The monthly service charge $S of mobile phone is the sum of two parts. One part is a constant and the other varies directly as the connection time t minutes. When the monthly service charge is $230, the connection time is 100 minutes. When the monthly service charge is $290, the connection time is 130 minutes.a) Express S in terms of t.b) Find the value of the connection time t when the monthly service charge$S is $330.
Answers
Since the monthly charge S is made from 2 parts,
A constant part, let it b
A part depends on a direct relationship between it and the time t
Then the form of S should be
[tex]S=mt+b[/tex]Where:
m is the rate of change
b is the constant amount
Since S = 230 at t = 100
Since S = 290 at t = 130
Substitute them in the equation above to make 2 equations of m, b and solve them
[tex]\begin{gathered} 230=100m+b\rightarrow(1) \\ 290=130m+b\rightarrow(2) \end{gathered}[/tex]Subtract equation(1) from equation (2) to eliminate b
[tex]\begin{gathered} (290-230)=(130m-100m)+(b-b) \\ 60=30m \end{gathered}[/tex]Divide both sides by 30 to find m
[tex]\begin{gathered} \frac{60}{30}=\frac{30m}{30} \\ 2=m \\ m=2 \end{gathered}[/tex]Substitute m in equation (1) by 2 to find b
[tex]\begin{gathered} 230=100(2)+b \\ 230=200+b \end{gathered}[/tex]Subtract both sides by 200
[tex]\begin{gathered} 230-200=200-200+b \\ 30=b \\ b=3 \end{gathered}[/tex]a) The equation of S is (substitute m by 2 and b by 30)
[tex]S=2t+30[/tex]b) Since the monthly fee is $330, then
S = 330
Substitute it in the equation to find t
[tex]330=2t+30[/tex]Subtract 30 from both sides
[tex]\begin{gathered} 330-30=2t+30-30 \\ 300=2t \end{gathered}[/tex]Divide both sides by 2 to find t
[tex]\begin{gathered} \frac{300}{2}=\frac{2t}{2} \\ 150=t \\ t=150 \end{gathered}[/tex]The value of the time is 150 minutes
Related Questions
Last month, Carl earned $4900 after working 152 hours. What does Brian make hourly? [Round your answer to the nearest cent.
Answers
We have the following:
To know the amount earned per hour, we must divide the total value of money by the total number of hours worked, like this
[tex]\frac{4900}{152}=32.24[/tex]Which means that per hour Carl earns $ 32.24
The cost (c), in dollars, charged by a car rental agency is calculated using the equation c = 12 +0.29m, where m represents the distancetraveled in miles.Calculate the distance traveled for the cost of $56. 37.
Answers
The distance taveled is 153 miles
Explanation:The cost function is given as:
c = 12 + 0.29m
Given cost of $56.37, the distance m is obtained from the following equation:
56.37 = 12 + 0.29m
0.29m = 56.37 - 12
0.29m = 44.37
m = 44.37/0.29
= 153
HELPPPPP ASAPPPP
What will it cost to carpet a rectangular floor measuring 27 feet by 15 feet if the carpet costs $19.05
per square yard?
...
Answers
If the carpet costs $19.05 per square yard, it would cost $857.25 to carpet a rectangular floor that is 27 feet by 15 feet.
How are calculations made per square yard?Multiplying the length by the breadth in feet and dividing by 9 yields the square yards (SQYDS). A square yard has a surface area of 9 square feet.Given: A floor rectangle with dimensions of 15 feet by 27 feet.
We need to determine the cost to carpet the floor if the carpet costs $19.05 per square yard.
Area of rectangular floor = 15 × 27
= 405 square feet
We know that,
1 square yard = 9 square feet
So,
405 square feet = 405/9 = 45 square yards
Cost to carpet 1 square yard = $19.05
Cost to carpet 45 square yards = 19.05 × 45
= $857.25
Therefore, Carpeting a rectangular floor measuring 27 feet by 15 feet costs $857.25 if the carpet costs $19.05 per square yard.
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Converting linear function formulas
Answers
A linear equation has the conventional form Ax+By=C. A slope-intercept form equation (y=mx+b) must have the x and y on the same side of the equal sign and the constant on the opposite side in order to be converted to standard form. To relocate terms, use inverse operations.
What is a formula for linear form?Linear equations come in three main types:
shape of a point-slope: y - y1 = m (x-x1)
typical form: Ax + By = c
Y = mx + b is the slope-intercept formula.
A linear equation with one variable is written in standard form as ax + b = 0, where a 0 and x is the variable. A linear equation with two variables is written as ax + by + c = 0, where the variables are a 0, b 0, x, and y.
A formula's initial sign is usually an equal sign (=).
To enter a formula, click the desired cell.Click in the formula bar to begin the formula with the function. ... or begin entering the formula into the cell.When the formula's arguments are full, press Enter to display the formula's output in the cell.To Learn more About linear equation, Refer:
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Using only a compass can you find points in a plane that are the same distance from points A and B
Answers
You can locate points on a plane (or more specifically, a line segment) that are equally spaced apart from points A and B using a compass.
How can you use a compass to make a locus of points that are equally spaced between A and B?
Draw a straight line AB=7 cm using a ruler.Draw an arc from A using a compass, and then draw another arc that intersects the first one at the point where it crosses AB.From A to the arc, draw a straight line, then extend it to M.Measure 5 cm with a ruler and write AC on the result.We have the required triangle by joining BC.From point C, draw an arc that cuts over AC and BC. From the point where it cuts across AC and BC, draw an arc that cuts across each other. Finally, draw a line that extends from point C to the junction of the two arcs.The same holds true for A as well as O, the intersection of the two lines.Draw a circle with O as the center. This circle will serve as our incircle. Next, draw a perpendicular from O to AB. This perpendicular will serve as the radius.AN is the set of points in our locus that are equally spaced from the lines AB and AC.We must create an incircle, which is a circle inside of a triangle. We can accomplish this by creating an angle bisector from two sides; the intersection point will serve as the incentre. The center of the required circle.
The location where two points are equally distant from one another is known as the angle bisector.
Therefore,
You can locate points on a plane (or more specifically, a line segment) that are equally spaced apart from points A and B using a compass.
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How to solve the equation: -2(x-2)+4=2x
Answers
Answer:
x = 2
Explanation:
Given the expression
-2(x-2)+4=2x
you are to find the value of x that will make the equation true
Open the bracket
-2x+4 + 4 = 2x
-2x + 8 = 2x
-2x - 2x = -8
-4x = -8
x = -8/-4
x = 2
Hence the solution to the equation is x = 2
The circle below has center A.The lenght of AB is in milliliters
Answers
ANSWER
[tex]AB=12\text{ }mm[/tex]EXPLANATION
We want to find the length of AB.
The length of AB represents the radius of the circle since it is the distance from the center of the circle to the circumference.
We are given that the diameter of the circle is 24 mm. The radius of a circle is half of its diameter, hence, the radius of the circle is:
[tex]\begin{gathered} r=\frac{24}{2} \\ r=12\text{ }mm \end{gathered}[/tex]Therefore, the length of AB is:
[tex]AB=12\text{ }mm[/tex]That is the solution.
A number line is drawn left to right with integers spaced 1 centimeter apart. An ant crawls onto the number line at +2. It then crawls 3.5 centimeters left, 4.8 centimeters right, and 7.9 centimeters left.
Answers
The ant is finally at a position -4.6 centimeters on the number line.
A number line is drawn left to right with integers spaced 1 centimeter apart.An ant crawls onto the number line at +2.This means the ant is at 2.0 on the number line.The ant then crawls 3.5 centimeters towards the left direction.This means the ant is at -1.5 on the number line now.The ant then crawls 4.8 centimeters towards the right direction.This means the ant is at 3.3 on the number line now.The ant then crawls 7.9 centimeters towards the left direction.This means the ant is at -4.6 on the number line now.To learn more about number line, visit :
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Describing Supplementary Angle Relationships
► Circle all the problems that show two labeled angles that are supplementary.
Then find the value of x for only the circled problems.
Answers
Additional Perspectives. A pair of supplementary angles are two angles whose sum measures 180°. A 110° angle and a 70° angle are two examples of supplementary angles
1) 4x+ 6 = 130
x= 31
2) 9x +36+45 =180
x=11
What is a supplementary angles ?Additional Perspectives. A pair of supplementary angles are two angles whose sum measures 180°. A 110° angle and a 70° angle are two examples of supplementary angles. Consider the following example: Here is a 180° straight line, let's call it Z.If a transversal cuts two parallel lines, the interior angles on the same side of the transversal are supplementary. If a transversal cuts two parallel lines, the exterior angles on the same side of the transversal are supplementary.
1) 4x+ 6 = 130
x= 31
2) 9x +36+45 =180
x=11
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Since the angles are supplementary, their measures add to 180°. In other words: 2x+(2x–2)=180. Solving this equation gives the value of x. In algebra, the letter "x" is frequently used to denote an unknown value. It is referred to as a "variable" or occasionally a "unknown." x is a variable in x + 2 = 7.
What exactly is supplemental angle?Two angles are said to be supplementary if their sums total 180 degrees. A linear pair's two angles, like angles 1 and 2 in the illustration below, are always supplementary. But two angles don't have to be close to one another to be supplementary. Since their measures sum up to 180 degrees, the numbers 3 and 4 in the following figure are supplementary.Complementary angles are two angles with a combined angle of 90 degrees, whereas supplementary angles have a combined angle of 180 degrees. Angles sum right angle, but supplementary and complementary angles don't have to be nearby (sharing a vertex and side, or close to each other).Two angles are said to be supplementary angles because they combine to generate a linear angle when their sum is 180 degrees. When two angles add up to 90 degrees, however, they are said to be complimentary angles and together they make a right angle.To know more about supplemental angle refer to:
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How does mentat health effect aninals
Answers
Mental health affects animals as it brings about anxiety, unfriendliness and depression
Whet is mental health?Our emotional, psychological, and social well-being are all parts of our mental health. It influences our thoughts, emotions, and behaviors. It also influences our ability to manage stress, interact with others, and engage in obsessive behaviors than those found in the wild.
Having a pet as company helps reduce your anxiety. enhancing one's confidence Pets don't judge you, are unconditionally loving, and make excellent listeners. This can boost your self-confidence, particularly if you experience loneliness or miscommunication. According to science, many non-human creatures experience psychological disorders. Although it is frequent in humans, at least one mental disorder appears to have spared all other animals:
When they are abused or when they are denied what they want or need, animals frequently exhibit signs of mental illness. Perhaps this explains why captive animals appear to engage in more obsessive activities than their wild counterparts.
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Which order pair represents point B in the graph (0, 2)(1, 0)(1, 2)(2, 1)
Answers
Notice that the point B is located two units away from the origin on the x-axis, and its one unit up fro the origin on the y-axis, thus, the point B is the ordered pair (2,1)
Hi, i need assistance with question 2! need to graph all equations! Precalculus homework!
Answers
The graphs of the equations have been obtained.
We are given some equations.
We will find some points for the equations.
And then, we will graph them.
a) y = 2 x + 5
x 0 1
y 5 7
b) 2 x + 3 y = 6
x 0 3
y 2 0
c) y - 4 = 3(x + 2)
y - 4 = 3 x + 6
y = 3 x + 10
x 0 1
y 10 13
d) 4(y - 5) = 2(x + 1)
4 y - 20 = 2 x + 2
4 y = 2 x + 22
x 1 3
y 6 7
e) y = x - 3
x - 2 6
y - 5 3
Therefore, we get that, the graphs of the equations have been obtained.
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The Wycoffs are planning their next family night. They always have dinner out somewhere and then do something fun together. There are 2 adults and 7 children in the family. Each family member is allowed 3 meal suggestions, and each child is allowed 4 activity suggestions. Assuming no family members choose the same thing, how many different family night possibilities are there?
Answers
Answer
756 possible family nights
Step-by-step explanation
There are 9 family members ( = 2 adults + 7 children)
Given that each family member is allowed 3 meal suggestions, then there are 9x3 = 27 meal suggestions.
Given that each child is allowed 4 activity suggestions, then there are 4x7 = 28 activity suggestions.
Each family night consists of 1 meal and 1 activity. Therefore, there are 27x28 = 756 possible family nights
sam is making bread dough. the recipe calls for 4/5 cups of flour and 7/8 teaspoons of salt. if sam wants to use 1 cup of flour how much salt is required to maintain the ratio
Answers
The amount of salt that is needed for 1 cup of flour is 1 3/32 cups of salt.
How much salt is needed?Ratio is used to compare two or more variables. It shows the relationship that exists between two or more numbers.
A fraction is a non-integer that is made up of a numerator and a denominator. An example of a fraction is 4/5.
In order to determine the salt that is needed for 1 cup of flour, divide the ratio of salt by the ratio of the cups of flour. Division is the operation that is used in maths to determine the quotient of two or more numbers.
7/8 ÷ 4/5
7/8 x 5/4 = 35 / 32 = 1 3/32 cups of salt
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Relative rates of growth, graphing calculator required. Not that difficult but some rules are needed. Ask me if you have any questions regarding the material. Thanks!
Answers
Given:-
[tex]f(x)=\sqrt[]{x},g(x)=\ln (x)[/tex]To find the required option, which is correct.
So we need to find the value when x tends to infinity. so to find the value we substitute infinity in place of x. so we get,
[tex]\begin{gathered} f(x)=\sqrt[]{x} \\ f(\infty)=\sqrt[]{\infty}=\infty \end{gathered}[/tex]Also we get,
[tex]g(x)=\ln (x)=\ln (\infty)=\infty[/tex]So the resulting value is infinity for both.
So the required option is The rate of growth cannot be determined.
Samuel was preparing for the triathlon. He did 3 activities every morning: Ran for 30 minutes, covering 4.5 miles. Swam for 20 minutes, covering 2/3 mi. biked for 45 min, covering 9 miles. What was Samuel's average speed during his morning training?
so nobody seems to know this answer so 20 points
Answers
Samuel's average speed was 0.26 kilometers per minute during his morning training.
What is Average speed?Average speed is defined as the ratio of the total distance traveled by a body to the total time taken for the body to reach its destination.
Given that Samuel was preparing for a triathlon. Every morning, he accomplished three things: I ran for 30 minutes and covered 4.5 miles. I swam for 20 minutes, covering around 2/3 miles. I biked for 45 minutes and 9 kilometers.
Here, we have the total distance traveled by Samuel = 4.5 + 2/3 + 9 = 14.17 kilometers
And the total time is taken by Samuel = 30 + 20 + 45 = 55 minutes
So, the average speed = distance / time
The average speed = 14.17/55
The average speed = 0.26 kilometers per minute
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We roll a pair of dice two times. Find the probability that a total of three is rolled each time.The probability that a total of three is rolled each time is ?
Answers
we have that
the favorable outcomes are
1 and 2 2 and 1
total outcomes=6*6=36
P(3 in one roll)=2/36=1/18
P(3 rolled 2 consecutive times)=(1/18)^2=0.0031
Write two angles coterminal to 5pi/7, one that’s positive and one that’s negative
Answers
As given by the question
There are given that the angle:
[tex]\frac{5\pi}{7}[/tex]Now,
To find a positive and negative coterminal angle, add and subtract 2pi to the given angle.
Then,
[tex]\begin{gathered} \frac{5\pi}{7}+2\pi=\frac{5\pi+14\pi}{7} \\ =\frac{19\pi}{7} \end{gathered}[/tex]And,
[tex]\begin{gathered} \frac{5\pi}{7}-2\pi=\frac{5\pi-14\pi}{7} \\ =\frac{-9\pi}{7} \end{gathered}[/tex]Hence, the positive and negative angles are shown below:
[tex]\frac{19\pi}{7}\text{ and -}\frac{9\pi}{7}[/tex]State the order and type of each transformation of the graph of the function f(X)=4(X+9)^2 as compared to the graph of the base function
Answers
Using translation concepts, the function f(x) was evaluated by comparing to the graph of a base function g(x) = x².
stretched vertically by a factor of fourShifted 9 units to the left.What exactly is a translation?In mathematics, a translation is the movement of a shape to the left or right and/or down or up. The translated shapes appear to be the same size as that of the original shape, and thus the shapes are congruent. They were simply shifted in one or even more directions. There's no change in shape because it is simply moved from one location to another.A translation is signified by a change with in function graph, based on operations in its definition including such multiplication or sum/subtraction.
The base function g(x) = x² in this problem was.Multiplied by 4, such that, stretched vertically by a factor of four.Shifted 9 units to the left.Thus, the resultant function is obtained as (X)=4(X+9)²
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Today, John ran 15 miles in 2 hours and 30 minutes. He wants to represent the relationship between the distance he ran, in miles, and the time, in hours, as proportional in order to examine his times at various distances. Write an equation that John can use to represent a proportional relationship between distance, d , in miles, and time, t , in hours.
Answers
Answer:
d = 6t
Step-by-step explanation:
Letting d = distance and t = time in hours
we have d = 15 miles
t = 2 hours 30 min = 2 1/2 hours = 5/2 hours
Average speed = 15 ÷ 5/2
= 15 x 2/5 = 6 mph
So the equation is
d = 6t
What is the answer and can you answer all 3 please
Answers
For the first question, the problem is about the comparison between a graph and a function given in this case for the height of a baseball after t seconds of two players A and B.
For the second question, the problem gives a graph for player A and a function for player B
For the third question we could ask for example if the two players reach the same height at the same time how much time takes both players to reach a certain height, the maximum height of player A is bigger than player B or less than.
What is the solution to the given inequality?½-½ x ²-1/O x₂ -1O xs-1O x ≥ 3O x≤ 3IntroSolve the inequality.1---X24Apply properties:AddMultiplySubtractDivideTo start over:ResetDone
Answers
Answer:
x ≤ 3
Explanation:
The given inequality is
[tex]\frac{1}{2}-\frac{1}{4}x\ge-\frac{1}{4}[/tex]To solve the inequality, we first need to subtract 1/2 from both sides
[tex]\begin{gathered} \frac{1}{2}-\frac{1}{4}x-\frac{1}{2}\ge-\frac{1}{4}-\frac{1}{2} \\ \\ -\frac{1}{4}x\ge-\frac{3}{4} \end{gathered}[/tex]Then, multiply both sides by -4. Since -4 is a negative number, the symbol of the inequality changes, so
[tex]\begin{gathered} (-4)(-\frac{1}{4}x)\leq(-4)(-\frac{3}{4}) \\ \\ x\leq3 \end{gathered}[/tex]Therefore, the answer is
x ≤ 3
a ski slope can be modelled by the equation of the tangent to the curve y=-0.12x^2+12 at the point where x=30
Answers
Answer:
y= -96
Step-by-step explanation:
y= -0.12x^2 +12
y= -0.12x 30^2+12
y= -96
I think the question isn't complete so I'm pretty sure I'm wrong but this is what I got :)
The velocity of a drone relative to the air is modeled by v = 13i + 3j. The drone encounters wind with velocity modeled by w = −7i − 2j. Which is the true velocity vector of the drone?
Answers
From the statement of the problem, we know that:
• the velocity of the drone relative to the air is:
[tex]v=13i+3j,[/tex]• the drone encounters wind with velocity:
[tex]w=-7i-2j\text{.}[/tex]The true velocity vector of the drone is given by the sum of the velocities:
[tex]v+w=(13i+3j)+(-7i-2j)=(13-7)i+(3-2)j=6i+j.[/tex]Answer: 6i + j
Which of the following could be an algebraic expression for the total cost of dinner, less a $5 coupon, divided by 6 people?
6x − 5
6x(5)
(x − 5) ÷ 6
5 − 6x
Answers
Answer:
6x - 5
Step-by-step explanation:
For the polynomial P(x) = 4x + 7x + 8 and c = 1, find P(c) by (a) direct substitution and (b) the remainder theorem
Answers
SOLUTIONS
For the polynomial P(x) = 4x^2 + 7x + 8 and c = 1
[tex]P(x)=4x^2+7x+8[/tex]where c = 1
(a) By direct substitution
[tex]\begin{gathered} P(c)=P(1) \\ P(x)=4x^2+7x+8 \\ P(1)=4(1)^2+7(1)+8=4+7+8=19 \\ P(1)=19 \end{gathered}[/tex](b) The Remainder Theorem states that when we divide a polynomial
P(x) by x - c the remainder R equals P(c)
[tex]4x^2+7x+8\div x-1[/tex]From the remainder theorem , the remainder = 19
Dontay has 1 5/8 cups of brown sugar .he needs 1/2 cups of brown sugar to make one batch of cookies. How may batches can dontay make ?
Answers
Answer:
3
Step-by-step explanation:
1 5/8 is 13/8, he needs 4/8 so 13/4=3R1 so 3
a fruit package company produced peaches last summer whose weights were normally distributed with the mean 14 ounces and standard deviation 0.4 ounce. among a sample of 1000 of those peaches about how many could be expected to have any weights of more than 12.6 ounces?round to the nearest whole number as needed
Answers
Let x be the random representing the weights of the peaches produced by the company. Since the weights are normally distributed and the population mean and standard deviation are known, we would apply the formula,
z = (x - mean)/standard deviation
From the information given,
mean = 14
standard deviation = 0.4
For the weights to be more than 12.6 ounce, the equation would be
[tex]z\text{ = }\frac{(12.6\text{ - 14)}}{0.4}[/tex]z = -3.5
Looking at the normal distribution table, the probability corresponding to the z score of - 3.5 is 0.00023
Since we want to determine propability for the weights greater than 12.6 ounce, the required probability would be
1 - 0.00023 = 0.99977
Given that the total number of peaches is 1000, the number of peaches expected to have weights more than 12.6 ounce is
0.99977 * 1000 = 999.77
Rounding to the nearest whole number, it becomes 1000
The number of peaches expected to have weights more than 12.6 ounce is approximately 1000
3. In a 2-dimensional object the label is always square units and notated as units^2 i.e. square inches or in^2. What is the name and notation of a 3-dimensional object?
Answers
When we have a 3-dimensional, then the units have to by to the third power because the dimensions multiply, for example, if each dimension is in meters, then
[tex]m\times m\times m=m^3[/tex]Hence, the name of a 3-dimensional object is cubic units, and the notation is units^3.In a state’s lottery, you can bet $1 by selecting three digits, each between 0 and 9 inclusive. If t he same three numbers Are drawn in the same order, you win and collect $400. How many different selections are possible
Answers
There are 1000 different selections possible.
There are 10 digits in total from 0 to 9.
It is required to make a three digit number using 10 digits, where repetition is allowed.
So, in the three digit number, the unit place has 10 possible choices, the tens place also has 10 choices, and the hundreds place has 10 possible choices.
So, the total number of different selections of three- digit numbers can be obtained by multiplying 10 by itself three times.
Total different selection possible = Total different choices to fill the units place ×Total different choices to fill the tens place × Total different choices to fill the hundreds place
Total different selection possible = 10×10×10
= 1000
As a result there are 1000 different selections possible.
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