on the first birthday, we light one candle; on the second birthday 2 candles; and on the 120th birthday 120 candles. how many candles do we light total in all 120 birthdays? use the proper summation formula we learned in class.

Solution of this polynomial equation is x = 4

In mathematics, polynomial equation can be defined as the equation which consist of coefficient, variables and exponents. A polynomial equation has positive numbers as their exponent which is also known as its degree. All the equations such as quadratic equation, cubic equation which has non  negative number as their powers are part of polynomial equation.

Types of polynomial equations :

Some examples of polynomial equation are :

According to question,

2x = 8

=> 2x / 2 = 8 /2

=> x = 4

Thus solution for given equation is x = 4.

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We need to know about linear and proportional relationship to solve this problem. Statement 2 is true, the description shows a linear relationship and a proportional relationship.

Linear relationship is a relationship between two variables where if one increases the other increases or if one decreases the other decreases. The varibales in a linear relationship form a straight line on graph. Proportional relationship is the relationship between two variables where the ratio between pairs of different data always remains constant. In the given question, a 12 ounce cup costs $1.97, a 16 ounce cup costs $2.62 and a 20 ounce cup costs $3.27. The price of each cup increases with increase in capacity of the cup, so we can say that the cup capacity and price have a linear relationship. The ratio between each pair can be given by

12/1.97=6.10

16/2.62=6.10

20/3.27=6.10

The ratios between every pair is same, so it is a proportional relationship.

Thus we found that the description shows a linear relationship and a proportional relationship between the cup capacity and it's price, statement 2 is the right option.

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De acuerdo a la información se puede inferir que su hijo nació en el año 22 antes de Cristo.

Una recta numérica es una herramienta gráfica de las matemáticas que nos sirve para ubicar números positivos y negativos en un gráfico con el objetivo de organizarlos con respecto al número cero.

Las líneas de tiempo con fechas Antes y Después de Cristo se pueden asociar a una recta numérica debido a que los años Antes de Cristo se ubican en la parte negativa de la gráfica (a la izquierda del cero) y los número Después de Cristo se ubican en la parte positiva (a la derecha del cero).

Para identificar el año de nacimiento del hijo debemos tener en cuenta que las fechas que se ubican en la zona negativa de la recta numérica aumentan de forma invertida, es decir que si su hijo nació 28 años después de ella se debe restar este número a su fecha de nacimiento como se muestra a continuación:

50 - 28 = 22

Entonces, el año de nacimiento de su hijo sería el año 22 Antes de Cristo.

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The time taken to travel the distance 70 Km/h is 11 hours.

Speed tells us how fast something or someone is travelling. You can find the average speed of an object if you know the distance travelled and the time it took.

The formula can be rearranged in three ways:

Given:

time = 9 hours

speed = 85 Km/h

Now, distance

=speed * time

=85 * 9

= 765 km

As, the speed is 70 km/h

time = distance/ speed

time = 765 / 70

time = 10.92

time= 11 hours

Hence, the time taken to travel the distance 70 Km/h is 11 hours.

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The translation of the question is:

A car takes 9 hours to travel a distance with a speed of 85km/h, how long will it take to travel the same distance at 70km/h?

Answer:x=6 x=-3

Step-by-step explanation:

3x(x^2-3x-18)=0

   (X-6)(x+3)=0

X-6=0.      X+3=0

 +6=+6.       -3=-3

X=6.             X= -3

The sidewalk around a lake is 9/10 mile long. You walk 3 laps Around the lake in the morning and 2 laps in the evening. Your friend walks the same total distance as you on a 3/2 mile track.

Given that

To find

So, according to the question

we have,

                                                     = (9 ×5)/10

                                                     = 4.5 miles.

Now, from question

So, Total laps walk by your friend

             = ( Total distance walk by you)/(Total length of your friends track)

             = [tex]\frac{4.5}{(\frac{3}{2}) }[/tex]

             = [tex]\frac{4.5\times 2}{3}[/tex]

             = 9/3 = 3

Answer:

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Answer:

is 7 more than 4 or 4 more than 7?

Step-by-step explanation:

JUST USE YOUR BRAIN!

Answer:

no

Step-by-step explanation:

of course not. since the denominators are the same, the numerators have to be equal. since the numerators aren't equal, the answer is no

After playing 100 times the player will loose $-16.67.

Given the outcomes and the probability is:

Outcome            Probability

-$10                       1 (cost to play)

$14 draw red          5/12

$12 draw yellow      4/12

therefore, expected probability = ∑x.p(x)

x is no of trials and

p(x) is probability of the results.

E(x) = (14)5/12 + (12)4/12 + (0)3/12 - 10

E(x) = -2/12

E(x) = -10.1667

For 100 games the expected value E(100x) =

E(100x) = E(x) × 100

E(100x) = -10.1667 × 100

E(100x) = -16.67 i.e loss after game.

Hence the player lose $-16.67 after 100 games.

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The value of the x is 1 in the linear equation. Thus, option C is correct.

According to the statement

We have to find that the value of the x.

So, For this purpose, we know that the

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.

From the given information:

The equation is:

4x−3=−12x+13

Then

we have to solve it

4x−3=−12x+13

4x+12x = 3+13

16x = 16

x = 16/16

x =1.

When we put x =1 in the given equation and then i satisfy the equation and give same values after calculation.

So, The value of the x is 1 in the linear equation. Thus, option C is correct.

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Answer:

The correct answer is 4(x-7)²-(x-7)+3.

Step-by-step explanation:

When we have captured (t*s)(x), that is as equivalent as t(s(x)). To solve this, we take the important role of s(x), x-7, and call in an alternative for it in for every x in t(x). Instead of 4x², we have 4(x-7)²; instead of -x, we have -(x-7). This gives us 4(x-7)²-(x-7)+3.

Answer:

Step-by-step explanation:

30 and 20

Answer:

5 and -5

This is because these 2 spots are exactly 5 spaces from 0.

Answer: 1

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

The missing numbers are 17,66,13, 9 3 and 15 respectively .

The rules given to us are-

first row consist of a number which is the sum of two numbers of middle row

Third row consist of a number which is the product of two numbers of middle row

The first part

The sum of 6 and 11 is 17 and the product of 6 and 11 is 66

       17

6                11

       66

The second part

To find the second number of middle row we need to divide 36 by 4 and we get 9 and the sum of 4 and 9 is 13

       13

4               9

       36

The third part

To find the numbers of middle row we need to find the factors of 45 that sum up to 18

The factors of 45 are 3*3*5

The factor 15 and 3 satisfy both the requirements

       18

3                15

       45

Hence, The missing numbers are 17,66,13, 9 3 and 15 respectively

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Answer:

codec log 8x + y =15

Step-by-step explanation:

have a good day!

The product of two factors is 1. One of the factors is 1. B. Yes; the other factor is 1 since 1 × 1 = 1.

From the information given, the product of two factors is 1 and one of the factors is 1.

Let the other number = y

The other number will be:

1 × y = 1

y = 1

Therefore, the other number is 1

In conclusion, the correct option is B.

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Answer:

p = - 12

Step-by-step explanation:

[tex]\frac{2}{3}[/tex] p - 11 = [tex]\frac{1}{3}[/tex] p - 15

multiply through by 3 to clear the fractions

2p - 33 = p - 45 ( subtract p from both sides )

p - 33 = - 45 ( add 33 to both sides )

p = - 12

Answer:

-12

Step-by-step explanation:

(sorry its a bit messy - hope it helps though!)

The correct order from best to worst of the sample groups is b→ a→ c.

The study conducted by the City Council of USA incorporates the reviewing for the funding for local sports-related activities.

There are 3 sample groups selected from the population of Anytown residents with an active interest in sports. They are:

a. High-school students at three different schools.

b. People randomly approached at a softball tournament, a swim meet, an athletic supply store, and a sports bar.

c. People randomly approached at a department store and at a shopping mall

All these groups are selected randomly.

But for (b), the people are obviously interested in sports activities, as they are selected from softball tournament, a swim meet, an athletic supply store, and a sports bar.

Next would be (a), because the students being younger is probably more interested in sports than elder ones.

The last would be the (c), people selected from the department store since they would be less aware of local- sports related activities.

So the order of samples from best to worst is b→ a→ c.

The question is incomplete. Find the complete question below:

The city council of Anytown, U.S.A., is reviewing the funding for local sports-related activities. To be better informed, it commissions a study. Order the sample groups, best to worst, based on how well they would represent the population of Anytown residents with an active interest in sports.

a. high-school students at three different schools

b. people randomly approached at a softball tournament, a swim meet, an athletic supply store, and a sports bar

c. people randomly approached at a department store and at a shopping mall

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Answer:Tenths

Step-by-step explanation:Hope it helps

An equivalent form of 5 / ( 2 + 2 i ) is ( 5 -5 i ) / 4 [ option I ]

Given,

5 / ( 2 + 2 i )

To find its equivalent form we need to simplify the term by using the concept of conjugates.

Conjugate of a term results in opposite power of the imaginary part.

The conjugate of 2 + 2 i = 2 - 2 i

Multiply and divide the term with the conjugate

=> 5 * ( 2 - 2 i ) / ( 2 + 2 i ) * ( 2 - 2 i )

=> 10 - 10 i / 2 ² - ( 2 i ) ²                [ ( a + b ) ( a - b ) = a ² - b ² ]

=> 10 - 10 i / 4 - (-4)                        [ i ² = - 1 ]

=> 10 - 10 i / 8

=> 5 - 5 i / 4

This matches with option I

Therefore, we get an equivalent form of 5 / ( 2 + 2 i ) as ( 5 -5 i ) / 4

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If Heavy Hulk is cutting their sign-up fee in half for new members. If Brett signs up at a gym today, the number of months that the cost of the memberships be the same is: 23 months.

Let x represent the number of months

Hence,

Formulate

$34.04x+24= $34.29x+(36.50/2)

Collect like terms

($34.04x -34.29x)= 24-(36.50/2)

0.25x=24-18.25

0.25x=5.75

Divide both side by 0.25x

x=5.75/0.25

x=23 months

Therefore If Heavy Hulk is cutting their sign-up fee in half for new members. If Brett signs up at a gym today, the number of months that the cost of the memberships be the same is: 23 months.

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The value of the expression log₃9 is 2.

The logarithmic function is the inverse of the exponential function. This means that the logarithm of a given number, say x, is the exponent to which another fixed number that is the base b, must be raised, so as to produce that number x.

Log a to the base b can be written as- log a/ log b.

Moreover, log [tex]a^{k}[/tex]= k log a, for all non negative values of a

Here, we are given a logarithmic expression- log₃9

We can expand this as-

log₃9 = log 9/ log 3

= log [tex]3^{2}[/tex]/ log 3

= 2 log 3/ log 3

= 2

Thus, the value of log₃9 is 2.

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Considering the definition of an equation and the way to solve it, the correct answer is the third option: Cadence baked 21 cupcakes on Monday.

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns.

The members of an equation are each of the expressions that appear on both sides of the equal sign.

The solution of a equation means determining the value that satisfies it. To solve an equation, keep in mind:

Being "x" the number of cupcakes baked by Cadence on Monday, and knowing that:

the equation in this case is:

3 + 2x= 45

Solving:

2x= 45 -3

2x= 42

x= 42 ÷ 2

x= 21

Finally, the correct answer is the third option: Cadence baked 21 cupcakes on Monday.

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Answer: The problem asks to solve for x. Equation B gives you the value of y, y = 2, so you can substitute 2 into Equation A for y.

Step-by-step explanation:

Answer:

The weight of the popcorn is off but the potato chips are safe. Simply determine whether each value is within the limit of deviation from eachother.

The correct option is (b) square root 112 units

By using Pythagoras theorem,

where a & b = legs of triangle and c = hypotenuse

Hence:

For logarithmic equation 1/2 log x + log 4 = 2, the value of x is 34,040.25

Step 1: Using exponentiation principles, isolate a logarithmic expression (with the same base) on both sides of the equation.

Step 2: balance the arguments.

Step 3: Solve the resultant equation.

Step 4: Double-check your answers.

Given,

1/2 log x + log 4 = 2

log x^(1/2) + log 4 = 2

using logₐ(m.n) = logₐ(m) + logₐ(n)

log e (4 (x^1/2)) = 2

e² = 4x^(1/2)

7.38 = 4√x

Squaring on both sides -

54.4644 = 16x

x = 54.4644 / 16

x = 34,040.25

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Answer:

75 degree

Step-by-step explanation:

35+70+75=180 degree

The required product of two rational numbers is 8y² - 28y + 4) / (6y² - 21y + 9).

What is a rational number?

Any real number that can be represented in the form of p/q, where q is not equal to 0 is called a rational number. The decimal expansion of rational numbers is terminating and repeating.

Calculation of the product of two rational numbers

Given two rational numbers,

8y - 4 / 10y - 5 and 5y -15 / 3y - 9

We need to multiply both the numbers i.e.

= (8y - 4 / 10y - 5) × (5y -15 / 3y - 9)

= (8y -4) × (5y - 15) / (10y - 5) × (3y - 9)

= (40y² - 140y + 20) / (30y² - 105y + 45)

= (8y² - 28y + 4) / (6y² - 21y + 9)

= (8y² - 28y + 4) / (6y² - 21y + 9)

The restriction is that the denominator, 6y² - 21y + 9 should not be 0.

Hence, the required product of two rational numbers is 8y2 - 28y + 4) / (6y2 - 21y + 9).

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