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a) An equation representing the situation where x represents the number of months when Plan A and Plan B cost the same is 80x = 630 + 45x.

b) Using inverse operations, we can state that 80x - 45x = 630 or 35x = 630, and x = 18.

c) From this equation, we determine that x is 18 months.

An equation is a mathematical statement that shows that two or more mathematical expressions are equal or equivalent.

Equations use the equation symbol (=) to depict the equality of the expressions.

                             Plan A      Plan B

Monthly charge      $80          $45

Free phone              $0         $630

Let Plan A = 0 + 80x

Let Plan B = 630 + 45x

The month the two plans' costs are equal can be derived by equating the two expressions above:

80x = 630 + 45x

80x - 45x = 630

35x = 630

x = 18 months

Thus, solving the equation, we can conclude that choosing Plan B will take 18 months to equal the cost of Plan A and thereafter, be considered cheaper than Plan A.

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Answer: 0.65=13/20

Step-by-step explanation: First, rewrite the decimal number as a fraction and put 1 in the denominator's place. 0.65/1
Then, multiply to get rid of 2 decimal places. Then, multiply top and bottom by 10^2 which equals 100

0.65/1 × 100/100= 65/100

Find the Greatest Common Factor or GCF of 65 and 100, and reduce the fraction by dividing both the numerator and denominator by GCF = 5,

[tex]\frac{65/5}{100/5}[/tex]=13/20

Hope this helps!

Using z-score calculations, we can say that around 13.14%of the young women have a BMI (Body Mass Index) of less than 18.5 and are underweight.

The formula for z-score is;

z = (x' - μ)/σ

We are given;

Population Mean; μ = 26.8

Population standard deviation; σ = 7.4

Average BMI; x' = 18.5

Thus;

z = (18.5 - 26.8)/7.4

z = -1.12

From online p-value from z-score calculator, we have;

p-value = 0.1314 = 13.14%

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Complete question is;

Your body mass index (BMI) is your weight by kilograms divided by the square of your height in meters. Online BMI calculators allow you to enter weight in pounds and height in inches. High BMI is a common but controversial indicator of being overweight or obese. A study by the National Center for Health Statistics found that the BMI of American young women (ages 20-29) is approximately Normally distributed with mean 26.8 and standard deviation 7.4

People with BMI less than 18.5 are often classed as “underweight.” What percent of young women are underweight by this criterion?

Answer: -1/2

Step-by-step explanation: To solve this problem, we can use the properties of logarithms to isolate the variable x on one side of the equation. The properties of logarithms tell us that the logarithm of a product is the sum of the logarithms of the factors, and that the logarithm of a power is the exponent times the logarithm of the base.

If log₂(4x + 6) = 4, we can rewrite the left side of the equation as follows: log₂(4x + 6) = log₂(2^4 * (2x + 3))

Then, using the property of logarithms that the logarithm of a product is the sum of the logarithms of the factors, we can simplify the equation as follows: log₂(4x + 6) = 4 + log₂(2x + 3)

Now, we can use the property of logarithms that the logarithm of a power is the exponent times the logarithm of the base to simplify the equation even further: log₂(4x + 6) = 4 + 1 * log₂(2x + 3)

Since the logarithm of a power is the exponent times the logarithm of the base, this means that the logarithm of a number is the logarithm of that number divided by the logarithm of the base. Therefore, we can divide both sides of the equation by log₂ to isolate the variable x on one side of the equation:

log₂(4x + 6) / log₂ = 4 + 1 * log₂(2x + 3) / log₂

(4x + 6) / 1 = 4 + (2x + 3) / 1

4x + 6 = 4 + 2x + 3

4x + 6 = 2x + 7

2x = -1

x = -1/2

Therefore, if log₂(4x + 6) = 4, then x = -1/2.

Answer:

1 or 3

Step-by-step explanation:

Step-by-step explanation:

i think its no, but im not sure.

Carleen owns a Dog as her pet.

The logical thinking definition is analysing a situation or problem using reason and coming up with potential solutions.

Given that, Amy, Brenda and Carleen own a cat, a dog and a fish, but not necessarily in that order.

It is saying that Amy hats a cat, which ca be meant she has a pet cat

Therefore, Amy owns a pet cat.

Now, Brenda can not have a hairy pet because she has allergic conditions, so the only pet in the given list with no hair is the fish

Therefore, Brenda owns a pet fish.

Now, only Carleen is left, and a pet dog is left.

Therefore, Carleen owns a pet dog.

Hence, Carleen owns a Dog as her pet.

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Answer:

g-games

r-rides

1.5 g + 2.5r= 16.5

g=2r

Step-by-step explanation:

g: # of games played

r: # of rides ridden

total amount spent:  1.50g + 2.50r = 16.50

relationship of games to rides: g = 2r

Hope this helped! :D

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The number of games is 3.

The number of rides is 8.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number of rides = m + 5

Number of games = m

Now,

Each game costs $1.50 and each ride costs $5. Isaac spent $44.50 altogether at the carnival.

This means,

1.50m + 5(m + 5) = 44.50

1.50m + 5m + 25 = 44.50

6.50m = 44.50 - 25

m = 19.5/6.50

m = 3

Now,

The number of games = 3.

The number of rides.

= m + 5

= 3 + 5

= 8

Thus,

The number of games is 3.

The number of rides is 8.

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Answer:

10^3.

Step-by-step explanation:

You can represent 1,000 as 10^3. 10 x 10 x 10 = 1000. is read as “10 to the third power” or “10 cubed.”

all numbers are base 10 unless the teacher says to use another base so

there are 3 zeroes so

10^3 is the answer

The time it would take the two sisters to paint 80 mugs is 8 hours.

From the question, we are to determine how long it would take the sisters to paint 80 mugs

From the given information,

"The younger sister can paint 2 mugs every half hour"

That is,

The younger sister can paint 4 mugs every hour

Also

"The older sister can paint 6 mugs every hour?"

Let x represent the number of hours it would take them to paint 80 mugs.

Then, we can write that

4x + 6x = 80

10x = 80

x = 80/10

x = 8

Hence, the time it would take is 8 hours

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Answer:

$1984.80

Step-by-step explanation:

165.40 times 12 equals 1984.80

Answer:

He pays $1984.80 on his loan in one year.

Step-by-step explanation:

If he pays 165.40 per month, and there are 12 months in one year, then we must multiply the values together.

165.4*12 = 1984.8

He pays $1984.80 on his loan in one year.

Total 9 rows will have exactly 42 projects.

The Fundamental mathematical operation are Addition,Subtraction

Multiplication and Division.

Given,

The total number projects in the science fair is 405.

The  coordinator displays the projects in rows of 42.

To know the exact number of rows having 42 projects

we will divide total project by 42 i.e; 405/42.

The quotient will be the number of row exactly having 42 projects

and the last row will contain less than 42 projects which is remainder.

i.e;  Dividing 405 by  42

    quotient will be 9.

      remainder will be 27.

So,Total 9 rows will have exactly 42 projects.

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There will be 0.48 grams will be left in the sample after 59 years.

Function is a type of relation, or rule, that maps one input to specific single output.

Since we have given that initial sample of 171 g of a radioactive substance decays according to the function

[tex]A(t) = 171e ^ {- 0.04(t) }[/tex]where t is given in years

Here, Initial amount of radioactive substance = 171 grams

We need to find the amount of substance that will be left in the sample after 59 years.

So, t = 59 years

So, it becomes,

[tex]A(t) = 171e ^ {- 0.04(59) }\\\\A(t) = 0.48[/tex]

Hence, there will be 0.48 grams will be left in the sample after 59 years.

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Answer:

1,519

Step-by-step explanation:

96 ( 32 ÷ n ÷ 2 ) –s –t^r

since n = 4, r = 3, s = 9, and t = 2. we will just substitute for the values like this

96 ( 32 ÷ (4 ÷ 2) ) –9 ( –2³)

96 ( 32 ÷ 2 ) –9 –8

96 ( 16 ) –17

=1,536 –17

=1,519

i hope i helped

Answer:

116.64

Step-by-step explanatio hope this helps

The percentage decrease of the depth of the lake from January to August is 20%.

The difference between the initial and final numbers is shown as a percentage reduction. It displays a percentage loss of value compared to the original regardless of the units. The decrease is equal to the initial amount less the final amount.

Given,

The depth of lake in January = 943 feet

The depth of lake in August = 754.4 feet

The difference is = (943-754.4) feet

                             = 186.6 feet

So, the percentage decrease of the depth of the lake from January to August will be =  (186.6 ÷ 943) × 100

                        = 20%

Therefore, the answer is 20%.

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Answer:

P-2l/2=w

Step-by-step explanation:

P = 21 + 2w

Solve for w

Subtract 21 from both sides.

P - 21 = 2w

Divide both sides by 2.

P-21/2 = w

Step-by-step explanation:

speed=distance÷time

A.V.S=440÷11=40m/s

hope it helps.. Please mark brainliest.

Answer:

40 m/s

Step-by-step explanation:

Find:

We are asked to find the unit rate, How many meters per 1 second?

Know:

440 meters in 11 seconds

Solve:

440 meters in 11 seconds

  ? meters in 1 second

   440/11  = 40 meters per second

Answer:

The average speed of the person is 40 m/s

Answer:

y = -x + 4

Step-by-step explanation:

m = y2-y1 / x2-x1

m = 4-6/ 0-(-2)

m = -2/2

m = -1

y = -x + b

4 = -(0) + b

b = 4

y = -x + 4

Could you please give me brainliest for this? Thanks!

Answer: x = 59

Step-by-step explanation:

i dont know what you are trying to figure out but x = 59 im guessing u need

Answer:

Step-by-step explanation:

First, add

90

and subtract

2

x

from each side of the equation to isolate the

x

term while keeping the equation balanced:

8

x

−

90

+

90

−

2

x

=

2

x

−

36

+

90

−

2

x

8

x

−

2

x

−

90

+

90

=

2

x

−

2

x

−

36

+

90

(

8

−

2

)

x

−

0

=

0

+

54

6

x

=

54

Now, divide each side of the equation by

6

to solve for

x

while keeping the equation balanced:

6

x

6

=

54

6

6

x

6

=

9

x

=

9

Answer:

Both answers C & E are correct

Step-by-step explanation:

[tex]\sf\frac{7}{10}-\frac{4}{40}[/tex]

First, make the denominator the same to solve the fraction.

For that, multiply both the numerator and denominator by 4 in the fraction 7/10.

[tex]\sf\frac{7*4}{10*4}-\frac{4}{40}\\\\\sf\frac{28}{40}-\frac{4}{40}\\\\\sf\frac{28-4}{40}\\\\\sf\frac{24}{40}[/tex]

To write the answer in its simplest form divide both the numerator and denominator by 8.

[tex]\sf\frac{3}{5}[/tex]

Therefore, the answer is [tex]\sf\frac{24}{40}[/tex] = [tex]\sf\frac{3}{5}[/tex]

Answer:

Step-by-step explanation:

1.5/0.15=10

1.5 is 10 times greater than 0.15

The solution is 10

The number of times the number 1.5 is greater than the number 0.15 is 10

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented A

Now , the value of A is

Let the first number be P = 1.5

Let the second number be Q = 0.15

Now , the number of times the number P is greater than Q is given by the equation

A = P / Q

Substituting the values in the equation , we get

A = 1.5 / 0.15

On simplifying the equation , we get

A = 10

Therefore , the value of A is 10

Hence , the number of times 1.5 is greater than 0.15 is 10 times

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The conjecture and rephrased statement of proof to demonstrate that the diagonals of a parallelogram cross each other, taking into account the provided figure, is: DE and EB are congruent to one another in the parallelogram EFGH, while AE is congruent to EC.

A unique variety of quadrilateral called a parallelogram has both pairs of its opposite sides parallel and equal.

The parallelogram's diagonals are the lines connecting its two opposed ends. Sharing into two equal portions is known as bisecting. Congruent refers to a copy that has the same dimensions as the original and may therefore be used in place of it. When the diagonals of a parallelogram bisect one another, it signifies that they split into two equal pieces that are congruent with one another.

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Answer:

50 inches, or 4 1/6 feet

Step-by-step explanation:

If one inch is equal to 6 1/4 feet, we can translate this number from feet to inches.

4 1/6 feet = 75 inches.

Now we can take 75 and find out 2/3 of it.

2/3 of 75 is 50.

The answer is 50 inches.

If you want to convert the answer from feet to inches, its simple.

12 × 4 = 48

50 - 48 = 2

2 inches is equal to 1/6 of a foot.

The answer in feet, is 4 1/6 foot.

After 15 minutes the pan will have a temperature of 36°F

Newton's Law of Cooling, if a body with temperature T₁ is placed in surroundings with temperature To, different from that of T₁, the body will either cool or warm to temperature T(t) after t minutes, where T(t) = T₀ + (T₁-T₀)e^(kt)

Given: T₁ = 120°F,  T₀ = 0°F. After 5 minutes, T(t) = 80°F

T(t) = T₀ + (T₁-T₀)e^(kt)

80 = 0 + (120-0)e^(5k)

80 = 120e^5k

e^5k = 80/120

e^5k = 2/3

5k = ln(2/3)

k = ln(2/3) / 5

k = -0.0811

The temperature of the pan after 15 minutes will be:

T(t) = T₀ + (T₁-T₀)e^(kt)

T(15) = 0 + (120-0)e^(-0.0811×15)

T(15) = 120e^(-0.0811×15)

T(15) = 36°F

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B(x) as a product of linear factors is B(x) = (x+2)(x+7)(x-1)

The linear factors of a polynomial are the first-degree equations that are the building blocks of more complex and higher-order polynomials. Linear factors appear in the form of ax + b and cannot be factored further.

if ( x+2) is a factor of the polynomial, then x+2 can divide the polynomial without remainder.

see attached document for detailed division of the polynomial [tex]x^{3}+8x^{2} +5x-14[/tex].

In conclusion B(x) as a product of linear factors is B(x) = (x+2)(x+7)(x-1)\

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The information given regarding the computation of the profit or loss shows that there's a loss of RS 500,000.

From the information given, it was stated that the real estate agent bought two triangular Kittas' having a common side as shown in the figure from two people for Rs 2000,000 altogether.

It was further depicted that he sold the land in the shape of a quadrilateral at Rs 1,500,000. In their case, the sale is less than the cost and therefore, there's a loss.

The loss will be:

= 2,000,000 - 1,500,000

= 500,000

Therefore, the information illustrated a loss of RS 500,000.

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Complete question

Mr. Gosain?(1 Aana = 31.8 m²) b) A real estate agent bought two triangular Kittas' having a common side as shown in the figure from two people for Rs 20,00,000 altogether. If he immediately sold the land in the shape of a quadrilateral at Rs 15,00,000 per Kattha, find his profit or loss.(1 Kattha= 338.63 sq. m) danta Excel in Mathematics - Book 9 86 36 m Approved by Curriculum Development Cen 20 m 29 m 25 m 21 m aktapur

Answer: ya

Step-by-step explanation:bc