If a store advertised a sale that gave a customer a 1/4 discount,what is the fraction part of the original price that the customer pay?

Remark

You can use a formula to get the right answer. Otherwise you will use a lot of paper adding 100 numbers together.

Givens

A = 1

L = 100

n = 100 numbers to be added together. There are 100 numbers between 1 and 100 numbers inclusive.

Formula

Sum = (A + L)*n/2

Solution

Sum = (1 + 100)*100/2     Substitute in the givens. Add what is inside the brackets

Sum = (101) * 100 / 2       Divide by 2

Sum = 101* 50                  Multiply

Sum = 5050                     Answer

The sum of the numbers from 1 to 100 is 5050

The sum of the numbers from 1 to 100 can be calculated using the formula for the sum of an arithmetic series. An arithmetic series is a sequence of numbers where the difference between two consecutive terms is constant. In this case, the difference between successive numbers is 1.

The formula for an arithmetic series's sum (S) is S = n/2 (a + l), where n is the number of terms, a is the first term, and l is the last term.

Here, n = 100 (because we're adding the numbers from 1 to 100), a = 1 (the first number) and l = 100 (the last number). Substituting these values into the formula gives us S = 100/2 * (1 + 100) = 50 * 101 = 5050.

So the sum of the numbers from 1 to 100 is 5050.

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[tex]Q2.\\\\1.\ \text{All real numbers}\ \mathbb{R}\\\\2.\ \{1,\ 2,\ 3,\ ...\}\ \mathbb{N}\\\\3.\ \{...,\ -3,\ -2,\ -1,\ 0,\ 1,\ 2,\ 3,\ ...\}\ \mathbb{Z}[/tex]

[tex]Q3.\\5\ not\ \text{because it's not true}\ 5 < 5\ \text{and}\ 5 > 8\\\\7\ not\ \text{because it's not true}\ 7 < 5\ \text{and}\ 7 > 8\\\\8\ not\ \text{because it's not true}\ 8 < 5\ \text{and}\ 8 > 8\\\\9\ yes\ \text{because it's true}\ 9 > 8[/tex]

In case of inequalities we have following two rules.

Rule 1:

If we have just greater than > or less than < sign , then we would use open cirlce.

An open dot means the function has no definition at the specific point

Greater Than, >, and Less Than, <, mean the solution does NOT contain the number

Rule 2:

For inequalities. Greater Than or Equal TO, >, and Less Than or Equal TO, <, mean the solution does contain the number.

So in that case we will use closed circle.

Hope that helps.

Closed circle for the first one

Open circle for the second one

The length of the first piece is 4 the second piece is 8 and the third piece is 27.  Your Welcome

The problem can be solved by setting up an equation where x represents the length of the first piece. Solving for x, we find that the lengths of the three pieces are 4 inches, 8 inches, and 27 inches.

To solve this question, you can define the length of the first piece as 'x'. According to the problem, the second piece is twice as long as the first one, so it can be represented as '2x'. And the third piece is three inches more than six times the first one, which can be represented as '6x+3'.

Because the total length of the steel is 39 inches, you can setup an equation to solve for 'x':

x + 2x + 6x + 3 = 39

This simplifies to:

9x + 3 = 39

Subtracting 3 from both sides:

9x = 36

Finally, divide each side by 9:

x = 4

Therefore, the lengths of the three pieces of steel are:

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Technically you should use "substitution" in place of "transitive property of equality", though they are very closely related ideas. If I were your teacher, then I would accept that answer as valid nonetheless.

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

Substitution says that if a = b and c = b, then a = c. We replace the 'b' in a = b with 'c'. Think of your substitute teacher who replaces your current teacher for a temporary basis. This is how to remember the term "substitution.

On the other hand, the transitive property of equality says that if a = b and b = c, then a = c. The equations chain together and can simplify into one single equation.

Answer:

Option B

Step-by-step explanation:

Given that f(x) = 3x+5 and g(x) = 3x^2-x-10

Hence the function f/g = (3x+5)/(3x^2-x-10)

Since denominator cannot be 0 we have

3x^2-x-10 cannot be 0

i.e. x should not take values where 3x^2-x-10 =0

Solving (3x+5)(x-2) =0

x cannot take value as 2 or -5/3

So we can cancel 3x+5 and write

f/g =1/ x-2

Hence x cannot take values as 2

Option B

Option: B is the correct answer.

The function is:  [tex](\dfrac{f}{g})(x)=\dfrac{1}{x-2}[/tex]

and the domain is:  The set of all real numbers except 2

We are given a function f(x) and g(x) in terms of variable x by:

[tex]f(x)=3x+5[/tex]

and

[tex]g(x)=3x^2-x-10[/tex]

Now, the function

[tex](\dfrac{f}{g})(x)[/tex] is given by:

[tex](\dfrac{f}{g})(x)=\dfrac{f(x)}{g(x)}[/tex]

i.e.

[tex](\dfrac{f}{g})(x)=\dfrac{3x+5}{3x^2-x-10}[/tex]

[tex]3x^2-x-10=3x^2-6x+5x-10\\\\i.e.\\\\3x^2-x-10=3x(x-2)+5(x-2)\\\\i.e.\\\\3x^2-x-10=(3x+5)(x-2)[/tex]

i.e.

[tex](\dfrac{f}{g})(x)=\dfrac{3x+5}{(3x+5)(x-2)}\\\\i.e.\\\\(\dfrac{f}{g})(x)=\dfrac{1}{x-2}[/tex]

Also, the domain of the function is the set of all the real values except where the denominator is equal to zero.

The denominator is equal to zero when x=2.

Hence, the domain is the set of all the real values except 2.

This one has two parts, first we have to find out the speed to drive 660 miles in 12 hours.  Divide 660 by 12 to get the speed of 55 miles per hour, that is your rate for the next part.

Next we need to find out how long it will take to drive 495 miles at the same pace of 55 mph.

Do the same thing 495/55.  That will give you your final answer.

495/55= 9

It will take him 9 hours to drive 495 miles at a rate of 55 mph.

Final answer:

Greg drives at a speed of 55 miles per hour. To drive 495 miles at this rate, it would take him 9 hours.

Explanation:

The question asks how long it would take Greg to drive 495 miles if he drove 660 miles in 12 hours. To solve this, we need to find his driving speed and then calculate how long it would take to drive 495 miles at that same speed.

First, we find the speed by dividing the distance traveled by the time:

Speed = Distance ÷ Time

Speed = 660 miles ÷ 12 hours = 55 miles per hour

Now that we know Greg drives at a speed of 55 miles per hour, we can calculate the time it would take him to drive 495 miles:

Time = Distance ÷ Speed

Time = 495 miles ÷ 55 miles per hour = 9 hours

Therefore, it would take Greg 9 hours to drive 495 miles at the same rate of speed.

$236.25 is how much money carrie got

$78.75 is how much juanita got

We are given that

a and b are integers and 71 < ab < 76

We will check each options

option-A:

b=18

we can plug it

[tex]71<a(18)<76[/tex]

we can divide both sides by 18

[tex]\frac{71}{18} <b<\frac{76}{18}[/tex]

now, we can simplify it

[tex]3.944<a<4.222[/tex]

Since, 'a' is a integer

so, a=4 lies on interval

so, this interval is true

so, this is FALSE

option-B:

b=8

we can plug it

[tex]71<a(8)<76[/tex]

we can divide both sides by 8

[tex]\frac{71}{8} <b<\frac{76}{8}[/tex]

now, we can simplify it

[tex]8.875<a<9.5[/tex]

Since, 'a' is a integer

so, a=9 lies on interval

so, this interval is true

so, this is FALSE

option-C:

b=12

we can plug it

[tex]71<a(8)<76[/tex]

we can divide both sides by 12

[tex]\frac{71}{12} <b<\frac{76}{12}[/tex]

now, we can simplify it

[tex]5.9166<a<6.333[/tex]

Since, 'a' is a integer

so, a=6 lies on interval

so, this interval is true

so, this is FALSE

option-D:

b=7

we can plug it

[tex]71<a(5)<76[/tex]

we can divide both sides by 7

[tex]\frac{71}{7} <b<\frac{76}{7}[/tex]

now, we can simplify it

[tex]10.14285<a<10.857[/tex]

Since, 'a' is a integer

so, no integer lies on this interval

so, this interval is false

so, this is TRUE

option-E:

b=5

we can plug it

[tex]71<a(5)<76[/tex]

we can divide both sides by 5

[tex]\frac{71}{5} <b<\frac{76}{5}[/tex]

now, we can simplify it

[tex]14.2<a<15.2[/tex]

Since, 'a' is a integer

so, a=15

so, this interval is true

so, this is FALSE

Answer: Speed of local bus is 50 mph  and speed of express bus is 75 mph

Step-by-step explanation:

let say speed of local bus = x

so speed of express bus = x + 25

Distance = Speed × Time

Distance traveled by local bus  = x × 10.2 = 10.2x

Distance traveled by express bus = (x + 25) × 6.8

since Distance traveled by local bus is same as Distance traveled by express bus

⇒10.2x = (x + 25) × 6.8

⇒ 10.2x = 6.8x + 170

⇒ 10.2x - 6.8x = 170

⇒ x = 170/3.4 = 50

So Speed of local bus = x = 50 mph

and Speed of express bus =  x + 25 = 50 + 25 = 75 mph

Final answer:

The speed of the local bus is 50 mph and the speed of the express bus is 75 mph.

Explanation:

Let's define the speed of the local bus as 'x'.

The speed of the express bus is 25 mph faster than the speed of the local bus, so the speed of the express bus can be represented as 'x + 25'.

We know that the time taken by the express bus is 6.8 hours and the time taken by the local bus is 10.2 hours.

Using the formula Speed = Distance / Time, we can set up two equations:

Distance / 6.8 = x + 25  (equation 1)

Distance / 10.2 = x  (equation 2)

Since the distance is the same for both buses (Sacramento to San Diego), we can equate the distances in equation 1 and equation 2:

x + 25 = (10.2/6.8) * x

x + 25 = 1.5x

0.5x = 25

x = 50

Substituting the value of x in equation 1, we can find the speed of the express bus:

Distance / 6.8 = (50 + 25)

Distance = 6.8 * 75

Speed of the express bus = Distance / 6.8 = 75

So, the speed of the local bus is 50 mph and the speed of the express bus is 75 mph.

To find the new price of an item that has been reduced by a certain percentage, multiply the original price by the percentage (converted to decimal form) to find the discount. Subtract this discount from the original price to get the new price. Therefore, the new price of the item originally priced at $39 and reduced by 85% is $5.85.

This is a basic percentage problem in mathematics. The phrase 'reduced by 85%' implies that we are subtracting 85% of the original price from the original price itself. To find the discount, we multiply the original price by the reduction rate (in decimal form). Then, to get the final price, we subtract the discount from the original price. So, if the original price is $39 and the item has been reduced by 85%, then the discount would be $39. The calculation would look like this:

So, the new price of the item is $5.85.

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Marshall retires from the partnership of? Marshall, Mark, and Dennis. Marshall had a capital balance of? $25,000. If Marshall received? $25,000 as final? settlement, how will this transaction affect the balance sheet?  The answer is equities will decrease.

Answer:

56

Step-by-step explanation:

Given that Lydia is painting flower vases.

Paint required for painting one flower case = 3/16 quart

total paint available with Lydia = 21/2 quart

We have to find the no of flower cases that can be painted.

This is a problem of direct variation since when no of flower cases increase paint required also increases.

3/16 quart for 1 flower case

Hence 21/2 quart for 21/2 divided by 3/16

= 21*16/(3*2)  (by rule for fraction division)

= 7(8)

= 56

The greatest number of tables needed to serve dinner to 55 guests, with each table having a different number of guests, is 10 tables.

To find the greatest number of tables needed to serve dinner to 55 guests so that each table has a different number of guests, we need to distribute the guests among the tables in a way that maximizes the number of tables. We can start by placing one guest at each table, then add one more guest to each subsequent table until there are no more guests remaining. This will result in the maximum number of tables, with each table having a different number of guests.

Let's see how this works:

After distributing the guests this way, we have used 10 tables, with each table having a different number of guests. Therefore, the greatest number of tables we could use to serve dinner to 55 guests, with each table having a different number of guests, is 10 tables.

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Search up line bisector, i just wanna slap you, i know your mom thinks your a failure, such an idiot

It's the third answer. This is because since there is no middle term where both variables are combined, that would lead to the signs of the 2 factors to be different. However, that still leaves 2 answers, 3 and 2. If we were to square i, you would get -1. This is because √-1 is equal to i. i^2 would be -1. Since the sign in the unfactored expression is positive and not negative, that would mean that the i in the factoring turned it around. that leads us to believe that answer 3 is the correct answer.

Answer:

A.-12x^2-5x-102

Step-by-step explanation:

We are given a polynomial of degree 2 where terms are not grouped and simplified.

We have

-21x^2+22x^2-13x^2-10x+5x-102

To get this in proper form we have to group the like terms first

x^2 term = -21x^2+22x^2-13x^2 = x^2 (-21+22-13)

= x^2(-34+22) = -12x^2

x terms are -10x+5x = x(-10+5) = -5x

Constant term is only one = -102

Hence the polynomial in simplified form is

-12x^2-5x-102

$12.80

sales tax = [tex]\frac{1}{2}[/tex] × $25.60 = $12.80

Answer:

the answer is:12 4/5=$12.80

Step-by-step explanation:

sales tax = 1/2 × 25 3/5 = $12.80

                         25.60        12 4/5

First you need to distribute

2x-10=6x-x+8

Add like terms

2x-10=5x+8

Subtract 8 from each side

2x-18=5x

Subtract 2x from each side

-18=3x

Divide each side by 3

X=-6

2x-10=6x-x+8

2x-10=5x+8

add 10 to both sides

2x=5x+18

subtract 5x from both sides

-3x=18

divide each side by -3

x=-6

Answer:

c.

Alexa is earning quite a bit more money than she was previously. This would be a good time for her to re-evaluate her budget. Part of the extra money she is making could be put in her savings account.

Step-by-step explanation:

Alexa's increased income has allowed her to increase her expenses in various categories, while still maintaining a balanced budget.

Alexa's increased income will have an impact on her budget. Let's compare her previous budget and her current budget:

As we can see, her expenses have increased in line with her increased income. Rent, utilities, groceries, and savings have all increased, while the cost of the bus pass remains the same.

The answer to this is the last option

Answer:

The correct answer is:

A line with 4 tick marks labeled Cat, Dog, Rabbit, and Guinea Pig. Cat has 3 crosses, Dog has 2 crosses, Rabbit has 1 cross, and Guinea Pig has 2 crosses. The line is labeled Number of Pets, and title of graph is Pet Owners.

Step-by-step explanation:

The survey is given as:

Pet                Frequency  

Cats                 3

Dogs              2

Rabbits            1

Guinea Pigs 2

When we will draw a line plot where the horizontal axis denote the pet and the cross above the pet represent the number of pets.

Hence, as the frequency of cat is three so there will be three cross above cat.

Similarly as the frequency of dogs is two so there will be two cross above dogs.

the frequency of rabbits is one so there will be one cross above rabbit.

the frequency of Guinea Pigs is two so there will be two cross above Guinea Pigs.

Keri walks approximately 4.29 kilometers in one week.

Keri walks her dog every morning. On weekdays, the length of the walk is 0.55 km. On weekends, the walk is 1.4 times as long as a walk on a weekday. To find out how many kilometers Keri walks in one week, we need to calculate the total distance she walks on weekdays and weekends.

Distance walked on weekdays = 0.55 km per day

Distance walked on weekends = 1.4 * 0.55 km per day = 0.77 km per day

Total distance walked in one week = (distance on weekdays * number of weekdays) + (distance on weekends * number of weekends)

Since there are 5 weekdays and 2 weekend days in a week, we can calculate the total distance:

Total distance walked in one week = (0.55 km * 5) + (0.77 km * 2) = 2.75 km + 1.54 km = 4.29 km

Keri walks approximately 4.29 kilometers in one week.

Answer: C

Step-by-step explanation:

Add like terms

    -1 + 6i

+   -4 + 2i

    -5 + 8i

Coordinates of the triangle ABC:

A(-2,2).

B(2,1)

C(-1,-2).

And the coordinates of the dilated triangle A'B'C':

A'(-4,4)

B'(4,2)

C'(-2,-4).

We can clearly see that each x and y-coordinate of triangle ABC is being multiplied by 2 to get the coordinates of triangle A'B'C'.

Therefore, triangle ABC is being dilated by a scale factor of 2.