A phone company charges for service according to the formula: C(n) = 19 + 0.08n , where n is the number of minutes talked , and C(n) is the monthly charge, in dollars .The rate of change in this equation is:The initial value in this equation is:
Answers
In a linear equation, the coefficient of the variable is the rate of change and the constant term is the initial value.
For example, a linear function with rate of change m and initial value b is:
[tex]f(x)=mx+b[/tex]In the given formula, the variable is n, its coefficient is 0.08 and the constant term is 19.
Since n is measured in minutes and C is measured in dollars (as well as the initial value), then, the coefficient 0.08 must have the units necessary for the minutes to cancel out, leaving dollars as the unit of 0.08n. Then, the units of the rate of change must be dollars per minute.
Since the constant term is 19, then the initial value is 19.
Therefore, the answers are:
The rate of change in the equation is 0.08 dollars per minute.
The initial value in the equation is 19 dollars.
Related Questions
members of the starting basketball team weigh 235,210,215,264,and 200 pounds. what is the average weight of starting team.
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Consider that the average of any discrete data is defined as,
[tex]\text{Average}=\frac{\text{ Sum of Observations}}{\text{ Number of Observations}}[/tex]Here the data is the weight (in pounds) of the starting basketball team members,
[tex]235,210,215,264,200[/tex]So the corresponding mean wieght of a team member is calculated as,
[tex]\begin{gathered} \text{Average}=\frac{235+210+215+264+200}{5} \\ \text{Average}=\frac{1124}{5} \\ \text{Average}=224.8 \end{gathered}[/tex]Thus, the average weight of starting team member is 224.8 pounds.
Given the graph of the function f(x), find x when f(x) =4
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x = -1
Explanations:Note:
f(x) is the vertical axis of the graph
x is the horizontal axis of the graph
To get the value of x when f(x) = 4:
Locate the point on the graph that is on the "4" on the vertical axis and trace it downwards to get the value of x.
If that is done, we would observe that x = -1 when f(x) = 4
a. Determine whether the function relating the year to the number of viewers is linear or nonlinear for each show. b. Which show has more viewers in its sixth year? Show A or Show B?
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Notice that:
1.- The number of viewers in millions of show A can be computed using the following expression
[tex]7(0.9)^t,[/tex]which is not a linear equation.
2.- The number of viewers of show B can be computed using the following expression:
[tex]5,000,000-(200,000t),[/tex]which is a linear expression.
Now, after 6 years, show A will have:
[tex]7(0.9)^6=3.72[/tex]millions of viewers and show B will have
[tex]5,000,000-200,000(6)=3,800,000[/tex]viewers.
Answer:
The function for Show A is nonlinear.
The function for Show B is linear.
Show B will have more viewers.
What is the range of the given function?{(-2, 0), (-4,-3), (2, -9), (0, 5), (-5, 7)}Ox|x=-5, -4, -2, 0, 2)O lyly = -9, -3, 0, 5, 7)Oxx-9, -5, -4, -3, -2, 0, 2, 5, 7)O lyly = -9, -5, -4, -3, -2, 0, 2, 5, 7)
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The range of the function is the values of y-coordinates of the ordered pairs
Since the function is
[tex]\lbrace(-2,0),(-4,-3),(2,-9),(0,5),(-5,7)\rbrace[/tex]Then the values of y-coordinates are
[tex]\lbrace0,-3,-9,5,7\rbrace[/tex]Then the range should be
[tex]\lbrace y:y=-9,-3,0,5,7\rbrace[/tex]The 3rd choice
What congruence rule does the triangle follow? Please write the congruence statement triangle EFH is congruent to ________?
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We can see here two triangles, and we can notice the following:
1. Since H is the midpoint of the segment EG, we can say that EH and HG are congruent segments.
2. Since these two triangles, namely, EFH and GFH share the same segment (HF), this side is also congruent to these two triangles.
3. Since EH is congruent to HG, and FH is congruent to itself, then EF is congruent to GF.
4. Angle E is congruent to angle G.
Therefore, we can say that:
Since we have that:
a. EF is congruent to GF
b. EH is congruent to GH
c. Angle E is congruent to angle G
We can conclude that the congruence rule, in this case, is SAS (Side-Angle-Side), because if two sides and the included angle are congruent to the corresponding parts of the other triangle, the triangles are congruent.
We also see that the three sides are congruent (and in this case, we can also conclude that the triangles are congruent by the rule SSS (side-side-side).
Likewise, we can also conclude that the triangle EFH is congruent to triangle GFH.
graph the line with the equation
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we have the equation
y=-(1/2)x+7
Remember that
To graph a line we need al lest two points
so
Find the intercepts
step 1
Find the y-intercept (value of y when the value of x is zero)
For x=0
y=-(1/2)(0)+7
y=7
y-intercept is (0,7)
step 2
Find the x-intercept (value of x when the value of y is zero)
For y=0
o=-(1/2)x+7
(1/2)x=7
x=14
x-intercept is (14,0)
step 3
Plot the intercepts and join them to graph the line
using a graphing tool
see the attached figure
please wait a secon to draw the line
Point A is located at (2, 6), and point M is located at (−1, 8). If point M is the midpoint of segment AB, find the location of point B. a(5, 4) b(0.5, 7) c(0, 6) d(−4, 10)
Answers
ANSWER:
d. (−4, 10)
STEP-BY-STEP EXPLANATION:
The midpoint has the following definition:
[tex]\left(x_m,y_m\right)=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)[/tex]We can calculate point B, using the following equations obtained taking into account the above:
[tex]\begin{gathered} x_m=\frac{x_1+x_2}{2} \\ \\ -1=\frac{2+x_2}{2} \\ \\ x_2+2=-2 \\ \\ x_2=-2-2=-4 \\ \\ \\ y_m=\frac{y_1+y_2}{2} \\ \\ 8=\frac{6+y_2}{2} \\ \\ y_2+6=16 \\ \\ y_2=16-6=10 \\ \\ \text{ Therefore, point B is located at \lparen-4, 10\rparen} \end{gathered}[/tex]The correct answer is: d. (−4, 10)
a) Form a suitable equation to show that x squared - 6x - 59 = 0b) Complete the square (x+p)squared-q= 0, and find the constants p and q.
Answers
Given:
There is a triangle given as
Required:
We want to find the sutiable form that show that
[tex]x^2+6x-59=0[/tex]and also complete the square
[tex](x+p)^2-q=0[/tex]and find the value of p and q
Explanation:
The area of triangle is
[tex]\begin{gathered} \frac{1}{2}(x+1)(x+5)=32 \\ \\ x^2+5x+x+5=64 \\ x^2+6x-59=0 \end{gathered}[/tex]hence proved for a
Now for second
[tex]\begin{gathered} x^2+6x+9-9-59=0 \\ (x+3)^2-68=0 \end{gathered}[/tex]now compare with
[tex](x+p)^2-q=0[/tex]we get
[tex]\begin{gathered} p=3 \\ q=68 \end{gathered}[/tex]Final answer:
p=3 and q=68
In a raffle where 8000 tickets are sold for $2 each, one prize of $4200 will be awarded. What is the expected value of a single ticket in the raffle?
Answers
It is given that 8000 tickets are sold for $2 each, one prize of $4200 will be awarded.
The expected value is determined as
[tex]\frac{1}{8000\times4198}+\frac{7999}{8000\times-2}[/tex][tex]\frac{1}{8000\times4198}-\frac{7999}{8000\times2}=\frac{1}{8000}(\frac{2-33,579,802}{4198\times2})[/tex][tex]\frac{1}{8000}(\frac{-3183600}{796})=\frac{-3183600}{6368000}=-0.499[/tex]The expected value of a single ticket in the raffle is -0.499 dollar.
hello I'm in the 7th grade and i need help with these word problems are you able to help and explain it to me so I can understand .. the title is called word Ratios
Answers
a) 12 goats ate 3 pizzas. To find goat per pizza, dividing the number of goats by the number of pizzas:
[tex]\frac{12\text{ goats}}{3\text{ pizzas}}=4\text{ }\frac{goat}{pizza}[/tex]b) 20 banks are robbed for a total of $50,000. To find the money per bank, divide the total money by the number of banks.
[tex]\frac{50,000}{20}=2500\text{ }\frac{\text{\$}}{bank}[/tex]c) In 86 years, 9 drops have formed. To find years per drop, divide the years by the number of drops.
[tex]\begin{gathered} \frac{86\text{ years}}{9\text{ drops}} \\ 9.6\text{ }\frac{years}{drop} \end{gathered}[/tex]d) 3 hippos eat 5 pumpkins
To find the number of pumpkins per hippo, divide 5 by 3.
[tex]\begin{gathered} \frac{5\text{ pumpkins}}{3\text{ hippos}}=1.7\text{ }\frac{pumpkins}{hippos} \\ \end{gathered}[/tex]Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end behavior to match the function with its graph.
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we have
f(x)=2x^4-4x^2
REmember that
The Leading Coefficient Test is the test which enables you to discover thebehavior of the graph in terms of rising and falling. This test utilizes the leading coefficientand whether the degree is odd or even to determine the behavior of the curves. The test goes as follows:
In this problem the leading coefficient is positive and even
sothe graph rises to the left and rises to the right.Use a calculator to help answer the question, Show that the point (6,1) is equidistant from points (9,0) and (3,0).The distance from (6,1) to (9,0) and the distance from (6,1) to (3,0) are both [ ] . Thus, (6,1) is equidistant from the two points.
Answers
First find the distance from (3,0) to (6,1)
We will use the distance formula
d = sqrt( (x2-x1)^2 + ( y2-y1)^2)
= sqrt( ( 6-3)^2 + ( 1-0)^2)
= sqrt( 3^2 + 1^2)
= sqrt( 9+1)
= sqrt(10)
Now we can find the distance between ( 6,1) and (9,0)
We will use the distance formula
d = sqrt( (x2-x1)^2 + ( y2-y1)^2)
= sqrt( ( 9-6)^2 + (0-1)^2)
= sqrt( 3^2+ (-1)^2)
= sqrt( 9+1)
= sqrt(10)
The distance is sqrt(10)
[tex]\sqrt[]{10}[/tex]what is 4/6 divided by 3/12 the qotient is..........
Answers
Answer:
2 2/3
Explanation:
If 4/6 is divided by 3/12, we write the mathematical expression as:
[tex]\frac{4}{6}\div\frac{3}{12}[/tex]To obtain the quotient, we follow the steps below:
Step 1: Change the division sign to multiplication and take the inverse of the fraction after the division sign.
[tex]\frac{4}{6}\times\frac{12}{3}[/tex]Step 2: Reduce the terms where possible.
[tex]\begin{gathered} =\frac{4}{1}\times\frac{2}{3} \\ =\frac{8}{3} \\ =2\frac{2}{3} \end{gathered}[/tex]The quotient is 2 2/3.
Savannah earned a score of 720 on Exam A that had a mean of 700 and a standarddeviation of 25. She is about to take Exam B that has a mean of 400 and a standarddeviation of 100. How well must Savannah score on Exam B in order to doequivalently well as she did on Exam A? Assume that scores on each exam arenormally distributed.
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Answer:
480
Explanation:
First, we need to standardize the score on Exam A. It can standardize as
[tex]z=\frac{\text{ score}-\text{ mean}}{\text{ standard deviation}}[/tex]Replacing score = 720, mean = 700, and standard deviation = 25, we get
[tex]z=\frac{720-700}{25}=\frac{20}{25}=0.8[/tex]Then, to do equivalently well on exam B, we need a standard value equal to 0.8. So, the score can be calculated as
[tex]\text{ score = z\lparen standard deviation\rparen + mean}[/tex]Replacing z = 0.8, standard deviation = 100 and mean = 400, we get
[tex]\begin{gathered} \text{ score = 0.8\lparen100\rparen+400} \\ \text{ score = 80 + 400} \\ \text{ score = 480} \end{gathered}[/tex]Therefore, the answer is 480
Where can I find L2 and L3 for a missing corresponding angles?
Answers
Answer:
Explanation:
Given:
<1=123.9°
<3=56.1°
Based on the given figure, the angles formed a straight line (Ex. <3 and <4). Angles on a straight line add up to 180°. So,
For <3 and <4:
We plug in what we know.
[tex]\begin{gathered} \angle3+\angle4=180 \\ 56.1+\angle4=180_{} \\ \text{Simplify and rearrange} \\ \angle4=180-56.1 \\ \angle4=123.9 \end{gathered}[/tex]For <2 and <1:
We plug in what we know.
[tex]\begin{gathered} \angle2+\angle1=180 \\ \angle2+123.9=180 \\ \angle2=180-123.9 \\ \angle2=56.1 \end{gathered}[/tex]Therefore, <2 = 56.1° while <4= 123.9°.
Josh bought a new scooter for $412. He plans to make equal payment of $42 each month until the scooter is paid in full. About how many payments will Josh make? 10 20 5 or 15
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Data:
T=Total price of the scooter: $412
M=Every month he pays: $42
t= number of payments
[tex]t=\frac{T}{M}[/tex][tex]t=\frac{412}{42}=9.8\approx10[/tex]The cost of custom-made cookies at a bakery is shown on the graph below, where x represents the number of cookies and y represents the total cost.
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The equation of a line is given by:
[tex]y=mx+b[/tex]where m is the slope and b is the y intercept. From the graph we notice that b=1. To find the slope we need to use the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Using the first two points on the graph (0,1) and (1,3) we have that the slope is:
[tex]m=\frac{3-1}{1-0}=\frac{2}{1}=2[/tex]Plugging the values in the first equation we have that the equationwe are looking for is:
[tex]y=2x+1[/tex]What formula do I use to get my answer? I’m getting 1/13, but my answer is incorrect. Thank you.
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We will have the following:
First, the probability of getting the first t-shirt white will be:
[tex]p_1=\frac{4}{9}[/tex]And the probability of getting the second t-shirt white will be:
[tex]p_2=\frac{3}{8}[/tex]Now, the probability of getting the two white t-shirts one after the other will be:
[tex]\begin{gathered} p_3=p_1\ast p_2\Rightarrow p_3=\frac{4}{9}\ast\frac{3}{8} \\ \\ \Rightarrow p_3=\frac{1}{6} \end{gathered}[/tex]So, the probability of getting the two white t-shirts one after the other is 1/6.
As smart phones have grown in popularity, regular cell phones have fallen out of favor. As a result, one electronics retailer estimates that 17% fewer regular cell phones will be sold every year. If the retailer sells 162,147 regular cell phones this year, how many will be sold 10 years from now?If necessary, round your answer to the nearest whole number.
Answers
Initially, the retailer sells 162,147 regular cell phones
The retailer stimates, that every year sales will fall a 17%
meaning that after one year, sales will be:
162,147 * (1-0.17) = 134582.01
then, after 2 years, sales will be:
134582.01 * (1-0.17) = 111703.0683
which is the same as
[tex]162147\mleft(1-0.17\mright)^2=111703.0683[/tex]in that way, we can create the following formula:
[tex]162147\cdot(1-0.17)^y[/tex]where y is time in years,
now, if we replace y = 10 we can obtain the solution we are looking for
[tex]162147\cdot(1-0.17)^{10}=25158.795[/tex]rounding to the nearest whole number: 25,159
Hello, please I need urgent help with this math question
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Given:
[tex]\sqrt[]{\frac{96}{8}}[/tex]Expand:
[tex]\sqrt[]{\frac{2^5\cdot3}{2^3}}[/tex]Simplify:
[tex]\sqrt[]{2^2\cdot3}[/tex][tex]=2\sqrt[]{3}[/tex]Therefore, the answer would be D. 2√3.
4. Find (1.1x + y)2.
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how many square inches, 1 in. by 1 in., fit in an area if 1 square foot, 1 ft by 1 ft?
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We have the following:
We must convert square feet to square inches
We have that 1 foot is equal to 12 inches
[tex]1ft^2\cdot\frac{(12in)^2}{(1ft)^2}=144in^2[/tex]Which means that one square foot equals 144 square inches.
Draw the dilation of ABC using center P and a scale factor of 1/3. Draw the dilation of ABC using center A and a scale factor of 2. Explain how they are similar. 3
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Both triangles are similar; while the first is a reduction, the second is an enlargement.
Let's begin by listing out the information given to us:
A(5,6), B(5,10), C(8,3)
A scale factor of 1 / 3 means the triangle will be smaller (reduction):
[tex]$$\begin{gathered}P=(2,3) \\A B=4 \Rightarrow A^{\prime} B^{\prime}=\frac{4}{3} \\B C=\sqrt{58} \Rightarrow B^{\prime} C^{\prime}=\frac{\sqrt{58}}{3} \\A C=\sqrt{18} \Rightarrow A^{\prime} C^{\prime}=\frac{\sqrt{18}}{3}=\sqrt{6}\end{gathered}$$[/tex]
A scale factor of 2 means the triangle will be bigger (enlargement):
[tex]$$\begin{gathered}A^{\prime \prime}=2 A=2(5,6)=(10,12) \\B^{\prime \prime}=2 B=2(5,10)=(10,20) \\C^{\prime \prime}=2 C=2(8,3)=(16,6)\end{gathered}$$[/tex]
Both triangles are similar; while the first is a reduction, the second is an enlargement
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What is the solution to the inequality below?1x1 < 5A. x < 5 or x>-5B. x>5 and x < -5C. x < 5 and x > -5D. x > 5 or x<-5
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The Solution is given by:
[tex]\lvert x\rvert<5[/tex]This means that:
[tex]-5So it follows that:[tex]x<5\text{ and x>-5}[/tex]Hence option C is correct.
in the following geometric sequence, find (i) the 7th term; (ii) the nth term:-1/3, 3/4, -9/8, .....
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Given the geometric sequence:
[tex]-\frac{1}{2},\frac{3}{4},\frac{-9}{8},\ldots.[/tex]The common ratio will be:
[tex]r=\frac{3}{4}\div-\frac{1}{2}=\frac{3}{4}\cdot-2=-\frac{3}{2}[/tex]The general rule of the geometric sequence will be:
[tex]a_n=a_1\cdot r^{n-1}[/tex]so, a7 will be:
[tex]a_7=-\frac{1}{2}\cdot(-\frac{3}{2})^{7-1}=-\frac{1}{2}\cdot(-\frac{3}{2})^6=-\frac{729}{128}[/tex]And an will be:
[tex]a_n=(-\frac{1}{2})\cdot(-\frac{3}{2})^{n-1}_{}[/tex]what 6 numbers equals 15 with out using save number twice
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On a hot day, Gabrielle poured 1/8 of a bucket of water into a plastic wading pool. A few minutes later she added another 1/2 of a bucket. How much water did Gabrielle pour into the pool?
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5/8 of a bucket of water
Explanation:Initial amount poured = 1/8 bucket of water
An addition of 1/2 bucket into the the pool
Total amount of water in the pool = 1/8 bucket of water + 1/2 bucket of water
[tex]\begin{gathered} \frac{1}{8}+\frac{1}{2},\text{ }LCM\text{ = 8} \\ \frac{1(1)\text{ +4(1)}}{8} \end{gathered}[/tex][tex]=\frac{1+4}{8}=\text{ 5/8}[/tex]Total water in the pool is 5/8 of a bucket of water
Explain how you determine if a function is linear or non-linear if you are given a graph
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A linear equation is used to represent a straight line in a graph, whereas non-linear equations are used to represent curves.
An equation is considered linear if it is in the form of y = mx+b where m is the slope of the equation and b is the y-intercept.
Notice how here, x can only be to the power of one. In here, the conditions are just simply m,b∈R.
Some examples include y = 5x+4, y = x−2, y = 0, and even some like
x = 1.
As you can see here, all of the following equations are represented using a straight line.
An equation is considered “non-linear” when it is not graphed using straight lines. Some examples include y = 3x2+1, y = 2x3−3, y = x5+43.
In conclusion, a linear equation will always be in the form of y = mx+b, where m is the slope of the equation, and b is the y-intercept of the equation.
Hence the answer is A linear equation is used to represent a straight line in a graph, whereas non-linear equations are used to represent curves.
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A caterer uses 4 pans of lasagna to serve 30 people. At this rate, how many pans of lasagna does the caterer use to serve 390 people?
A. 13
B. 52
C. 90
D. 98
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Complete the proof. Given: CM LAB 3= 4 Prove: AMC BMC Use the information provided to complete a two-column proof.
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Perpendicular Bisector Theorem:
In the shown figure, the line segment AB is bisected by line CM since it is given in the question.
[tex]CM\perp AB[/tex]Which simply means that the line CM bisected line AB at 90°.
So, that means we have two Right angled triangles, these are triangle AMC and BMC
This also means that the line CM is equal for both triangles since it is common to both.