Two types of transformations that can be used to transform f(x) to g(x) are horizontal and vertical stretching/shrinking.
What is transformation ?
A transformation is a function that changes the position, size, or shape of an object or a graph. In mathematics, transformations are often used to map a function from one coordinate space to another. There are several types of transformations, including translations, rotations, reflections, and scalings.
Part A: Two types of transformations that can be used to transform f(x) to g(x) are horizontal and vertical stretching/shrinking.
Part B:
Horizontal stretching/shrinking: k is the horizontal scale factor.
Vertical stretching/shrinking: k is the vertical scale factor.
Part C:
Horizontal stretching/shrinking: g(x) = f(kx)
Vertical stretching/shrinking: g(x) = kf(x)
Two types of transformations that can be used to transform f(x) to g(x) are horizontal and vertical stretching/shrinking.
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6. A family's income amount is $25,000. They budget out of their income:
Food: 20%
Shelter: 25%
Clothing: 15%
How much money is allotted for each of these items?
Food
Shelter
Clothing
Answer:
To find out how much money is allotted for each of these items, we can multiply the percentage of the income allocated to each item by the total income.
Food: 20% of $25,000 = $25,000 x 0.20 = $5000
Shelter: 25% of $25,000 = $25,000 x 0.25 = $6250
Clothing: 15% of $25,000 = $25,000 x 0.15 = $3750
So the family has $5000 for food, $6250 for shelter and $3750 for clothing.
Solve the system of equation using elimination.
7x−12y=−3−7x+12y=2
Multiple choice question.
cross out
A)
(−114,112)
cross out
B)
(−1,−13)
cross out
C)
infinitely many solutions
cross out
D)
no solution
The given system of equation has no solution.
What is elimination method?
The elimination method is a way to get rid of one of the variables in a system of linear equations by using multiplication or division of the variable coefficients along with addition or subtraction of the variables and their coefficients.
Substitution, elimination, and augmented matrices are the three approaches that are most frequently used to solve equation systems.
Consider, the given system of equations
7x - 12y = -3 ..(1)
-7x + 12y = 2 ..(2)
Adding equation (1) and (2).
7x - 12y = -3
+ -7x + 12y = 2
___________________
0 = -1
0 = -1 is false.
Hence, the given system of equation has no solution.
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(c) Suppose that L is a line tangent to the boundary of the golf green and parallel to the path of the ball. Let Q be the point where the line is tangent to the circle. Notice that there are two possible positions for Q. Find the possible x-coordinates of Q:
The value x-coordinates which is required is found out to be as Q = -19.41 and +19.41.
The given values are,
radius , r = 35 feet
speed of ball = 11 ft./sec
location of the cup = (0, 0)
starting location the ball = (-40. -50)
In order to find the possible x-coordinates of Q,
The coordinates of the rightmost edge of the golf course = (35, 0)
slope = m = ( y2 - y1)/ ( x2 - x1)
now , the equation for a circle is known as , (x - h)² + (y - k)² = r²
and the center of the course is given as , (h, k) = (0, 0)
Therefore the equation becomes (x - 0)² + (y - 0)² = x² + y² = 35²
equation of tangent , y = -3x/2
putting this value in the tangent = x² + ( -3x/2 )² = 35²
13x² /4 = 35²
x = √ ( 35² x 4 )/ 4 = 35²
x = 70/13√ 13 = 19.41
Therefore, the coordinates of Q are found out to be as -19.41 and +19.41
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The five-number summary for the number of years of experience for each teacher at Carlson High School is shown in the following table. Min 2
Q1 5
Median 8
Q3 11
Max 16
The five-number summary suggests that about 25% of Carlson High School teachers have fewer than how many years of experience?
Answer: 5
Step-by-step explanation:
We are looking for the number of years below the 25th percentile, which is given by the first quartile.
Since the first quartile is 5, we know that about 25% of Carlson High School teachers have fewer than 5 years of experience.
PLEASE HELP!!! The seventh grade teachers want to buy the principal a giant stuffed tiger for his office costing $50.00 However the store is having a 10% off sale. Tax is 6% . What is the total cost of the tiger? If we pay $60.00 how much change do we have left?
Answer:
i think 48.00
Step-by-step explanation:
10% of 50 is 5 while 6% of 50 is 3 so 50-5+3 is 48
The large rectangle below represents one whole.
What percent is represented by the shaded area?
%
Is 0 positive real number?
Zero is not a real number that is positive. Because it lies between positive and negative real numbers. Therefore, it is considered neither a positive nor negative real number.
Real numbers are founded on the idea of the number line: the positive numbers to the right of zero and the negative numbers to the left of zero. Any number that fits on this number line can be considered real.
All numbers that are either rational or irrational are also referred to as real numbers. A real number that is positive and bigger than zero is known as a positive real number. Any real number that is not a positive integer is either zero or negative. Therefore, 0 is neither positive nor negative.
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According to government data, 22 percent of children in the United States under the age of 6 years live in households with incomes that are classified at a particular income level. A simple random sample of 300 children in the United States under the age of 6 years was selected for a study of learning in early childhood. If the government data are correct, which of the following best approximates the probability that at least 27 percent of the children in the sample live in households that are classified at the particular income level
The best equation that approximates the probability that at least 27 percent of the children in the sample live in households that are classified at a particular income level is [tex]p(z > \frac{0.27-0.22}{\frac{\sqrt{0.22*0.78} }{300} })[/tex] .
What is Probability Sampling?Probability sampling is the process of selecting a sample from a population when the selection is based on the randomization principle, often known as chance or random selection. In general, probability sampling is more difficult, time-consuming, and expensive than non-probability sampling. However, since units from the population are chosen at random and the selection probability for each unit can be determined, accurate estimates can be generated and statistical conclusions about the population may be drawn.Given:
Probability of children who live in households with incomes that are classified at a particular income level,p = 22/100 = 0.22
Number of children in a simple random sample,n = 300
Probability of children who do not live in households with incomes that are classified at a particular income level, q = 1-p = 0.78
The probability of children in the sample living in households that are classified at a particular income level,p₁ = 27/100 = 0.27
Now, we know
[tex]p(z > \frac{p_{1} -p}{\frac{\sqrt{p.q} }{n} } )[/tex]
So,
[tex]p(z > \frac{0.27-0.22}{\frac{\sqrt{0.22*0.78} }{300} })[/tex]
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two hikers start at a ranger station and leave at the same time. one hiker heads due west at 3 miles/hour. the other hiker heads due north at 4 miles/hour. how far apart are the hikers after 2 hours of hiking?
The hikers will be 8 miles apart after 2 hours of hiking.
The formula used to calculate the distance apart is the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is the distance between the two hikers, and the other two sides are the distances each hiker has traveled in the two directions: 3 miles to the west, and 4 miles to the north. The formula is written as a^2 + b^2 = c^2, where a and b represent the side lengths, and c represents the hypotenuse. Plugging in the values, 3^2 + 4^2 = c^2, or 9 + 16 = c^2. Solving for c, c^2 = 25, so c = 5. Therefore, the distance between the two hikers is 5 miles after two hours of hiking.
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Hint: Find the value of x first, then substitute the answer into 2x - 24.
The measure of angle BFG is
The measure of the value of corresponding angle is found as : ∠BFG = 76.
Define the term corresponding angles?Corresponding angles refer to the angles on the similar corners of two lines, which are often parallel and are crossed with another line (referred to as the transversal). The angles created when a transversal intersects two parallel lines have been known as corresponding angles. Typical examples of equivalent angles include opening and closing a lunchbox, resolving a Rubik's cube, as well as endless parallel railroad tracks.For the given question:
Given values:
∠BCD = x + 26∠BFG = 2x - 24∠BCD = ∠BFG (Corresponding angles)
x + 26 = 2x - 24
2x - x = 26 + 24
x = 50
Then,
∠BFG = 2*50 - 24
∠BFG = 100 - 24
∠BFG = 76
Thus, the measure of the value of corresponding angle is found as : ∠BFG = 76.
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the complete question is-
Hint: Find the value of x first, then substitute the answer into 2x - 24.
The measure of angle BFG is ___.
∠BCD = x + 26
∠BFG = 2x - 24
1. the probability you'll see a falling star in the sky over the course of one hour is 0.44. what's the probability you'll see one over half an hour? (asked by citadel)
The probability you'll see one over half an hour is 0.26
The term probability in math is defined as the possibility of the outcome of any random event
Here we have given that the probability you'll see a falling star in the sky over the course of one hour is 0.44.
Then in an hour can be taken as two half hours so we can write the probability to see a falling star as
Then it can be written as,
=> (1-P)*(1-P) = 1 - 0.44
When we simplify this one then we get
=> (1 - P)² = 0.56
Here we need to value of p then it can be written as,
=> 1 - P = √0.56
Then the value of P is calculated as,
=> -P = 0.74 - 1
=> P = 0.26
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Georgina had total stock earnings of $395.50 and a real return of $275.80. The difference is (5 points) due to a sudden drop in the stock market investments due to taxes, inflation, and fees due to a payout to the stockholders due to property taxes and fees charged on gains
The difference between Georgina's total stock earnings and her real return is $119.70. he difference between Georgina's total stock earnings and her real return is $119.70.
What is the difference?
The term "difference" refers to the amount by which one quantity is greater or less than another.
The difference between Georgina's total stock earnings and her real return can be calculated as follows:
Difference = Total stock earnings - Real return
Difference = $395.50 - $275.80
Difference = $119.70
Hence, the difference between Georgina's total stock earnings and her real return is $119.70.
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Jeremy borrowed money from his dad for a car repair. The graph represents the amount
remaining that Jeremy owes his dad.
a. Write an equation to represent the situation.
b. What does the slope mean in the context of
the situation?
c. What does the y-intercept mean in the context
of the situation?
Therefore , the solution of the given problem of equation comes out to be the equation is: y = -700/9 * x + 700.
Explain the equation.Equation construction is the process of connecting two expressions with the equivalent sign. An equation is, for illustration, 7x - 5 = 40. By solving this equation, we can determine that the value of the variable x is 6.
Here,
Given :
Regarding the details provided:
The formula is: y = -700/9 * x + 700
B) The slope represents the amount owned's rate of change.
c) Y-intercept represents the sum borrowed from his father.
thus , the solution is given above
Therefore , the solution of the given problem of equation comes out to be the equation is: y = -700/9 * x + 700.
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(PLEASE HELP ASAP)
Solve the given system using your choice of either graphically or algebraically. Show and explain all work.
-4x + 9y = 14
12x - 10y = - 8
Answer:
w
Step-by-step explanation:
11. the data shows mean concentrations (mg/l) of pollutants in rainwater leaving either green or conventional roofs. which would be needed to calculate the total amount of a pollutant leaving the roof during and following a rainstorm
The data shows mean concentrations (mg/l) of pollutants in rainwater leaving either green or conventional roofs. Correct Option is: (D)The Total Volume of Rainfall is needed to calculate the total amount of a pollutant leaving the roof during and following a rainstorm.
Volume:
Precipitation intensity is the water depth (mm) recorded during a shower divided by the duration of the shower (hours).
Expresses water depth per hour in millimeters (mm/hour).
[tex]rainfall intensity = total amount of rainwater(mm)/ duration of the rainfall (hours)[/tex]
A volume is a measure of three-dimensional space. Often quantified numerically using SI units (such as cubic meters and liters) or using various imperial or US customary units (such as gallons, quarts, and cubic inches). The definition of length (cube) relates to volume. Container volume is generally understood to mean the capacity of the container. That is, the amount of liquid (gas or liquid) that the container can hold, not the amount of space that the container itself moves.
In ancient times, volume was measured using similarly shaped natural vessels and later standardized vessels. The volume of some simple 3D shapes can be easily calculated using arithmetic formulas. The volume of more complex shapes can be calculated using integral calculations if there is an equation that constrains the shape. Zero, one, and two dimensional objects have no volume. In four dimensions and above, a concept analogous to ordinary volumes is a hypervolume.
Volume of Rainfall:
The Average Rainfall = Depth x Radius x Radius x 3.14. The area at the top of the bucket (this is the area where rain is collected). Dividing the precipitation by this area will give you the precipitation.
Complete Question:
The data in the table show mean concentrations (mg/L)(mg/L) of pollutants in rainwater leaving either green or conventional roofs. Which of the following data would be needed to calculate the total amount of a pollutant leaving the roof during and following a rainstorm?
A) Distance from street level to roof
B) Duration of the rain event
C) Total number of plants on the roof
D) Total volume of rainfall
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Central High School plays Eastern High School in a basketball game. Eastern had double the score of Central
before Central scored a three-pointer as the game ended.
The variable, c, represents Central's score before the three-pointer. Express the total points scored in the game as a
variable expression. Check all that apply.
2c + c
3c + 3
2c +3
2c + c-3
2c-c+3
2c +c+ 3
Answer:
Step-by-step explanation:
The total points scored in the game is a sum of the points scored by both teams.Given that Eastern had double the score of Central before Central scored a three-pointer as the game ended, Eastern's score can be represented as 2c.So the total points scored in the game is:Central's score before the three-pointer + Eastern's score before the three-pointer + the points scored by Central in the last three-pointer.So the total points scored in the game can be represented as:c + 2c + 3 = 2c + 3So the correct answer is C) 2c +3
Is it possible to construct a triangle with 2cm 3cm 7cm justify your answer?
It is not possible to construct a triangle with 2cm, 3cm, and 7cm.
The sides measure 2 cm, 3 cm, and 7 cm in length.
Only when the third side is greater than the sum of any two sides can a triangle be drawn. This the condition.
Let's verify the rule now.
2 + 3 > 7 Not true
2 + 7 > 3 True
3 + 7 > 2 True
As 2 + 3 > 7 does not satisfy the condition.
Hence, it is not possible to construct a triangle having 2cm, 3cm, and 7cm in length.
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please solve for area and perimeter
The area of the shaded region is 36.53 cm^2 and the perimeter of the shaded region is 8π cm.
What is area and perimeter?
The area of a shape or figure is its area, whereas the perimeter of a shape is its outer boundary over a given distance. Area is measured in square units or unit2 while perimeter is measured in the same unit.
The circumference of a shape is known as its perimeter. The lengths of all four sides must be added in order to determine a rectangle's or square's perimeter.
Radius, r = 8 cm
Perimeter of a circle = 2πr
Perimeter of s quarter circle = 2πr/4 = 1/2πr
Perimeter of Shaded part = 1/2 * 2πr
= 1/2 × 2 × π × 8
= 8πcm.
Area of a circle = 2πr²
Area of quarter circle = 2πr²/4 = 1/2πr²
Area of a square = length ²
Area of Shaded part = Area of Quarter-circle - Area of Square
= 0.5π(8)² - 8²
= 0.5π(64) - 64
Area of Shaded part = 36.53 cm^2
Hence, the area of the shaded region is 36.53 cm^2 and the perimeter of the shaded region is 8π cm.
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8.04 Rotations Assignment
The angle of rotations are 90° , 180° and 270° counterclockwise
What is Rotation?The measure of the amount a figure is rotated about the center of rotation is called the angle of rotation. The angle of rotation is usually measured in degrees. We specify the degree measure and direction of a rotation.
90° clockwise rotation: (x,y) becomes (y,-x)
90° counterclockwise rotation: (x,y) becomes (-y,x)
180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)
270° clockwise rotation: (x,y) becomes (-y,x)
270° counterclockwise rotation: (x,y) becomes (y,-x)
Given data ,
Let the point be represented as A
Now , the value of A is
a)
Let the coordinates of the point be A = A ( 4 , 1 )
Now , the rotation angles are 90° , 180° and 270° counterclockwise
90° counterclockwise = A' ( -1 , 4 )
180° counterclockwise = A'' ( -4 , -1 )
270° counterclockwise = A''' ( 1 , -4 )
b)
Let the coordinates of the point be A = A ( 0 , -7 )
Now , the rotation angles are 90° , 180° and 270° counterclockwise
90° counterclockwise = A' ( 7 , 0 )
180° counterclockwise = A'' ( 0 , 7 )
270° counterclockwise = A''' ( -7 , 0 )
c)
Let the coordinates of the point be A = A ( -2 , 9 )
Now , the rotation angles are 90° , 180° and 270° counterclockwise
90° counterclockwise = A' ( -9 , -2 )
180° counterclockwise = A'' ( 2 , -9 )
270° counterclockwise = A''' ( 9 , 2 )
d)
Let the coordinates of the point be A = A ( -12 , -4 )
Now , the rotation angles are 90° , 180° and 270° counterclockwise
90° counterclockwise = A' ( 4 , -12 )
180° counterclockwise = A'' ( 12 , 4 )
270° counterclockwise = A''' ( -4 , 12 )
Hence , the rotation of coordinates are solved
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What is the volume of the composite solid? Use 3.14 for pie and round your answer to the nearest cm3. cylinder height is 2.5 radius : 3 inches, cone is height of 3 inches and radius of inches.
(A) 471 cm3
(B) 733 cm3
(c) 707 cm3
(D) 1099cm3
The volume of the composite solid, given the dimensions for the cylinder and cone, is D. 1, 099 cm ³
How to find the volume ?First, find the volume of the cone which can be found by the formula:
= π x radius ² x ( height / 3 )
Height = 3 inches
Radius = 3 inches
The volume is:
= π x radius ² x ( height / 3 )
= π x 3 ² x ( 2.5 / 3 )
= 28.27 inches ³
The volume of the cylinder is :
= π x radius ² x height
= π x 3² x 2. 5
= 70. 69 inch ³
The volume of the composite solid is:
= 28. 27 + 70. 69
= 98.96 inch³
In cm³, this is:
= 98. 96 x 16.3871
= 1, 099 cm ³
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(b) Using a scale of 2 cm to 1 unit on x-axis and 2 cm to 2 units on the y-axis, draw on a graph sheet two perpendicular axes Ox and Oy for -5≤x≤5 and -12 ≤ y ≤12
A graph will be drawn where a scale of 2 cm to 1 unit on x-axis and 2 cm to 2 units on the y-axis, draw on a graph sheet two perpendicular axes
What is called graph?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.
What are the 6 types of graphs?Types of Graphs and Charts
Statistical Graphs (bar graph, pie graph, line graph, etc.)
Exponential Graphs.
Logarithmic Graphs.
Trigonometric Graphs.
Frequency Distribution Graph.
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plss help me in time!!!
The correct statements are given below.
What are functions?Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given here: The graph of two functions plotting distance vs time of two Alberto and Bianca
1) Early in the race Alberto runs faster.
2) Alberto maintains a contain speed of 20 km/hr
3) Meanwhile Bianca's Speed is 8.33 km/hr
4) The first person to cross the finish line is Bianca.
Hence, Bianca reached the finished line before Alberto.
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consider an undirected graph with n vertices and m edges. what are the minimum and maximum number of connected components that the graph could have, respectively?
The maximum is N*(N-1)/2 and the minimum is N-1 if there are N vertices.
Proof:
Consider an adjacency matrix where each entry is either 1 (to denote the presence of an edge) or 0 (to indicate the absence of an edge) (to indicate the absence of an edge). Each row of the upper triangle must have at least one "1" in order for a graph to be connected.
By merely placing one 1 in each row of the upper triangle, the minimum is reached. Now, if the adjacency matrix is N by N, the first row will have N-1 elements in the upper triangle, the second row will have N-2 elements, the third row will have N, the fourth row will have N, and so on until the last row will have 0 items. Consequently, there are N total rows "with an upper triangle", each with only one 1. Hence, the number of edges in N-1.
The maximum occurs if every element of the upper triangle has one. Now, the number of elements in the upper triangle of the whole matrix is
1 + 2 + ... + (N-2) + (N-1) = N*(N-1)/2.
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A race is made up of 4 separate stages. Round each stage’s distance to the nearest thousand|:
Stage Name Distance Rounded Distance
Le Start 30,060 m m
The Uphill 21,111 m m
The Downhill 33,501 m m
Le Finish 49,840 m m
According to the round off rule, the resulting value of the total distance is 135,000
As we al know that if the rounded number increases then the given number is said to be rounded up on the other hand if the rounded number decreases then it is said to be rounded down.
Here we have given the details about the race is made up of 4 separate stages.
Now, we need to find the total distance, that can be calculated by adding all the given distance, then we get,
=> 30,060 + 21,111 + 33,501 + 49,840
=> 134512.
Now, we have to round off the value to the nearest thousandth term, then it can be written as,
Here we need rounded to the nearest thousands place. The 4 in the thousands place rounds up to 5 because the digit to the right in the hundreds place is 5.
=> 135,000
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a small bag of 10 identical apples weighs n ounces, and a large bag of n of these apples weighs less than 40 ounces, where n is an integer. in ounces, what is the greatest possible weight of the large bag? express your answer as a mixed number.
The greatest possible weight of the large bag is 1.9n ounces.
How do you get a mixed number?Divide the numerator by the denominator of an improper fraction to get a mixed number. The mixed number is represented by the answer's whole number, and the fractional portion of the mixed number is represented by the answer's remaining fractional component. No change is made to the denominator.Given:
Weight of 10 apples = n ounces
Weight of 1 apple = n/10 ounces
Weight of n apples = n²/10 ounces
It is given that a large bag of n of these apples weighs less than 40 ounces,
= n²/10 < 40
= n²< 400
= n < 20
So, the large bag contains at most 19 apples.
Hence, the weight of the large bag is at most 1.9n ounces, or (19/10)(n) ounces.
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IF THE PROBABILITY OF WINNING IS 0.3 THEN WHAT IS THE PROBABILTY OF NOT LOSE?
Answer:
0.7
Step-by-step explanation:
if we set the total race of win and lose is 1
then we use 1-0.3=0.7
If x is 300 then what is the answer to this equation, 3x plus 10 minus 17x
Answer:
-4190
Step-by-step explanation:
910-5100
Which of these formulas describes the sequence 4, 5, 6, 7,...? (1) 22 n an =+ (3) 3 n an =+(2) 2 21 n ann =++ (4) 31 n an =+
The formula describes the sequence will be aₙ = n + 3. Then the correct option is 3.
What is an arithmetic sequence?A series of integers called an arithmetic succession or arithmetic chain of events has a fixed difference between the terms.
Let a₁ be the first term and d be a common difference.
Then the nth term of the arithmetic sequence is given as,
aₙ = a₁ + (n - 1)d
The sequence is given below.
4, 5, 6, 7, ....
The first term is 4 and the common difference is given as,
d = 5 - 4
d = 1
Then the formula is given as,
aₙ = 4 + (n - 1) × 1
aₙ = 4 + n - 1
aₙ = n + 3
The formula describes the sequence will be aₙ = n + 3. Then the correct option is 3.
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you are choosing between two different cell phone plans. the first plan charges a rate of 23 cents per minute. the second plan charges a monthly fee of $34.95 plus 12 cents per minute. how many minutes would you have to use in a month in order for the second plan to be preferable? give the exact number of minutes (do not approximate).
In order for the second plan to be preferable, a greater amount of 249.6 minutes would have to be used in one month.
Let
x -----> the number of minutes in a month
y ----> the charge monthly
we know that
First Plan
y= 0.23 x ----> equation A
Second Plan
y= 0.12x+34.95 ----> equation B
Equate the equations A and B and solve for x
so x= 249.6
For x< 249.6 ----> is preferable the first plan
For x> 249.6 ----> is preferable the second plan
therefore
In order for the second plan to be preferable, a greater amount of 249.6 minutes would have to be used in one month.
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Grace is making cookies. She has 6 tablespoons of baking soda left in the container. If she uses 2 teaspoons of baking soda for her recipe, how many teaspoons of barking soda will be left??
Answer: 16 Teaspoons
Hope this helps! :)
Step-by-step explanation:
1 Tablespoon= 3 Teaspoons
6 Tablespoons= (6*3) 18 Teaspoons
18 - 2= 16 tsp
