Hans cell phone plan cost $200 to start, then there is a $50 charge each month.a. what is the total cost ( start-up fee and monthly charge) to use the cell phone plan for one month? b. what is the total cost for x months?c. graph the cost of the cell phone plan over a. Of 2 years using months as a unit of time. Be sure to scale your access by labeling the grid line with some numbers.(pt2 to letter c) what are the labels for the axes of the graph (for x and y)d. is there a proportional relationship between time and the cost of the cell phone plan?Explain how you know!e. Tyler cell phone plan cost $350 to start then there is a $50 charge each month on the same grid as Hans plan in part C above graph the cost of Tyler cell phone plan over Of 2 yearslastly, describe how hans and Tyler's graphs are similar and how they are different..
Answers
We know that
• The cost is $200 to start and $50 per month. This can be expressed as follows.
[tex]C=200+50m[/tex](a) The cost for one month would be
[tex]C=200+50\cdot1=200+50=250[/tex](b) The cost for x months is
[tex]C=200+50x[/tex](c) To graph the equation, we use the month as a unit of time, the table values would be
m C
1 250
2 300
3 350
4 400
5 450
6 500
7 550
8 600
9 650
10 700
11 750
12 800
Now, we graph all of these points.
The x-axis label is Months, and the y-axis label is Cost.
(d) The given situation does not show a proportional relationship because a proportional relationship is modeled by the form y = kx, which we do not have in this case.
(e) If the initial fee is $350, the equation is
[tex]C=350+50m[/tex]Let's graph it.
The graphs are similar because they have the same slope but they are different because they have different y-intercepts.
Related Questions
At the end of the first half of a basketball game, UCONN and SCSU were tied. During the second half UCONN scored 48 points and SCSU scored twice as many points as they had in the first half. What was the final score of UCONN won by 2 points?
Answers
Okay, here we have this:
Let's take the endpoints of UCONN as x and those of SCSU as y. So:
x=y+2
And:
So the UCONN points of the first half are: x/3. And since they were tied SCSU had the same points at the first half.
And those UCONN points of the second half are 2x/3, and the SCSU points at the end were then x/3+48.
So, we obtain that:
y=x/3+48
x=(x/3+48)+2
x=x/3+50
x-x/3=50
2x/3=50
2x=150
x=75
And, replacing in y:
y=75/3+48=25+48=73
Finally we obtain that the final score was: UCONN 75: SCSU 73
Write (3-2i)^3 in simplest a + bi form.
Answers
SOLUTION
We want to write
[tex]\begin{gathered} \mleft(3-2i\mright)^3\text{ in simplest form } \\ a+bi \end{gathered}[/tex]This means we have to expand
[tex](3-2i)^3[/tex]Applying perfect cube formula, we have
[tex]\begin{gathered} \mleft(a-b\mright)^3=a^3-3a^2b+3ab^2-b^3 \\ \text{where } \\ a=3,\: \: b=2i \end{gathered}[/tex]We have
[tex]\begin{gathered} (a-b)^3=a^3-3a^2b+3ab^2-b^3 \\ \mleft(3-2i\mright)^3=3^3-(3\times3^2\times2i)+(3\times3\times(2i)^2)-(2i)^3_{} \\ =27-(27\times2i)+(9\times(2i)^2)-(2i)^3_{} \end{gathered}[/tex]This becomes
[tex]\begin{gathered} \text{note that i = }\sqrt[]{-1} \\ i^2=\sqrt[]{-1^2}=-1 \\ So\text{ we have } \\ =27-(27\times2i)+(9\times(2i)^2)-(2i)^3_{} \\ 27-54i+(9\times4i^2)-(8i^2\times i) \\ 27-54i+(9\times4\times-1)-(8\times-1\times i) \\ 27-54i-36+8i \\ -9-46i \end{gathered}[/tex]Hence the answer is
[tex]-9-46i[/tex]Given that f(x) = 9x2 - 180 = 0, find x. A) x = +2 V5 B) x = +3 v5 C) x = +5 V2 D) x=+5 v3
Answers
Given data:
The given function is f(x)=9x^2-180=0
The given expression can be written as,
[tex]\begin{gathered} 9x^2-180=0 \\ 9(x^2-20)=0 \\ (x^2-20)=0 \\ x=\pm2\sqrt[]{5} \end{gathered}[/tex]Thus, option (A) is correct.
If ABCDE is reflected over the x-axis and then translated 3units left, what are the new coordinates B?E..ADO A. (1, -2)O B. (7,-2)C. (4, -2)D. (-7,2)CBX
Answers
Recall that the rule of transformation for a point (x,y) reflected over the x-axis is:
[tex](x,y)\rightarrow(x,-y),[/tex]and the rule of transformation for a point translataled n units to the left is:
[tex](x,y)\rightarrow(x-n,y).[/tex]Therefore, point B(4,2) reflected over the x-axis:
[tex](4,2)\rightarrow(4,-2),[/tex]and then translated 3 units to the left has as image the following point:
[tex](4,-2)\rightarrow(4-3,-2)=(1,-2).[/tex]Answer:[tex]\begin{equation*} (1,-2). \end{equation*}[/tex]For which equation would x = 12 NOT be a solution?Options:X\1=12x\4=2x\3=4x\2=6
Answers
Given:
[tex]x=12[/tex]is given.
Required:
Which option is not appropriate.
Explanation:
Now we check all the option for this
[tex]\begin{gathered} \frac{x}{1}=12 \\ x=12 \end{gathered}[/tex]which is appropriate
[tex]\begin{gathered} \frac{x}{4}=2 \\ x=8 \end{gathered}[/tex]which is not appropriate
[tex]\begin{gathered} \frac{x}{3}=4 \\ x=12 \end{gathered}[/tex]which is appropriate
[tex]\begin{gathered} \frac{x}{2}=6 \\ x=12 \end{gathered}[/tex]which is appropriate
Final answer:
Solve in inequality 0.2 (30 + x). - 0.3 (30-x) >2
Answers
The inequality 0.2 (30 + x) - 0.3 (30 - x) >2 is solved to get x > 10
How to solve the inequalityThe given inequality is 0.2 (30 + x) - 0.3 (30 - x) >2
0.2 (30 + x) - 0.3 (30 - x) >2
expanding the parenthesis
6 + 0.2x - 9 + 0.3x > 2
collecting like terms
6 - 9 + 0.2x + 0.3x > 2
-3 + 0.5x > 2
0.5x > 2 + 3
0.5x > 5
dividing by the coefficient of x which is 0.5
x > 10
Learn more about inequality here:
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Convert the radian measure to degreemeasure. Then, calculate the arc length thatcorresponds to a circle with a 35-centimeterdiameter. Round your answer to the nearesttenth.
Answers
We will have the following:
First,:
[tex]\frac{4\pi}{15}=\frac{4\pi}{15}\ast\frac{180}{\pi}=48[/tex]Then, the arc length will be:
[tex]\begin{gathered} s=(\frac{15}{2})(\frac{4\pi}{15})\Rightarrow s=2\pi \\ \\ \Rightarrow s\approx6.3 \end{gathered}[/tex]So, the arc length is approximately 6.3 cm.
determine whether the graph of the given equations are parallel, perpendicular, or neither.y=2x+15y= -2x+3
Answers
1. When two lines have the same slope they are parallel.
2 . When the quotient of two lines is -1 they are perpendicular.
The slope of
y = 2x + 15 is 2
the slope of
y = -2x + 3 is -2
since -2/2 = -1 they are perpendicular :)
ine temperaturtemperature at midnight?-53Allie scores 4 points in the first round of a card game. In the next round, she loses 6 points. Then she scores 4more points. How many points does Allie have after three rounds?on
Answers
3
Allie scores 4 points in the first round of a card game. In the next round, she loses 6 points. Then she scores 4.
How many points does Allie have after three rounds?
First round: 4 points (positive)
Second round = lose 6 points (negative)
Third round = scores 4 (positive )
Add and subtract all the points
4-6+4 = 2
If points P and Q lie in the interior of ∠ABC, then overline{PQ} lies in the interior of ∠ABC.True or false?
Answers
PQ is just the line segment that connects the points P and Q, so if both point are in the interior of and angle, the line segment connecting them has to be also in the interior of this angle, so true.
an average bath use 35 liters if water,while a five minutes shower only uses 12.5 liters of water.how many milliliters are you saving if you take a five minutes shower instead of a bath
Answers
To find the saving of water you have to substract the average bath to the average shower
[tex]35-12.5=22.5[/tex]So you save 22.5 liters of water.
Now we have to convert the liters to mililiters, this can be done if we rememeber that a liter contains 1000 mililiters, then we multiply our result by 1000.
[tex]22.5(1000)=22500[/tex]Therefore we save 22500 mililiters of water.
17. What is the value of x in the rhombusbelow?AC(x+40)B3x"D
Answers
Remember that
In a rhombus, diagonals bisect each other at right angles (perpendicular)
so
that means
(x+40)+(3x) =90 degrees ---------> by complementary angles
solve for x
4x+40=90
4x=90-40
4x=50
x=12.5An experiment consists of spinning the spinner shown. All outcomes are equally likely. Find P(<7). Express your answer as a fraction in simplest forn
Answers
There are 8 total outcomes. Now, we need to find where P(<7).
This means the outcomes where the number is less than 7.
There are 6 numbers under the 7 = 1,2,3,4,5,6
The probability is given by the next formula:
[tex]P=\frac{\text{Number of favorable outcomes}}{\text{Total of possible outcomes}}[/tex]Where:
Number of favorable outcomes = 6
Total of possible outcomes = 8
Replacing these values:
[tex]P=\frac{6}{8}[/tex]Simplify the expression, divide both numbers by 2:
[tex]P=\frac{3}{4}[/tex]The correct answer is the second one.
How much do I need to increase a radius of a circle to increase it's area 10 times?
Answers
Given that
It is said that we have to find the amount by which the radius will be increased such that the area is increased by 10 times.
Explanation -
The formula for the area of the circle is given as
[tex]\begin{gathered} Area=\pi\times r^2 \\ \\ A=\pi r^2-----------(i) \\ \\ where\text{ r is the radius of the circle.} \end{gathered}[/tex]Now the new area is 10 times the previous one.
Let the new area be A' and the new radius be R.
Then,
[tex]\begin{gathered} A^{\prime}=\pi\times R^2 \\ \\ As\text{ A'=10}\times A \\ \\ Then\text{ substituting the value of A' we have} \\ \\ 10\times A=\pi\times R^2 \end{gathered}[/tex]Now again substituting the value of A we have
[tex]\begin{gathered} \pi\times R^2=10\times\pi\times r^2 \\ \\ R^2=10r^2 \\ \\ R=\sqrt{10}\times r \end{gathered}[/tex]Hence the new radius will be √10 times the initial radius such that the area gets increased by 10 times.
Final answer - Therefore the final answer is √10 times.
What is the slope of y= -4
Answers
Hello!
We have the equation of the line y = -4.
Let's put this equation in a cartesian plane:
Notice that this equation will be always constant. So, as we just have a straight line with no inclination, the slope is 0.
an 20. Dequan spent 44 minutes yesterday cleaning 3 bathrooms and the kitchen at home. He spent the same amount of time cleaning each place, and then 8 minutes putting all the supplies away after. Write an algebraic equation and then solve to find out how many minutes m he spent on each room.
Answers
Let:
b = minutes spent cleaning the 3 bathrooms
k = minutes spend cleaning the kitchen
He spent the same amount of time cleaning each place, therefore:
k = b
He spent 44 minutes in total, besides he spent 8 minutes putting all the supplies away after:
b + k + 8 = 44
since k = b = m:
m + m + 8 = 44
2m + 8 = 44
Solving for m:
2m = 44 - 8
2m = 36
m = 36/2
m = 18
Therefore, he spent 18 minutes in each room
In January, it snowed 36.45 inches. In December it snowed 19.7 inches. How many more inches did it snow in January than in December?
Answers
Determine the difference in height of snow.
[tex]\begin{gathered} h=36.45-19.7 \\ =16.75 \end{gathered}[/tex]Thus, 16.75 inches more snowed in
Which expression has a quotient of about 7? F 7:2 G 23 : 7 H 36 : 5 J 13:6 Type here to search O | a 3
Answers
The question simply means when you divide two numbers, the one that will result to 7
Hence;
36 ÷ 5 = 7.2
H is the correct option
Sandra has a bag of animal cookies. The bag contains the cookies below. What is the probability that Sandra chooses a bear cookie first, eats it, and thenselects a lion cookie?9 lions5 elephants 3 tigers9 Bears 18/5218/5181/65081/676
Answers
ANSWER:
The probability of choosing a bear first then a lion is 81/650
SOLUTION:
This is a permutation and probability problem
The total cookies are 26
The combination for the total cookies is 26 * (26-1) = 26*25
The permutation for choosing a bear then a lion is 9 * 9
The probability is the permutation of choosing the bear over the permutation in total combination for total cookies
[tex]\frac{9\times9}{26\times25}=\frac{81}{650}[/tex]put each improper fraction into a mixed number 50/9
Answers
Divide the numerator by the denominator:
50 divided by 9 = 5 with a reminder of 5
Write the whole number (5) , and use the remainder as a numerator and 9 as the numerator:
5 5/9
how to solve 2(q+4)=16how to solve 7j+2=12+5jhow to solve 12z=60-3z
Answers
Answer:
Given that to solve
a) 2(q+4)=16
we get,
[tex]\begin{gathered} 2\mleft(q+4\mright)=16 \\ 2q+8=16 \end{gathered}[/tex][tex]2q=16-8[/tex][tex]2q=8[/tex]Dividing 2 on both sides we get,
[tex]q=4[/tex]Answer is: q=4
b)7j+2=12+5j
we get,
[tex]7j+2=12+5j[/tex][tex]7j-5j=12-2[/tex][tex]2j=10[/tex]Dividing 2 on both sides, we get
[tex]j=10[/tex]c) 12z=60-3z
we get,
[tex]12z=60-3z[/tex][tex]12z+3z=60[/tex][tex]15z=60[/tex]Dividing 15 on both sides we get,
[tex]z=4[/tex]
I need help question
Answers
as x approaches 8, x approaches 8
it's just 8
Determine the point estimate of the population mean and margin of error for the confidence interval.
Lower bound is 17, upper bound is 29.
The point estimate of the population mean is
The margin of error for the confidence interval is
...
Answers
The point estimate of the population mean is 23 and the margin of error for the confidence interval is 6.
In the given question, we have to find the value of the point estimate of the population mean and the margin of error for the confidence interval.
From the given question,
Lower bound is 17.
Upper bound is 29.
So the point estimate of the population mean is
Point Estimate = (Lower Bond+Upper Bond)/2
Point Estimate = (17+29)/2
Point Estimate = 46/2
Point Estimate = 23
Now finding the margin of error for the confidence interval.
Margin of error = Upper Bound-Point Estimate
Margin of error = 29-23
Margin of error = 6
To learn more about Margin of error link is here
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4. Write an equation for a line that isperpendicular to y = -4.
Answers
The equation y = -4 is a horizontal line at the point -4 in the y-axis.
In order to find a perpendicular line to this equation, we can choose any vertical line in the form:
[tex]x=a[/tex]Where 'a' is any real constant.
So an equation for a line perpendicular to y = -4 would be:
[tex]x=2[/tex]Tyler has already taken 35 credit hours and plans on taking 15 hours per semester until he graduates. Does this describe a linear or exponential function?
Answers
Given:
Tyler has already taken 35 credit hours.
He plans on taking 15 hours per semester.
Let the number of semesters = x
So, the function that describes this will be:
[tex]y=15x+35[/tex]So, the function represents a line.
So, the answer will be a Linear function.
Sindy surveyed a group of students. The table represents the hours, h, they spent studying and their scores, s.What does the slope of the trend line equation s = 32.4h + 302.6 represent? For an increase of 1 h in study time the test score will increase by approximately 302.6.For an increase of 302.6 h in study time the test score will increase by approximately 1.For an increase of 32.4 h in study time the test score will increase by approximately 1.For an increase of 1 h in study time the test score will increase by approximately 32.4.
Answers
The slope of the trend line is 32.4, and it represents the change of s per 1 hour.
Then, as the slope is 32.4 it represents: For an increase of 1 h in study time the test score will increase by approximately 32.4
A=1/2(a+b)h solve for h can you please explain as well?
Answers
h = 2A/(a+b)
Explanation:
A=1/2(a+b)h
To solve for h, we will make h the subject of formula
The first thing we will do is bring the 1/2 to the other side of the equation:
[tex]\begin{gathered} A\text{ = }\frac{(a+b)h}{2}\text{ cross multiply} \\ 2A\text{ = (a+b)h} \end{gathered}[/tex]To make h stand alone, we would divide both sides by the values in the bracket:
[tex]\begin{gathered} \frac{2A}{(a+b)}\text{ = }\frac{(a+b)h}{(a+b)} \\ h\text{ = }\frac{2A}{a\text{ + b}} \end{gathered}[/tex]Therefore, h = 2A/(a+b)
What is eight times the square root of two square root of two
Answers
Given expression is
[tex]8\sqrt[]{2\sqrt[]{2}}[/tex]Now, solving it as:
[tex]8\sqrt[]{2\sqrt[]{2}}=8\cdot2^{\frac{3}{4}}[/tex]So,
[tex]8\cdot2^{\frac{3}{4}}[/tex]is the required solution.
The illumination provided by a car's headlight varies inversely as the square of the distance from the headlight. A car's headlight produces an illumination of 3.75 footcandles at a distance of 40 feet. What is the illumination when the distance is 50 feet?
Answers
The illumination should be represented by y, while the distance from the headlight should be represented by x, therefore the inverse relationship between both variables is shown as;
[tex]\begin{gathered} y=\frac{k}{x^2} \\ \text{When y=3.75, then x=40. Therefore;} \\ 3.75=\frac{k}{40^2} \\ 3.75=\frac{k}{1600} \\ 3.75\times1600=k \\ k=6000 \\ \text{Hence, when the distance (x) is 50 feet} \\ y=\frac{k}{x^2} \\ y=\frac{6000}{50^2} \\ y=\frac{6000}{2500} \\ y=2.4 \end{gathered}[/tex]The illumination at a distance of 50 feet is therefore 2.4 footcandles
.The balance on Mr. Finch's credit card is -$210. It is 3 times the balance on Mr. Nguyen's credit card. Find the quotient -210 ÷ 3 and explain what it means in this context.
Answers
Given: Balance of Finch's card is = -$210.
This is 3 times the balance on Mr. Nguyen's credit card.
To find: -210/3.
Explanation:
Let the balance on Mr. Nguyn's card be = x.
The balance of Mr. Finch's card is 3 times Mr. Nguyen's card.
Mathematically this can be expressed as:
[tex]-210=3x[/tex]Now, the value of x or "Mr. Nguyen's credit card balance" can be calculated as:
[tex]\begin{gathered} x=\frac{-210}{3} \\ x=-70 \end{gathered}[/tex]Therefore, the term -210/3 represents Mr. Nguyen's credit card balance and its value is -$70.
Final Answer: The term -210/3 represents Mr. Nguyen's credit card balance and its value is -$70.