You are going to order some of your favorite cookies. If you order two boxes it will cost you $14. If you place an order for eight boxes it will cost you $26. Write an equation that represents the cost of ordering your favorite cookies.
Step 1: Decide what information represents your two points.
Hint: The points are in the format (number of boxes of cookies, cost) as these are your two variables.
Point 1: Point 2:
Step 2: Use your two points to write an equation.
Which of the following statements best describes the relationship between a line and a point in a plane?
Marianna buys a snack combo for $2.50 if the sales tax rate is 8% what is the total price of the combo including tax
To find the total price of an item including sales tax, convert the tax rate to a decimal and multiply by the item's cost. The total cost for a $2.50 snack combo with an 8% tax is $2.70.
The question involves calculating the total price of an item including sales tax. To find the total cost including tax, we need to first figure out the amount of sales tax by converting the tax rate from a percent to a decimal. Then, we will multiply this decimal by the initial cost of the item to get the tax amount.
Here's a step-by-step explanation using the provided example:
Convert the sales tax rate from a percent to a decimal: 8% as a decimal is 0.08.Multiply the decimal tax rate by the cost of the item: 0.08 \\times $2.50 = $0.20.Add the tax to the initial cost to get the total price: $2.50 + $0.20 = $2.70.Therefore, the total price of the snack combo including an 8% sales tax is $2.70.
The weekly demand and supply functions for Sportsman 5 × 7 tents are given by
p = −0.1x^2 − x + 33
p = 0.1x^2 + 2x + 13
respectively, where p is measured in dollars and x is measured in units of a hundred. Find the equilibrium quantity. Find the equilibrium price.
To find the equilibrium quantity and price for tents, we equated the demand -0.1x² - x + 33 with the supply 0.1x² + 2x + 13, solved the equation, and found the equilibrium quantity to be 500 units and the equilibrium price to be $25.50.
To find the equilibrium quantity and price for the Sportsman 5 x 7 tents, we need to set the demand function equal to the supply function.
Demand function: p = -0.1x² - x + 33
Supply function: p = 0.1x² + 2x + 13
Setting them equal to each other:
-0.1x² - x + 33 = 0.1x² + 2x + 13
Now, combine like terms to solve for x:
-0.1x² - 0.1x² - x - 2x + 33 - 13 = 0
-0.2x² - 3x + 20 = 0
To find the equilibrium quantity x, we solve this quadratic equation.
By dividing the entire equation by -0.2 to simplify:
x² + 15x - 100 = 0
The factored form of the equation is (x + 20)(x - 5) = 0, this yields two solutions for x: x = -20 (which we dismiss as a negative quantity that does not make sense in this context) and x = 5. Therefore, the equilibrium quantity is 5 (in hundreds of units).
To find the equilibrium price, substitute x = 5 into either the demand or supply function:
p = -0.1(5)² - (5) + 33
p = -2.5 - 5 + 33
p = 25.5
So the equilibrium price is $25.50.
Need help! Please. It could be a integer or a decimal
If a polygon has eight sides then it is an octagon. True or False
Write an equation for the line through p that is parallel to l and perpendicular to l
if a 40-foot tree casts a 12-foot shadow,find the length of a shadow cast by a 23-foot tree
The length of the shadow cast by the 23 feet tree is 6.9 feet
What is Proportion?
The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
Given data ,
Let the height of the tree A = 40 feet
The height of the shadow of the tree A = 12 feet
Now ,
The height of the tree B = 23 feet
Let the height of the shadow of the tree B = x
So , the proportion equation is
height of the shadow of the tree A / height of the tree A = height of the shadow of the tree B / height of the tree B
And the proportion will be ,
12 / 40 = x / 23
Multiply by 23 on both sides , we get
x = ( 12 × 23 ) / 40
x = ( 3 × 23 ) / 10
x = 69 / 10
x = 6.9 feet
Therefore , the value of x is 6.9 feet
Hence , The length of the shadow cast by the 23 feet tree is 6.9 feet
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When the blue trapezoid is translated to the green one, the new coordinates of the point (0, 0) will be
A) (-6, -2).
B) (-2, -8).
C) (-8, -6).
D) (-6, -8).
Answer: The correct option is (D) (-6, -8).
Step-by-step explanation: we are given to find the new co-ordinates of the point (0, 0) when blue trapezoid is translated to the green one in the figure.
As shown in the given figure, to translate blue trapezoid to green one,
the x-coordinate of each vertex of blue trapezoid is decreased by 6 units,
and
the y-coordinate of each vertex of blue trapezoid is decreased by 8 units.
So, the new co-ordinates of the point (0 0) becomes
(0, 0) ⇒ (0-6, 0-8) = (-6, -8).
Therefore, the new co-ordinates of the point (0 0) are (-6, -8).
Thus, (D) is the correct option.
The sum of two numbers is 154. if four timesfour times the smaller number is subtracted from the larger number, the result is 14. find the two numbers.
Thirty-one books are arranged from left to right in order of increasing prices. The price of each book differs by $2 from that of each adjacent book. The price of the book at the extreme right is equal to the price of the middle book plus a book adjacent to the middle one. Give an expression for the cost of the $n$th book in terms of $n$
Students received these scores: 70, 75, 80, 90, 95, 95, and 100. the score of 95 is what?
I need math help. Look at the attachment. No multiple choice.
there are 4 quarters per year
if annual rate = 8%
quarterly rate would be 8%/4 = 2%
so the (1+r) beomes (1+0.02) = 1.02
Give an example of an open equation
A high-speed catamaran operates between city and city
b. the catamaran can make the 157-mile trip in about 2 1/2 hours. find the catamaran speed for this trip.
The clean up hitter on a baseball tean batted 1/3 of the runs the team scored. The hitter batted in 3 runs. Select the equation that represents the number of n of runs the team scored. Then solve the equation:
A.1/3n=3
B.n/3=1/3
C.3n=1/3
D.3n=9
Defined by two lines or rays diverging from a common point.
A) arc
B) angle
C) parallel lines
D) perpendicular lines
Defined as bounded by two distinct end points that contain every point on the line between its end points.
A) circle
B) line segment
C) parallel lines
D) perpendicular lines
Answer:
1. Angle
2. Line Segment
Step-by-step explanation:
Two lines or rays diverging from a common point defines an 'angle', which is a figure forming from two rays starting from the same end-point.
Now, a figure bounded by two distinct end points which contain every point on the line between its end points defines a 'line segment'.
Hence, the answer are: Angle and Line Segment respectively.
Prove that a triangle with sides n^2 1, n^2 - 1 and 2n (for n > 1) is a right triangle
mVUT =175, mVUJ=17x-3, and mJUT=17x+8. Find x
Final answer:
To find the value of x, the student needs to set up an equation based on the sum of angles in a triangle, which is given as 175 degrees. The algebraic expressions for the other angles are used to establish the equation, which is solved for x, resulting in x = 5.
Explanation:
The student is asking for help with a geometric problem where the sum of the measures of angles in a triangle is given along with two algebraic expressions for the other angles. The fact that the angles add up to 175 degrees helps us establish an equation: mVUT = mVUJ + mJUT. Substituting the given values, we get 175 = (17x-3) + (17x+8). Simplifying this, we get 175 = 34x + 5. Subtracting 5 from both sides, we get 170 = 34x. Dividing both sides by 34, we find that x = 170 / 34, which simplifies to x = 5. Therefore, the value of x is 5.
There are entrees available at a restaurant. from these, archie is to choose for his party. how many groups of entrees can he choose, assuming that the order of the entrees chosen does not matter?
Jeff Simmons sold 27 cars last month.This 36 fewer cars than he sold during the same time period one year ago
juan drives to work. Due to traffic, he averages 22 miles per hour. He returns home averaging 32 per hour. The total time is 22.5 hours. Write and solve an equation to find the time juan spends driving to work.
Alan drove 756 miles in 12 hours. at the same rate, how many miles would he drive in 8 hours?
Alan would drive 504 miles in 8 hours.
Explanation:To find out how many miles Alan would drive in 8 hours, we can set up a proportion using the information given. Since Alan drove 756 miles in 12 hours, we can write the proportion as:
12 hours / 756 miles = 8 hours / x miles.
To solve for x, we can cross-multiply and then divide:
12 * x = 8 * 756
x = (8 * 756) / 12
x = 504
Therefore, Alan would drive 504 miles in 8 hours.
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What is the answer for 7-2n=n-14
Which property is illustrated by the following equation?
- 10 + 8 = 8 + ( - 10 )
In a lottery, a 4 digit number from 0000 to 9999 is randomly selected. Find the probability that the number selected begins with a 3 and ends in a 2 or 0.
Since the choices is from 0000 to 9999, therefore there are a total of 10,000 possibilities.
The possibilities that the number begins with a 3 and ends in a 2 or 0 is:
possibilities = 1 * 10 * 10 * 1 + 1 * 10 * 10 * 1 = 200
Therefore the probability is:
P = 200 / 10,000 = 0.02 = 2%
So there is a 2% probability.
Final answer:
The probability that a randomly selected 4-digit number begins with a 3 and ends with a 2 or 0 is 0.0200 or 2%.
Explanation:
To find the probability that a randomly selected 4-digit number begins with a 3 and ends in a 2 or 0, we can use the rule of product for independent events. Since the first digit must be 3, there is one choice for the first digit. For the second and third digits, they can be any number from 0 to 9, so we have 10 choices for each. The last digit can be either 2 or 0, which provides 2 possibilities.
Thus, the total number of favorable outcomes is 1 (for the first digit) × 10 (for the second digit) × 10 (for the third digit) × 2 (for the last digit) = 200 favorable outcomes. The total number of possible 4-digit numbers is 10000 (ranging from 0000 to 9999).
So the probability is calculated as the number of favorable outcomes divided by the number of total possible outcomes: Probability = 200 / 10000 = 0.02. After rounding to four decimal places, as instructed, the probability is 0.0200 or 2%.
Mr. rancher wants to build a pen for his horse. he wants the pen to be 40 yards long and 50 yards wide. if the fencing comes in 5 foot pieces, how many pieces does mr. rancher need to buy?
There are 36 pieces need to buy by Mr. rancher.
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The length of pen for his horse = 40 yards
The width of pen for his horse = 50 yards
And, The fencing comes in 5 foot pieces,
Now,
The perimeter of the pen for his horse = 2 (50 + 40)
= 2 x 90
= 180 yards
Since, The fencing comes in 5 foot pieces,
Hence, Number of pieces to buy by Mr. rancher = 180 / 5
= 36
Thus, There are 36 pieces need to buy by Mr. rancher.
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2 times as many as 8 is 16
Answer:
or 16 is the result of doubling 8
Step-by-step explanation:
Kim estimates that the faucet in her kitchen drips at a rate of 1 drop every 2 seconds. Erik wants to know how many times the faucet drios in a week
The formula for the area of a triangle is a = 1 2 bh, in which b represents the length of the base and h represents the height. if a triangle has an area of 192 mm2 and the height is 16 mm, what is the measure of the base?