Adam drew a line that was 6 4/10 inches long. If he drew a second line that was 2 2/3
inches longer, what is the length of the second line? Answer as a mixed number.

Given:-

Michiko record the colors of all cars passing through an internection.

To find:-

Probability that the next car through the intersection will be red.

So to calculate the probabilty. we add all the number of cars and we divide 11 with that number and multiply with 100. To get the required solution.

So the total cars is,

So now we simplify. we get,

So the required solution is 18.3%

So the correct option is OPTION 1.

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Answer:

11y is the exact value.

Step-by-step explanation:

Answer:

x > -5, so the correct answer is C.

The least common denominator for the function \(\frac{11x}{x^2 + 4x - 12} - \frac{7}{2x^2 - 4x}\)

is (x -2).

What is least common denominator?

The least common multiple of a group of fractions' denominators is known as the lowest common denominator, or Least Common Denominator.

According to the given question:

Consider the given expression, \(\frac{11x}{x^2 + 4x - 12} - \frac{7}{2x^2 - 4x}\)

Further simplifying the equation by factorization of the denominator part

= \(\frac{11x}{x^2 + 6x - 2x - 12} - \frac{7}{2x(x-2)}\)

= \(\frac{11x}{(x+6)(x-2)} - \frac{7}{2x(x-2)}\)

= \(\frac{1}{x-2} [\frac{11x}{(x+6)} - \frac{7}{2x}]\)

Therefore, from the above result, it is found that (x-2) is the least common denominator that can be taken.

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Answer:

The equation c = 0.02p+149 represents micks commission.

Step-by-step explanation:

Given that:

Amount earned by Nick on sale of each boat = $149

Commission earned = 2% of the purchase price

p represent the purchase price

Commission earned = \(\frac{2}{100}*p\)

Commission earned = 0.02*p

Commission earned = 0.02p

Total commission = c = 0.02p + 149

Hence,

The equation c = 0.02p+149 represents micks commission.

According to the situation described, we have that:

a) The arithmetic sequence that gives the number of seats in the nth row is given by:

\(a_n = 24 + 7n\)

b) The 38th row has 290 seats.

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The nth term of an arithmetic sequence is given by:

\(a_n = a_1 + (n - 1)d\)

Item a:

The first row has 31 seats, the second has 38, the third has 45 and so on, hence:

Then, the rule is:

\(a_n = a_1 + (n - 1)d\)

\(a_n = 31 + 7(n - 1)\)

\(a_n = 24 + 7n\)

Item b:

This is the nth row, for which \(a_n = 290\), hence:

\(a_n = 24 + 7n\)

\(290 = 24 + 7n\)

\(7n = 266\)

\(n = \frac{266}{7}\)

\(n = 38\)

The 38th row has 290 seats.

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The given expression is,

The factors of 120 are, 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

The factors of 50 are, 1, 2, 5, 10, 25, 50

From this, we can infer that, the greatest common factor of 120 and 50 is,

10.

Therefore, we can write,

Let's call the speed of the boat in still water as x.

One part of the trip is 10 miles downstream, where the speed of the boat and the speed of the current add together and the other part of the trip is the trip back the 10 miles upstream, where the speed of the current works against the speed of the boat, which gives to us the following equation:

Solving for x, we have:

Using the quadratic equation, the solution for our equation is:

The answer is 20.81 mph.

The domain restricted to the function is 0 <= x <= 10

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the given parameters are:

Amount in the account = $350

Amount deducted each week = $35

Let the number of weeks be x, and the total amount be y

So, we have:

y = 350 - 35x

When the amount is 0, we have:

350 - 35x = 0

This gives

35x = 350

Divide by 35

x = 10

Hence, the domain restricted to the function is 0 <= x <= 10

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Answer:

x is greater than or equal to 0 but less than or equal to 10

Step-by-step explanation:

Answer:

The rock will reach to the canyon floor in 3.99 seconds.

Step-by-step explanation:

The height h (in feet) of an object t seconds after it is dropped can be modeled by the quadratic equation

Where, h0 is the initial height of the object.

It can be written as

The height of the object is zero if it will reach to the canyon floor.

Quadratic formula:

Here a=-16, b=0 and c=255.

Time cannot be negative, therefore the rock will reach to the canyon floor in 3.99 seconds.

Answer:

The distance between the points

d = LM = 10.24

Step-by-step explanation:

Step(i):-

Given that the points are L ( 7,-1) and M (-2,4)

The distance formula

  LM = \(\sqrt{(x_{2} -x_{1})^{2} +(y_{2} -y_{1} )^{2} }\)

Step(ii):-

\(LM= \sqrt{(-2-7)^{2} +(4-(-1) )^{2} }\)

LM = \(\sqrt{(-9)^{2} +(5)^{2} }\)

LM = √106

LM = 10.29

The distance between the points

d = LM = 10.24

The method is: Find the increase and find the ratio of the increase and the old price.

The percentage increase is 20%

A percentage is defined as the ratio that can be expressed as a fraction of 100.

The method below shows how you would calculate the % increase.

First step: Find the increase:

increase = 480 - 400 = $80

Second step: Find the ratio of the increase and the old price and multiply by 100 to express in percentage:

80/400 * 100 = 20%

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The actual consumer spending at a price of $27 per unit is $268.26.

Substitute the given price into the supply equation to get the corresponding quantity supplied:

p = q + 10

27 = q + 10

q = 17

Substitute q = 17 into the demand equation to get the corresponding price:

4q² + p² = 1405

4(17)² + p² = 1405

p² = 1405 - 1156

p² = 249

p = 15.78

The actual consumer spending can be calculated by multiplying the quantity demanded by the price:

Actual consumer spending = quantity demanded x price per unit

= 17 x 15.78

= $268.26

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The demand and supply equations for a certain product are given by space 4 q squared plus p squared equals 1405 and p equals q plus 10 where p is in dollars per unit and q is in units. For a price of $27 per unit, determine the actual consumer spending.

Answer:

The distance between point N and S is 8 units.

Step-by-step explanation:

count the distance from the x-values:

- from -2 to 6

OR

plot them on a graph and count the units that are between them.

hope this helps ya!! :))

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Answer:

116 / 45

Step-by-step explanation:

To add fractions with unlike denominators, we need to find their common denominator.

One way to do this is by finding the least common multiple (LCM) of the denominators.

The LCM of 3, 5, 9 and 15 is 45.

We then convert each fraction so that its denominator is 45:

1/3 = 15/45

3/5 = 27/45

7/9 = 35/45

13/15 = 39/45

Now we can add the fractions:

15/45 + 27/45 + 35/45 + 39/45

To simplify, we can add the numerators and keep the common denominator:

(15 + 27 + 35 + 39) / 45

Which gives us:

116 / 45

Therefore, the sum of the fractions 1/3 + 3/5 + 7/9 + 13/15 is, 116 / 45.

You just have to underline the word that connects two sentences .

for example: In number 2. Sophia ate a lot. She is still hungry. These are two sentences the word 'yet' connects two sentences. that is called conjunction.

1.= under line so

2.= under line yet

3.= under line but

4.= under line so

Answer:

Cost for each pound of jelly beans:  $2.75

Cost for each pound of almonds:  $3.75

Step-by-step explanation:

Let J be the cost of one pound of jelly beans.

Let A be the cost of one pound of almonds.

Using the given information, we can create a system of equations.

Given 3 pounds of jelly beans and 5 pounds of almonds cost $27:

\(\implies 3J + 5A = 27\)

Given 9 pounds of jelly beans and 7 pounds of almonds cost $51:

\(\implies 9J + 7A = 51\)

Therefore, the system of equations is:

\(\begin{cases}3J+5A=27\\9J+7A=51\end{cases}\)

To solve the system of equations, multiply the first equation by 3 to create a third equation:

\(3J \cdot 3+5A \cdot 3=27 \cdot 3\)

\(9J+15A=81\)

Subtract the second equation from the third equation to eliminate the J term.

\(\begin{array}{crcrcl}&9J & + & 15A & = & 81\\\vphantom{\dfrac12}- & (9J & + & 7A & = & 51)\\\cline{2-6}\vphantom{\dfrac12} &&&8A&=&30\end{array}\)

Solve the equation for A by dividing both sides by 8:

\(\dfrac{8A}{8}=\dfrac{30}{8}\)

\(A=3.75\)

Therefore, the cost of one pound of almonds is $3.75.

Now that we know the cost of one pound of almonds, we can substitute this value into one of the original equations to solve for J.

Using the first equation:

\(3J+5(3.75)=27\)

\(3J+18.75=27\)

\(3J+18.75-18/75=27-18.75\)

\(3J=8.25\)

\(\dfrac{3J}{3}=\dfrac{8.25}{3}\)

\(J=2.75\)

Therefore, the cost of one pound of jelly beans is $2.75.

Answer:

1+2x-63x^2

Step-by-step explanation:

(1-7x)(1+9x)

1-7x+9x-63x^2

1+2x-63x^2

Answer:

Domain: {4,5,7,10}

Range: {2,4,8}

Not a function

Step-by-step explanation:

The domain is all the x-values.

The range is all the y-values.

However, this isn't a function because two different inputs have the same output. If it were a function, there would be one unique output for every input.

Answer:

Minimum--> 250

Q1--> 255

Q2--> (Median): 307

Q3--> 433

Maximum-->507

Step-by-step explanation:

To find the five-number summary of this data set, we need to determine the minimum value, maximum value, and three quartiles (Q1, Q2, Q3) which divide the data into four equal parts.

First, we need to sort the data set in ascending order:

{ 250, 253, 255, 267, 307, 425, 433, 435, 507 }

Minimum: 250

Maximum: 507

To find the quartiles, we need to find the median of the entire data set (Q2) and then the medians of the two halves of the data set, which will give us Q1 and Q3.

Q2 (Median): The median of the entire data set can be found by averaging the two middle numbers.

Q1: The median of the lower half of the data set is 255, which is the middle value of { 250, 253, 255, 267, 307 }. Therefore, Q1 = 255.

Q3: The median of the upper half of the data set is 433, which is the middle value of { 425, 433, 435, 507 }. Therefore, Q3 = 433.

Solving a system of equations we can see that:

We can use the variables:

x = mass of the 60% solution.

y = mass of the 85% solution.

We can write a system of equations.

x + y = 70

x*0.6 + y*0.85 = 70*0.8

We can isolate x on the first equation to get:

x = 70 - y

Replace that in the other one:

(70 - y)*0.6 + y*0.85 = 70*0.8

Now we can solve this for y.

y*0.25 = 70*0.8 - 70*0.6

y = 14/0.25 = 56

Then he needs to use 56 ounces of the 85% solution, and 14 ounces of the 60% solution.

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Answer:

Step-by-step explanation:

4.375

Answer:

2.25

Step-by-step explanation:

Answer:

2.25

Step-by-step explanation:

Answer:

I'm sorry but I can't answer it because the factoring in the question can't be put together

Step-by-step explanation:

The groups have no common factor and can not be added up to form a multiplication.