Sum of two rational numbers are 2/15 , if one rational number is 2/3 . Find the other rational number

There could have been 2,5,6, and 9 singers

1) Regarding 775,710 as an even number then for sure there could have been 2 singers on this TV Show

2) On the other hand, 775710 is also divisible by 5, for its last number is 0. So there could also have been 5 singers.

3) This number of teenagers can also be divided by 6 (for it is divisible by 2 and by 3) and by 9 as well ( the sum of the digits of 775710, 7+7+5+7+1+0=27 is also divisible by 9).

Hence, there could have been 2,5,6, and 9 singers since 775,710 can be divided exactly by 2,5,6, and 9.

The most appropriate choice for supplementary angle will be given by-

x = 25.2°

∠AFB = 158.4°

∠RST = 21.6°

What is supplementary angle?

Angle is formed when two straight lines meet at a common point.

The common point is the vertex of the angle and the lines are called the arms of the angle.

Two angles are said to be supplementary if their sum is 180°

Here,

∠AFB = 7x - 18

∠RST = 72 - 2x

Sum = 7x - 18 + 72 - 2x

        = 5x + 54

By the problem,

[tex]5x +54=180\\5x = 180-54\\5x =126\\x= \frac{126}{5}\\x = 25.2[/tex]

∠AFB = [tex]7 \times 25.2 -18\\[/tex]

          = [tex]176.4 - 18\\[/tex]

          = [tex]158.4^{\circ}[/tex]

∠RST =

             [tex]72 - 2\times 25.2\\72 - 50.4\\21.6^{\circ}[/tex]

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The given graph representing function is a relation.

For the given question,

For every singles value of 'x' there is value on y. Thus, no domain element is repeating for the graph.

Thus, the graph shows the relation of the function.

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a We have fractions in order to order from least to greatest we will convert the fractions into decimal number

as we can see the least number is -3/8 then -3/16 and the greatest number is 7/4

10 degrees celsius

The formula for converting temperature in degree Farenheit to degree Celcius is:

Answer: 8 + 7x

Step-by-step explanation:

      The perimeter is the same as all the side lengths added together. We will set up an expression, then simplify it by combining like terms.

      (4 - x) + (7x - 1) + (6x + 13) + (-8 - 5x)

      4 - x + 7x - 1 + 6x + 13 - 8 - 5x

      4 - 1 + 13 - 8 - x + 7x + 6x - 5x

      8 + 7x

1) Solving that linear system using the elimination method, we'll proceed this way.

1.1 Choose one variable to be canceled out firstly. Let's choose the x variable:

6x + 5y = -15

-2x -3y= 17 Multiply this whole equation by 3

6x + 5y = -15

-6x -9y= 51 Add both equations

----------------------

0 -4y =36 Divide both sides by -4

y = -9

2) Now let's plug into any equation, usually the one with smaller numbers y= -9

-2x -3(-9) = 17

-2x +27 = 17 Subtract 17 from both sides

-2x =17-27

-2x = -10 Divide both sides by -2

x= 5

3) So the solution is (5, -9)

-

-When y = 0 :

10*x -8*0 = 16 (Replacing y=0)

10x = 16 (Multiplying)

x = 16/10 (Dividing on both sides of the equation by 10)

x= 8/5 (Simplifying)

- When x= 0:

10*0 -8*y = 16 (Replacing x=0)

-8y = 16 (Multiplying)

y= 16/(-8) (Dividing on both sides of the equation by -8)

y= -2 (Dividing)

- When x= 2

10*2 -8*y = 16 (Replacing x=2)

20 - 8y = 16 (Multiplying)

20 = 16 + 8y (Adding 8y to both sides of the equation)

20 - 16 = 8y (Subtracting 16 from both sides of the equation)

4 = 8y (Subtracting)

4/8 = y (Dividing on both sides of the equation by 8)

1/2 = y (Simplifying)

- When y= 4

10*x -8*4 = 16 (Replacing y=4)

10 x - 32 = 16 (Multiplying)

10x = 32 + 16 (Adding 32 to both sides of the equation)

10x=48 (Adding)

x = 48/10 (Dividing on both sides of the equation by 10)

x=24/5 (Simplifying)

So, the complete chart would be:

x tea chart : 8/5,0,2, 24/5

y tea chart: 0,-2,1/2,4

Given:

We have given fraction

Required:

We have to find the required data which is equal to above fraction solution.

Explanation:

In the above fraction we have same base in numerator and denominator and hence,

when the base is same power are added.

Required answer:

Option d is correct.

which is equal to our calculated answer.

ANSWER

1.) YES! Maryse used her equation correctly.

2.) NO! Maryse did not use her equation correctly.

EXPLANATION

Given:

A bike ride model: y = 7x

where:

1). x is the time Maryse spent riding,

2). y is the distance she traveled

Now, she rode 14 miles in the first two hours of her trip

That is:

y = 7x

where y = 14 miles and x = 2 hours

14 = 7(2)

14 = 14

She indeed used her equation correctly.

When she predicted that she would travel 40 miles if she rode for four hours.

That is:

y = 7x

where y = 40 miles and x = 4 hours

Hence, She indeed used her equation correctly in part one but she did not use her equation correctly in part two.

Graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma negative 120 through the point 2 comma negative 100

Decorations for the dance cost $120

the club is charging $10 per student that attends.

In the graph, the x axis is labelled with number of students and the y axis with amount of money collected

As they spend $120 for the decorations of the dance the starting point for the money raised is -120, upon charging 2 students the money they will get is 2 x 10 = 20

So the money raised will be

-120 + 20 = -100

The line will pass from point (0, -120) through (2, -100)

Therefore, graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma negative 120 through the point 2 comma negative 100 is correct.

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Answer:

Step-by-step explanation:

A middle school club is planning a homecoming dance to raise money for the school. Decorations for the dance cost $100, and the club is charging $10 per student that attends.

Which graph describes the relationship between the amount of money raised and the number of students who attend the dance?

Answer:

Printer B prints the fastest

The percent of bags of cookies will contain between 48 and 68 cookies is 68.29%.

The average of the specified collection of numbers is what is referred to as mean. It indicates that values in a particular data set are distributed equally.

μ = 58,  σ = 5,

Z₁ = X₁  - (μ/ σ)

= 48 - (58/5)

= 36.4

again,

Z₂=  X₂ - (μ/ σ)

= 68 - (58/5)

= 56.4

Thus, we know P( 48 < X < 68)

= p(-1 < Z < 1)

= 0.6829

= 68.29%

68.29% bags of cookies will contain between 48 and 68 cookies.

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The total value of the exponential expression is a³

What is Exponentiation ?

Exponentiation is a mathematical operation that involves the base number (b) and the exponent (or power) number (n), and is represented as bⁿ. Its pronunciation is "b (raised) to the (power of) n." Exponentiation corresponds to repeated base multiplication where n is a positive integer; so, bⁿ is the result of multiplying n bases.

Now, The given expression is :

a^3 (2a^2 + 4bc^4)^ 0

From the properties of exponents we know that:

a⁰ = 1

Therefore the value of the part of the expression (2a² + 4bc⁴)⁰ is 1

Hence,  The total value of the exponential expression is a³

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The least number of decimal places in the other factor is 2

A factor simply means the number that can b multiplied with another number to get the original number.

Based on the question asked, lat the whole number be represented as 2. In this case the multiplication will be:

= 2 × 17.22

=34.44

In this case, one can see that 17.22 has 2 decimal places.

Therefore, the correct option is 2.

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Answer:

Let x = amount in low risk account, then 10000-x is amount invested in high risk account. To earn 10% of 10000:

(.10)(10000) = (.055)x + .12(10000-x)

1000 = 1200 -.045x

x = 4444.44 in low risk and 5555.56 in high risk

Answer:

the correct answer is 15.2

The growth of the real GDP per capita from 2019 to 2020 is 1.4.

Therefore, the formula to compute real GDP per capita = Real GDP / Population.

The real GDP in 2019 is $100B.

And the real GDP in 2020 is $240B.

The growth rate of real GDP = current value - previous value / previous value

Therefore, the growth of the real GDP per capita from 2019 to 2020 is 1.4.

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We will investigate the evaluation of recursive sequences.

A iterative sequences are categorized by two values i.e one value preceding and the current value. The current value is evaluated on the basis of the previous value. In other words the current value is a function of preceeding value or depends on it.

All iterative relations of a sequence are expressed mathematically by two values as follows:

A iterative relation is a unique mathematical relationship between the current term f ( n ) and the previous value given as follows:

For this particular relationship the first term value is given as follows:

We will now start determining the terms in the sequence by plugging the respective term numbers ( n ) and use the mathematical relationship for the sequence as follows:

We have evaluated the 2nd term in the sequence as 13. We will repeat the above steps for all term numbers ( n = 3 , 4 , 5 , 6 ).

And them lastly for the 6th term in the sequence as follows:

Hence, the answer to the 6th term number is:

An inverse function which represents the average sales each day for the real estate company is: D. S⁻¹ = (t + 4)/(t - 5).

In order to determine equation which represents the average sales each day for the real estate company, we would factorize the numerator and denominator of the given inverse function as follows:

Numerator = t² + 3t - 4

Next, we would solve the quadratic equation by using the factorization method:

t² + 3t - 4 = t² + 4t - t - 4

t² + 4t - t - 4 = t(t + 4) - 1(t + 4)

t² + 4t - t - 4 = (t - 1)(t + 4)

Numerator = (t - 1)(t + 4)

For the denominator, we have:

t² - 6t + 5 = t² - 5t - t + 5

t² - 5t - t + 5 = t(t - 5) - 1(t - 5)

t² - 5t - t + 5 = (t - 1)(t - 5)

Denominator = (t - 1)(t - 5)

Now, we would rewrite the inverse function as follows:

S⁻¹ = Numerator/Denominator

S⁻¹ = (t - 1)(t + 4)/(t - 1)(t - 5)

S⁻¹ = (t + 4)/(t - 5)

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Given the interval of the distribution as

a) To find the mean, we will calculate the mid-value of the interval, this is shown below

Hence, the mean is 5.38

b) To find the standard deviation

Hence, the standard deviation is 0.2194

c) The probability that the child will be older than 5 years will be

Hence, the probability that the child will be older than 5 years is 1.0

d) The probability that the child age is between 5.4 and 5.6 years old will be

Hence, the probability that the child age is between 5.4 and 5.6 years old is 0.2632

e) If the child is at the 53rd percentile, the age of the child will be

Hence, at the 53rd percentile, the age of the child is 5.4028 years old

Problem

Solution

For this case we can conclude that:

DE = r

DF= s

EF= t

Holly ate two [tex]\frac{1}{6}[/tex] fractions.

Holly ate 1 more brownie, then Tori

     = 1+2

      = 3

She ate [tex]\frac{3}{9}[/tex] fraction

Two equivalent fractions = [tex]\frac{3}{9} = 2x[/tex]

           [tex]x = \frac{1}{6}[/tex]

Holly ate two [tex]\frac{1}{6}[/tex] fractions.

What are Fractions?

Fractions are referred to as the components of a whole in mathematics. A single thing or a collection of objects might be entire. When we cut a slice of cake in real life from the entire cake, the part represents the percent of the cake. The word "fraction" is derived from Latin. "Fractus" means "broken" in Latin. The fraction was expressed verbally in earlier times. It was afterward presented in numerical form.

A piece or sector of any quantity is another name for the fraction. It is indicated by the sign "/," such as a/b. For instance, in the fraction 2/4, the bottom part represents the denominator, and the top part the numerator. This article's focus is on going to learn the meaning of fractions in mathematics, different sorts of fractions, how to convert fractions to decimals, and a ton of problems that have been solved and well explained.

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The answer to the given expression is 2

To "solve" or "isolate" a variable is to place it on its own side of the equation.

All other variables or constants should be moved to the opposite side of the equation using inverse operations. The operations must be applied to both sides of the equation in order to maintain the equation's balance.

Given : x = 5 and y = 7

To find :  [tex]\frac{y^{2} - x }{y + 3x}[/tex]

When we substitute the values mentioned above in this above expression we get;

[tex]\frac{7^{2}- 5 }{ 7+ 3X5}[/tex]

⇒ [tex]\frac{49 - 5}{ 7 + 15}[/tex]

⇒ [tex]\frac{44}{22}[/tex]

On dividing it with 22 we get

[tex]\frac{44}{22}[/tex] = 2

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SOLUTION

The given expression is

Recall the formula for combination

Solving the given expresssion

This further gives

This further gives

Therefore the solution is 8

From the given question, we have the following parameters

Cost of a small greeting card = $1.60

The cost of a large greeting card = $4.05.

Cost of 5 small greeting cards = 5(1.60)

Cost of 5 small greeting cards = $8.00

Cost of 4 large greeting cards = 4(4.05)

Cost of 4 large greeting cards = $16.2

Cost of 5 small and 4 large = $8.00 + $16.2

Cost of 5 small and 4 large $24.2

Hence it would cost $24.2 to get 5 small greeting cards and 4 large greeting cards

Similarly;

Cost of x small greeting cards = 1.60x

Cost of y large greeting cards = 4.05y

Cost of small greeting cards and y large greeting cards = 1.60x + 4.05y

Hence it would cost $(1.60x + 4.05y) to get x small greeting cards and y large greeting cards

At first, we will change the feet to the yard because the cost of carpet is per square yard

Since 1 yard = 3 feet, then

Divide each dimension by 3 to change it from feet to yard

Since the length of the room = 24 feet, then

The length of the room = 24/3 = 8 yards

Since the width of the room = 15 feet, then

The width of the room = 15/3 = 5 yards

The rule of the area of the rectangle is

Area = Length x width, then

The area of the room = 8 x 5 = 40 square yards

Since we will add extra 4 square yards to it, then

The total area needs to cover = 40 + 4 = 44 square yards

Since the cost of 1 square yard = $36, then

Multiply the area by the cost to find the cost of the carpet

The total cost = 44 x 36 = 1584

The cost of the carpet is $1584

Given: Linh buys $11.23 worth of groceries and pays for them with a $20 bill.

So, the change will be = 20 - 11.23 = $8.77