first quartile (Q1). The median of the data set's upper half represents the third quartile (Q3).

The data set's lower half consists of:

50, 51, 51, 52, 53, 53, 54, 55

The data set's upper half is as follows:

58, 58, 58, **60**, **61**, **62**, **63**, **65**, **65**, **66**, **66**

First quartile (Q1):

(53 + 54) ÷ 2 = **53.5**

Third quartile (Q3) comprises:

(65 + 65) ÷ 2 = **65**

With all of this knowledge at hand, you can now develop a box-and-whisker plan.

Given below:

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The required probability is 0.4408.

The operating characteristics of the loading gate problem are:

L = λ/ (μ - λ)

W = 1/ (μ - λ)

Lq = λ^2 / μ (μ - λ)

Wq = λ / μ (μ - λ)

ρ = λ / μ

P0 = 1 - λ / μ

Where, L represents the average number of cars either being loaded or waiting.

W represents the average time a car spends either being loaded or waiting.

Lq represents the average number of cars waiting.

Wq represents the average waiting time of a car.

ρ represents the utilization factor.

ρ = λ / μ represents the ratio of time the worker spends loading cars to the total time the system is busy.

P0 represents the probability that the system is empty.

The probability that there will be more than six cars either being loaded or waiting is to be determined. That is,

P (n > 6) = 1 - P (n ≤ 6)

Now, the probability of having less than or equal to six cars in the system at a given time,

P (n ≤ 6) = Σn = 0^6 [λ^n / n! * (μ - λ)^n]

Putting the values of λ and μ, we get,

P (n ≤ 6) = Σn = 0^6 [(6/ 48)^n / n! * (8/ 48)^n]

P (n ≤ 6) = [(6/ 48)^0 / 0! * (8/ 48)^0] + [(6/ 48)^1 / 1! * (8/ 48)^1] + [(6/ 48)^2 / 2! * (8/ 48)^2] + [(6/ 48)^3 / 3! * (8/ 48)^3] + [(6/ 48)^4 / 4! * (8/ 48)^4] + [(6/ 48)^5 / 5! * (8/ 48)^5] + [(6/ 48)^6 / 6! * (8/ 48)^6]P (n ≤ 6) = 0.5592

Now, P (n > 6) = 1 - P (n ≤ 6) = 1 - 0.5592 = 0.4408

Therefore, the required probability is 0.4408.

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Answer:

it takes 13 votes to win a majority

Step-by-step explanation:

half+1 in the case of 25

it takes 13 votes to win a majority ( because there is nothing called half vote)

The distribution of weight is based on a continuous random variable.

What is Continuous Random Variable?

In statistics, a continuous random variable can take on any value within a certain range, as opposed to a discrete variable, which can only take on a finite number of values.

Qualitative variables are categorical variables that do not have a numerical value, but instead represent characteristics or qualities of a population or sample.

Therefore, the weight of an offensive linesman is an example of a continuous random variable.

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The length of the rectangle shaped sticker of stated dimensions is 8 centimetres.

Rectangle is the four shaped structure with two parallel sides. The area of rectangle is given by the formula -

Area of rectangle = length of the rectangle × breadth of the rectangle

Keep the values in formula to find the value of length of rectangle

56 = length × 7

Rewriting the equation in terms of length to find its value

Length = 56/7

Performing division on Right Hand Side of the equation

Length = 8 cm

Hence, the length of rectangle is 8 centimetres.

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The number of push-ups did sara did during gym class if for every 7 push-ups Dulce can do, Sara can do 6 is 24 push ups.

Number of push ups Dulce can do : number of push ups Sara can do

Let

number of push ups Sara does = x

7 : 6 = 28 : x

7/6 = 28/x

cross product

7 × x = 28 × 6

7x = 168

divide both sides by 7

x = 168/7

x = 24

Therefore, Sara does 24 push ups during the gym class.

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Answer:

( - 5, 1 )

Step-by-step explanation:

( \(\frac{x_{1} +x_{2} }{2}\) , \(\frac{y_{1} +y_{2} }{2}\) )

( \(\frac{-3-7}{2}\) , \(\frac{8-6}{2}\) ) = ( - 5, 1 )

We have successfully factored the trinomial using the factoring by grouping method.

To factor the trinomial f(X) = 14X² + X - 3, we need to find two binomials that, when multiplied together, give us the original trinomial.

We can use a method called "factoring by grouping" to do this.

Here are the steps:

Multiply the coefficient of the X² term by the constant term.

In this case, we get:

14 × (-3) = -42

Find two factors of -42 that add up to the coefficient of the X term, which is 1.

In this case, we can use -6 and 7:

-6 × 7 = -42

-6 + 7 = 1

Rewrite the middle term of the trinomial using the two factors from Step 2. We get:

14X² - 6X + 7X - 3

Group the first two terms and the last two terms and factor out the greatest common factor from each group. We get:

2X(7X - 3) + 1(7X - 3)

Notice that both groups have a common factor of (7X - 3).

Factor out this common factor to get:

(7X - 3)(2X + 1)

The factored form of the trinomial f(X) = 14X² + X - 3 is (7X - 3)(2X + 1).

We can check our answer by multiplying these two binomials together using the distributive property:

(7X - 3)(2X + 1) = 14X² + 7X - 6X - 3

= 14X² + X - 3

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Answer:

10% of $1400 is $140
$500 + $140 = $640

Step-by-step explanation:

Answer:

-Max has $10.00. He earns $25.75 for every lawn that he mows.

-Sasha sells a scarf for $10.00 and x jackets for $25.75 each.

Step-by-step explanation:

The answers are presented below:

The quadratic function can be represented by a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.

The vertex of an up-down facing parabola of the form ax²+bx+c is \(x_v=\frac{-b}{2a}\)  . Knowing the x-coordinate of vertex, you can find the y-coordinate of vertex. When a vertical line passes through the vertex of the parabola, it  is called the axis of symmetry.

The y-intercept is the point where the function crosses the y-axis. And, the x-intercept is the point where the function crosses the x-axis, in other words, when y=0.

First, you should convert the given equation to Standard form.

f(x) = -(c+7)² + 4

f(x)= - (c²+14c+49)+4

f(x)= -c²-14c-49+4

f(x)= -c²-14c-49+4

f(x)= -c²-14c-45

After that, you should check each option of the question.

Correct because present a degree 2 -- f(x)= -c²-14c-45

Incorrect because it is a quadratic function and this function is represented by a parabola.

The coefficients are: a=-1, b=-14, c=-45. Therefore,

\(c_v=\frac{-b}{2a}=-\frac{-14}{2*(-1)} =-\frac{-14}{-2}=-(7)=-7\)

Incorrect because x-coordinate of vertex is -7

Correct because  \(c_v=\frac{-b}{2a}=-\frac{-14}{2*(-1)} =-\frac{-14}{-2}=-(7)=-7\)

You can find the y-intercept using c=0, then f(x)= -c²-14c-45 will be:

f(x)=-45.

Incorrect because the y-intercept is (0,-45).

The coefficient a of a quadratic function is negative, thus the function has a point maximum. A relative maximum point is defined as the point where the function changes your direction. In other words, the values of the function increase before the relative maximum and the values decrease after the relative maximum.

Correct, see the attached image.

It is possible to find the number of roots or solutions from discriminant.

For quadratic equation the discriminant is determined by D=b²-4ac, where: a, b and c are coefficients.

If D > 0 - the function will have two real solutions;

If D = 0 - the function will have one real solution;

If D < 0 - the function will have imaginary solutions;

For given equation, the coefficients are: a=-1, b=-14, c=-45. Thus, D=(-14)²-4*(-1)*(-45)

D=196-180=16

D=16 thus D > 0

Incorrect because the D>0.

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There, ages are as follows:

Madhu's grandfather age = 72 years

Madhu father's age = 46 years

Madhu age = 17 years

Madhu's father is 26 years younger than Madhu's grandfather and 29 years older than Madhu.

The sum of the ages of all three is 135 years.  

Therefore, let's find their ages as follows:

Let

Madhu's grandfather age = x

Madhu father's age = x - 26

Madhu age = x - 26 - 29 = x - 55

Therefore,

x + x - 26 + x - 55 = 135

3x = 135 + 81

3x = 216

divide both sides by 3

x = 216 / 3

x = 72

Hence,

Madhu's grandfather age = 72 years

Madhu father's age = 72 - 26 = 46 years

Madhu age = x - 26 - 29 = 72 - 55 = 17 years

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Answer:

Step-by-step explanation:

The estimated product is 600, the two factors are 30 and 20.

Adjusting a number's digits so that it produces an approximation of a result is known as rounding.

Given numbers are 33.2and 21.

33.2 × 21

Round the numbers to the nearest ten:

30 × 20

=600

Hence, the estimated product is 600, the two factors are 30 and 20.

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The percentage of the students who wore a silly hat is 64 %.

The percentage is defined as a ratio expressed as a fraction of 100.

We have been given that Last Tuesday was a silly hat day at Aaron's school. 64 students wore a silly hats and 36 students did not.

We have to determine the percentage of the students who wore a silly hat

The total number of students = 64 students wore silly hats and 36 students did not.

The total number of students = 64 + 36 = 100

We have to determine the percentage of the students who wore a silly hat

The percentage of the students wore a silly hat = (64/ 100) × 100

The percentage of the students wore a silly hat = 0.64 × 100

The percentage of the students wore a silly hat = 64 %

Thus, the percentage of students who wore silly hats is 64 %.

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Answer:

No

Step-by-step explanation:

Without any side lengths, the most three angles can determine is similarity, not congruency. This means you can determine the ratio of the lengths of the sides, but not any of the sides individually.

Answer:

A. Jan 1

Dr cash $800,000

Cr Bonds payable $800,000

B. Dr Interest expense $72,000

Cr Interest Payable $72,000

Step-by-step explanation:

Preparation of the entries to record the issuance of the bonds and the first annual interest accrual on December 31

A. Preparation of the entries to record the issuance of the bonds

Jan 1

Dr cash $800,000

Cr Bonds payable $800,000

(Being to record issuance of the bonds)

B. Preparation of the Journal entry to record first annual interest accrual on December 31

Dec 31

Dr Interest expense $72,000

Cr Interest Payable $72,000

($800,000*9%)

(Being to record the first year interest expense accrued)

Answer: A and C are true.

A) \(f\left(x\right)=2\sqrt{x}\ \ and\ \ f\left(x\right)=\sqrt{x}\) both has domain and range = [0, ∞). So A is true.

B) \(f\left(x\right)=-2\sqrt{x}\) has range = (-∞, 0] and \(\ f\left(x\right)=\sqrt{x}\) has range = [0, ∞). So B is false.

C) Both \(\ f\left(x\right)=-\sqrt{x}\ and\ \ f\left(x\right)=\sqrt{x}\) has domain = [0, ∞).

Range of \(\ f\left(x\right)=\sqrt{x}\) is =  [0, ∞).

Range of \(f\left(x\right)=-\sqrt{x}\) is = (-∞, 0]

So range are different. C is true.

D) Both \(f\left(x\right)=\frac{1}{2}\sqrt{x}\ and\ \ f\left(x\right)=\sqrt{x}\) has range = [0, ∞).

So D is false.

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Answer: A and C

Step-by-step explanation:

From the intercepts of the given graph, we have that:

Morgan’s house is located 35 miles from Robin's house, and it took Robin 40 minutes to drive that distance.

For this problem, the axis are given as follows:

The intercepts are given as follows:

y = 35, x = 40.

Hence:

Morgan’s house is located 35 miles from Robin's house, and it took Robin 40 minutes to drive that distance.

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As you consider the various factors involved in starting a group, the most important factor you have to judge is the group's purpose or goal.

Step 1: Identify the group's purpose or goal - This is crucial because it will guide all other decisions, including membership criteria, communication methods, and meeting schedules.

Step 2: Assess the needs and resources of potential members - This will help you understand their motivations and ensure the group can support their needs while accomplishing its goal.

Step 3: Establish clear membership criteria and expectations - This will ensure that everyone in the group is on the same page and committed to the same goals.

Step 4: Choose an appropriate communication method - This will facilitate smooth and efficient communication among group members.

Step 5: Develop a meeting schedule that works for all members - Regular meetings help keep the group on track and provide opportunities for collaboration and feedback.

By focusing on the group's purpose or goal, you can create a solid foundation for a successful and productive group.

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Answer:

h(k(x)) = 2x + 11

Step-by-step explanation:

Step 1: Define

h(x) = 2x + 5

k(x) = x + 3

h(k(x))

Step 2: Substitute and Evaluate

k(x) = x + 3 = x

h(k(x)) = 2(x + 3) + 5

h(k(x)) = 2x + 6 + 5

h(k(x)) = 2x + 11

Answer:

0 | -6

____

3 | -15

Step-by-step explanation:

just plug in the numbers they give u in the chart

when x = 0 -> y = -3*0-6 = -6

when y = -15 -> -15 = -3x-6 -> x = 3

The graph of the line y = -3x -6 is giving the solution (0,-6) and (3,-15).

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

The given equation of the line is y = -3x - 6. the two points on the graph are satisfying the equation.

x = 0 , y = -3 x 0-6 = -6

y = -15 -> -15 = -3 x-6 -> x = 3

Therefore, the graph of the line y = -3x -6 is giving the solution (0,-6) and (3,-15).

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Answer:

h = 440.94 feet

Step-by-step explanation:

It is given that,

An architect is standing 370 feet from the base of a building, x = 370 feet

The angle of elevation is 50°.

We need to find the approximate height of the building. let it is h. It can be calculated using trigonometry as follows :

\(\tan\theta=\dfrac{P}{B}\\\\\tan\theta=\dfrac{h}{x}\\\\h=x\tan\theta\\\\h=370\times \tan50\\\\h=440.94\ \text{feet}\)

So, the approximate height of the building is 440.94 feet

Answer:

4x+28

Step-by-step explanation: