Tara's office recycled a total of 60 kilograms of paper over 3 weeks. How many weeks will it take Tara's office to recycle a total of 80 kilograms of paper? Solve using unit rates.

Answer: [tex]x^4 - 12x^3 - 27x^2 +486x[/tex]

Step-by-step explanation:

[tex](f \cdot g)(x)=f(x)g(x)\\\\=(x^2 -3x-54)(x-9)\\\\=x^3 - 9x^2 - 3x^2 + 27x - 54x + 486\\\\=x^3 -12x^2 -27x+486\\\\\therefore x(f \cdot g)(x)=x(x^3 -12x^2 -27x+486)\\\\=x^4 - 12x^3 - 27x^2 +486x[/tex]

The first transformation is the hardest to write using algebraic notation.

The technique of altering an existing graph or graphed equation to create a different version of the following graph is known as graph transformation.

Notice the first figure, the graph is translated 4 units to the left.

But, the second figure shows a vertical stretch of 2 times.

Let the function be y=f(x).

Then, the translation 4 units to the left using algebraic notation is written as:

y = f(x+4)

And, the vertical stretch of two times is:

y = 2f(x)

Clearly, the first transformation is the hardest to write using algebraic notation.

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The person that has the higher average speed is Teresa.

Average speed is calculated by dividing the total distance that something has travelled by the total amount of time it took it to travel that distance.

Therefore, Karl drove 40 miles in 50 minutes and Teresa drove 35 miles in 42 minutes.

The person that has the higher average speed can be calculated as follows;

average speed of Karl = distance / time

average speed of Karl = 40 / 50

average speed of Karl = 4 / 5 miles per minutes

average speed of Teresa = distance / time

average speed of Teresa = 35 / 42

average speed of Teresa = 5 / 6 miles per minutes

Therefore, Teresa had the higher average speed.

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Answer:

A. [tex]9n - 190 = 5n[/tex]

Step-by-step explanation:

Dora earning 5 dollars per song is represented by [tex]5n[/tex].

Gary earning 9 dollars a song but paying the $190 fee is represented by [tex]9n - 190[/tex] because the fee from the coffee shop is subtracted from his total earnings.

Answer: Extrapolation ,from the above can be defined as using a linear regression equation and any x- value to predict any y-value.

Step-by-step explanation:

Extrapolation regression makes use of estimated regression equation to predict a new value y for specific X values not in the range of the sampled data used to estimate our regression equation

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Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression. Since 6 + 6 equals 12, the variable x in the example above is equal to 6. If we are aware of the values of our variables, we can substitute those values for the original variables before evaluating the expression.

The idea of an expression number makes use of the method of allocating single-digit numbers (1 to 9) to the letters of the English alphabet, starting with A. The main mathematical advancements utilizing these number patterns are highlighted in the next section.

An expression is, for instance, 3x - 2. While an equation, on the other hand, denotes the connection between two separate expressions via an equal to sign.

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Answer: I don't know why I'm here

Step-by-step explanation: help

Answer:

x= -8/41

y= 27/41

Step-by-step explanation:

7y=2x+5

3x+10y=6

maybe divide all parts of first equation by 7 to leave y by itself: y=2/7x+5/7

Then plug that in for y in the second equation:

3x+10(2/7x+5/7)=6

Then just solve for x:

x= -8/41

Substitute value of x into first equation:

7y=2(-8/41)+5

Solve for y:

y=27/41

In systems of equations, the values of x and y are -8 and 3, respectively.

Given systems of equations are:

7y=-2x+5 .....(i)

3x+10y=6 .....(ii)

We want both equations to be in standard form (Ax + By = C) so we need to fix the first equation.

For the equation (i), simply add 2x from both sides, so that x & y are on the same side of the equal sign

2x + 7y = 5 .....(i)

3x + 10y = 6 .....(ii)

To get the same x value in both equations (i) and (ii), we must now multiply equation (i) by 3 and equation (ii) by 2.

3(2x + 7y = 5) .....(i)

2(3x + 10y = 6) .....(ii)

Simplify.

6x + 21y = 15 .....(i)

6x + 20y = 12 .....(ii)

Now, subtract equations (ii) from (i)

y = 3

Now, substitute value of y = 3 in equation (i).

2x + 7y = 5 .....(i)

2x + 7(3) = 5

2x + 21 = 5

Then, subtract 21 from both sides.

2x + 21 - 21  = 5 - 21

2x = - 16

Divide both sides by 2.

2x / 2 = - 16 / 2

x = -8

So, x = -8 & y = 3

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Answer:

Step-by-step explanation:

I believe the answer is D!

SOLUTION

Given the question in the question tab, the following are the solution step to get the number of books they have altogether.

Step 1: Write the notations for Joseph's and Mike's books

Step 2: Write the statements in a mathematical form

Step 3: Solve to get the value of j by using substitution method

Therefore, Joseph had 84 books initially.

Step 4: Get the number of books they had altogether by summing the number of books for the each of them initially

Hence, they both had 112 books altogether.

Answer:

y=(5/2)x-4

Step-by-step explanation:

1) You would have to find the slope by using the slope equations

(x1-x2)/(y1-y2)

(6-1)/(4-2)

Slope =5/2

2) the next is to find the y-axis

the line land on the x=0 at -4

y-axis=-4

3) plug into slope intercept form

y=mx+b

m=slope

b=y-axis

y=(5/2)x+(-4)

y=(5/2)x-4

Answer:

[tex]y=\frac{5}{2}x-4[/tex]

Step-by-step explanation:

1. we pick 2 points from a graph...one is (0,-4) and the other is (1,2)

2. we find the gradient between the two points using this equation m=[tex]\frac{y2-y1}{x2-x1}[/tex]

3. we plug the value in the equation

4. m = 5/2

5. equation of a straight line is y = mx +c

-where c is the intercept of the graph and m is the gradient

-4=5/2(0)+c

c =-4

therefore [tex]y=\frac{5}{2}x -4[/tex]

The increase in the selling price is 1.818.

Test statistic:

A test statistic is a statistic used in statistical hypothesis testing. A hypothesis test is typically specified in terms of a test statistic, considered as a numerical summary of a data-set that reduces the data to one value that can be used to perform the hypothesis test.

The given values are:

a = 0.1

x = 94

μ = 90

The formula for test statistic will be:

t = ((x- μ) / ([tex]\frac{s}{vn}[/tex])

Now put the values in the given equation we have:

t = (94-90) / ([tex]\frac{22}{10}[/tex])

 = 4/2.2

  = 1.818

Therefore the increase in the selling price is 1.818.

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The p-value of the test corresponding to study a was found to be 0. 40. and the p-value for study b is 0.80

The entire area under the crucial range of values on both sides of the curve in a two-tailed test represents the likelihood of occurrence (negative side and positive side)

As a result, the connection below provides the probability values for a two-tailed test when compared to a one-tailed test.

Here

By replacing the supplied value in the previous equation, we obtain -

values of the probabilities for a two-tailed test

p-value = P (alpha/2) +  P (alpha/2)

p-value = 0.40 + 0.40

            =0.8

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Answer:

(a)Vertex

(c)3 seconds

Explanation:

Part A

The maximum point on a parabola is called the Vertex.

Part C

To find out how much the plain was in the air, find the values of t at which the height, h=0.

Next, subtract the second value of t from the first value.

First, set h=0:

Factorize:

Therefore, the plane hits the ground after 3 seconds.

Answer:

1.25 hours.

68.75 miles from the city

Step-by-step explanation:

Eltan's train (E) is travelling 65mph west.

Dmitri's train (D) is travelling 55mph west.

In terms of vectors, we can write E as 65E and D as 55W

The miles travelled by each is a function of time, T, in hours.

Each train's distance is:

 E:  T*65E

 D:  T*55W

They are 150 miles apart.  They will meet with the combined miles travelled is 150 miles.

 150 miles = T*65E + T*55W

150 miles = T(120 miles/hour)

T = (150 miles/120 miles/hour)

T = 1.25 hours

Make Demitri's train mile 0 and Eitan's train at mile 150 at the start.

They will have travelled the following miles in 1.25 hours:

Demitri:  (1.25hr)(55 m/hr) = 68.75 miles

Eitan:      (1.25hr)(65 m/hr) = 81.25 miles

Total = 150 miles

Dimitri is headed away from the city.  After 1.25 hours, his train will have travelled 68.75 miles when he sees Eitan passing him on the adjacent track (hopefull) headed into the city.  They meet 68.75 miles from the city.

Answer:

question one is B and question 2 is C

Step-by-step explanation:

A function is a reletion with one output for each input. Then, in a ordered pair inputs and outputs represent a relationship between two values.

Some relationships make sence (one output for each input) and others dont't.

Functions are relationsips that make sence.

Answer:

-31, 9, 1, 5, 37

Step-by-step explanation:

f(x) = -2(-2)^2 + 1

f(x) = 4^2 + 1

f(x) = 8+1

f(x) = 9

f(x) = -2(0)^2 +1

f(x) = 0^2 + 1

f(x) = 0 + 1

f(x) = 1

f(x) = -2(1)^2 + 1

f(x) = -2^2 + 1

f(x) = 4+1

f(x) = 5

f(x) = -2(3)^2 + 1

f(x) = -6^2 + 1

f(x) = 36+1

f(x) = 37

Answer: False

Step-by-step explanation: The two lines do not overlap so they do not intercept.

The slope of the line will be positive 9. Then the correct option is C.

The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall and the difference between the abscissa is called run.

The slope is given as,

Slope = m = (y₂ - y₁) / (x₂ - x₁)

Determine whether a line's slope, which represents the linear connection, is positive, negative, zero, or undefined without using a graph. Next, locate the slope. A babysitter may make $9 per hour and $36 per 4 hours.

Slope = (36 - 9) / (4 - 1)

Slope = 27 / 3

Slope = 9

The slope of the line will be positive 9. Then the correct option is C.

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Answer:  70

Step-by-step explanation:

easy addition

x+119°=180°(Co-interior angles are supplementary m || n)

[tex]x = 180 - 119 \\ x = 61[/tex]

y=119°(alternate angles are equal m ||n)

GOODLUCK.

The addition symbol (+) can be used in between the two parentheses to show that you will be using the distributive property.

Distributive property:

The distributive property states that multiplying the sum of two or more addends by a number produces the same result as when each addend is multiplied individually by the number and the products are added together.

It can be written as,

a x (b + c) = (a x b) + (a x c)

Where a, b and c are the values of the variables.

Given,

Here we have the expression:

8 x 57 = (8 x 50) _____(8x7)

Here we need to find the symbol that can be used in between the two parentheses to show that it will be using the distributive property.

Based on the definition of the distributive property we have know that the symbol (+) can be used to make this one as distributive property used equation.

Therefore, the expression is written as,

8 x 57 = (8 x 50) + (8x7)

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answer:

8.00 dollars

Step-by-step explanation:

4 x 1.50 = 6.00

38,00 - 6.00 = 32.00

32.00 divided by 4= 8.00

1) Wrong statement:

The difference between the experimental and theoretical probability is 1/10

Correct statement:

The difference between the experimental and theoretical probability is 3/200

2) Wrong statement:

The difference between the experimental and theoretical probability is 1/10

Correct statement:

The difference between the experimental and theoretical probability is 3/200

N(Pennies) = 6

N(Nickels) = 8

N(Dimes) = 4

N(quarters) = 7

N(total) = 6 + 8 + 4 + 7

N(total) = 25

1) The theoretical probability of selecting a dime = 4/25

The experimental probability of selecting a dime = 30/150 = 1/5

B is wrong because theoretical probability is 4/25, not 9/50

Wrong statement:

The theoretical probability of selecting a dime is

Correct statement:

The theoretical probability of selecting a dime is 4/25

2) The experimental probability of selecting a penny = 45/200 = 9/40

The theoretical probability of selecting a penny = 6/25

Difference between experimental and theoretical probability = 6/25 - 9/40

Difference between experimental and theoretical probability = 3/200

Wrong statement:

The difference between the experimental and theoretical probability is 1/10

Correct statement:

The difference between the experimental and theoretical probability is 3/200

The mean age of customers is 27.35 years.

It is well known that age has a normal distribution with a 5-year standard deviation. Additionally, 30% of the time, customers are under the age of 30.

Mathematically,

P (age ≤ 30) = 0.70

Let μ be the mean age of the customer.

P [z ≤ (30 - μ) / σ] = 0.70

The equivalent of "age" in a conventional normal distribution is the z-score or z. It is evident from the usual normal distribution table that when z=0.53, 0.70 probability is reached.

Thus,

z = (30 - μ) / σ

⇒ 0.53 = (30 - μ) / 5

⇒ μ = 27.35

As a result, the average consumer is 27.35 years old.

The probability at each z-score in a standard normal table is represented by the associated z-score. We will look for the number 0.70 in the table, then the row value of 0.5 and the associated column value of 0.03 will be examined. They add up to 0.53 when combined.

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From the given question

There are given that the :

After two weeks, the total miles is 276 and after 3 weeks, the total miles are 413

Now,

The total miles did they ride in the third week is:

Hence, the total miles in the third week is 137.

Answer:

Angle 1: 159

Angle 2: 21

Angle 4: 21

Step-by-step explanation:

According to Table B, There is a series that is being followed next, i.e.,

m = (m+1) * (m-1)

In the given data,

Input is 5, then given output is 6 * 4, similarly

Input is 10, then given output is 11 * 9 which implies that

Output is the products of one more than input and one less than input

⇒5 = (5+1) * (5-1)

⇒5 = 6 * 4

again with 15 = (15+1) * (15-1) ⇒ 16 * 14

with 300 = (300+1) * (300-1) ⇒ 301 * 299

At last, we can construct a series from these data,

m = (m+1) * (m-1)

Where m is input and (m+1) * (m-1) is output of data.

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It seems there is some missing info on this question. However, if you are simplifying, then the simplified version of the given expression would be...

[tex]10a^1^9[/tex]

Hope this helps!