Which of the following are solutions to the inequality below? Select all that apply.
Answers
Step-by-step explanation:
1.12+8×10<66
12+80<66
92<66
2.12+8×3<66
12+24<66
36<66
3.12+8×8<66
12+64<66
76<66
4.12+8×4<66
12+32<66
44<66
therfore the answer is 2 and 4
Related Questions
y=-5x+6y=-3x-2x=y= and the grap
Answers
y = -5x + 6 .................1
y = -3x - 2......................1
first equate the two equations to find x and y
-5x + 6 = -3x - 2
-5x +3x = -2 - 6
-2x = -8
x = -8/-2
x = 4
Next substitute x in equation 1
y = 5(4) + 6
y = 20 + 6
y = 26
Graphically,
y = -5x + 6
for x = 0
y = -5 x 0 + 6
y = 6
for y = 0
0 = -5x + 6
5x = 6
x = 6/5
x = 1.2
fiirst plot the coordinate (0,6) and (1.2,0) on the graph for the first equation to get the first straight line.
y = -3x - 2
x = 0
y = -3 x 0 - 2
y = -2
y = 0
0 = -3x - 2
3x = -2
x = -2/3
x = -0.67
plot the coordinate on the graph
solution for this question is (4,26)
A linear equation written in the form y = mx + b is in ?
Answers
A linear equation is written in the form
[tex]y=mx+b[/tex]it is the Slope-intercept form
explain why 4 x 3/5=12x 1/5
Answers
Answer:
They equal because when you simplify each side, you will arrive at the same answer.
[tex]\begin{gathered} 4\times\frac{3}{5}=\frac{4\times3}{5} \\ =\frac{12}{5} \end{gathered}[/tex]also;
[tex]\begin{gathered} 12\times\frac{1}{5}=\frac{12\times1}{5} \\ =\frac{12}{5} \end{gathered}[/tex]Explanation:
We want to explain why;
[tex]4\times\frac{3}{5}=12\times\frac{1}{5}[/tex]They equal because when you simplify each side, you will arrive at the same answer.
[tex]\begin{gathered} 4\times\frac{3}{5}=\frac{4\times3}{5} \\ =\frac{12}{5} \end{gathered}[/tex]also;
[tex]\begin{gathered} 12\times\frac{1}{5}=\frac{12\times1}{5} \\ =\frac{12}{5} \end{gathered}[/tex]So, they give the same answer when simplified.
Also you can derive one from the other;
[tex]\begin{gathered} 4\times\frac{3}{5}=12\times\frac{1}{5} \\ 4\times3\times\frac{1}{5}=12\times\frac{1}{5} \\ 12\times\frac{1}{5}=12\times\frac{1}{5} \\ \frac{12}{5}=\frac{12}{5} \end{gathered}[/tex]Therefore, both sides are equal.
a lampshade has a radius of 9in what is the circumference of the top of the shade use 3.4 to approximate Pi round your answer to the nearest whole number
Answers
The top of the lampshade is circular in shape
[tex]\begin{gathered} \text{The circumference of a circle = 2}\pi r \\ \text{where }\pi=3.14,\text{ r= radius of the circle} \\ \text{The radius , r=9 in} \\ \text{Circumference = 2 x 3.14 x }9 \\ \text{Circumference = }56.52\text{ in} \end{gathered}[/tex]The circumference of the top of the shade is 56.52 inches
2. (02.01 LC)While researching the industry she is interested in, Charlize sees that the average employment rate is 97.3%. How many people, out of every 250, are employed? (1point)24.33O 234.66Ο Ο243.25O 256.93
Answers
EXPLANATION
We can compute the average by multiplying the average by 0.973, as shown follows:
[tex]\text{Amount of people}=250\cdot0.973=243.25[/tex]In conclusion, the amount of people is equal to 243.25
If Nintendo had sold 12.2 million games in March and they had thought that they had sold 20.9 million how off was there percent error?
Answers
First let's calculate the absolute error by subtracting both values:
[tex]20.9-12.2=8.7[/tex]So the absolute error is 8.7 millions.
Now, in order to find the percent error, we just need to divide the absolute error by the number of games sold:
[tex]\frac{8.7}{12.2}=0.7131=71.31\text{\%}[/tex]So the percent error is 71.31%.
9Use the expression 43 + 8 – to find an example of each kind of expression.уKind of expression ExampleQuotientу9SumyVariable43 + 8Stuck? Review related articles/videos or use a hint.Repc
Answers
A quotient is a division between two terms. In this expression, and example of a quotient is "9/y".
An example of a sum from this expression is"4^3+8".
NOTE: A substraction can be also expressed as a sum by changing the sign of the second term.
In this case, the only variable is "y" which can take different values.
Answer:
Quotient: 9/y
Sum: 4^3+8
Variable: y
10. A city has a population of 125,500 in the year 1989. In the year 2007, its population is 109, 185. A. Find the continuous growth/decay rate for this city. Be sure to show all your work.B. If the growth/decay rate continues, find the population of the city in the year 2021.C. In what year will the population of the city reach 97,890? Be sure to show all your work.
Answers
SOLUTION
A.
To solve this question, we will use the compound interest formula.
Which is:
[tex]\begin{gathered} A=P(1-\frac{r}{100})^{nt} \\ Since\text{ we are dealing with a yearly statistics, n = 1} \end{gathered}[/tex][tex]\begin{gathered} \text{From 1989 to 2007, there is a year difference of 18 years} \\ t=18 \\ A=109,185 \\ P=125,500 \\ We\text{ are looking for the continuous growth rate (r)} \\ \text{Now, we will substitute all these given parameters into the formula } \\ \text{above.} \end{gathered}[/tex][tex]\begin{gathered} 109,185=\text{ 125,500(1-}\frac{r}{100})^{18} \\ \frac{195185}{125500}=\frac{125500}{125500}(1-\frac{r}{100})^{18} \\ 0.87=(1-\frac{r}{100})^{18} \\ \text{take the natural logarithm of both sides:} \\ \ln 0.87=18\ln (1-\frac{r}{100}) \\ -0.1393=18\ln (1-\frac{r}{100}) \\ \frac{-0.1393}{18}=\ln (1-\frac{r}{100})_{}_{}_{}_{}_{} \\ -0.007737=\ln (1-\frac{r}{100}) \\ \end{gathered}[/tex][tex]\begin{gathered} e^{-0.007737}=(1-\frac{r}{100}) \\ 0.9922=1-\frac{r}{100} \\ \frac{r}{100}=1-0.9922 \\ \frac{r}{100}=0.007707 \\ r=100\times0.007707 \\ r=0.771\text{ \%} \end{gathered}[/tex]The continuous decay rate is 0.771%
B.
Using the same formula:
[tex]\begin{gathered} A=P(1-\frac{r}{100})^{nt} \\ t=2021-2007=14 \\ P=109,185 \\ n=1 \\ A=\text{?} \\ r=0.771 \\ \text{Substitute all the parameters into the formula above:} \end{gathered}[/tex][tex]\begin{gathered} A=P(1-\frac{r}{100})^{nt} \\ A=109,185(1-\frac{0.771}{100})^{1\times14} \\ A=109,185\times0.89730607 \\ A=97,972.36 \\ A=97,972\text{ (to the nearest person)} \end{gathered}[/tex]The population of the city in the year 2021 is 97,972.
C.
We will use the same formula:
[tex]\begin{gathered} A=P(1-\frac{r}{100})^{nt} \\ A=97,890 \\ P=125,500 \\ r=0.771 \\ t=\text{?} \\ \text{Substitute all these parameters into the formula above:} \\ \end{gathered}[/tex][tex]\begin{gathered} 97890=125,500(1-\frac{0.771}{100})^t^{} \\ \frac{97890}{125500}=\frac{125500}{125500}(0.99229)^t \\ 0.78=0.99229^t \\ \ln 0.78=t\ln 0.99229 \\ -\frac{0.2485}{\ln 0.99229}=t \\ t=32.101 \\ SO\text{ the year that the population will reach 97,890 will be:} \\ 1989+32.101=2021.101 \\ \text{Which is approximately year 2021.} \end{gathered}[/tex]5. The number of hours spent in an airplane on a single flight is recordedon a dot plot. The mean is 5 hours. The median is 4 hours. The IQR is 3hours. The value 26 hours is an outlier that should not have been includedin the data. When 26 is removed from the data set, calculate the following(some values may not be used):*H0 2 4 6 8 10 12 14 16 18 20 22 24 26 28number of hours spent in an airplane1.4 hours1.5 hours3 hours3.5 hoursWhat is themean?OWhat is themedian?оOOWhat is the IQR?OOOO
Answers
Solution
Since the outlier that is 26 has been removed
We will work with the remaining
Where X denotes the number of hours, and f represent the frequency corresponding to eaxh hours
We find the mean
The mean (X bar) is given by
[tex]\begin{gathered} mean=\frac{\Sigma fx}{\Sigma f} \\ mean=\frac{1(2)+2(2)+3(3)+4(3)+5(2)+6(2)}{2+2+3+3+2+2} \\ mean=\frac{2+4+9+12+10+12}{2+2+3+3+2+2} \\ mean=\frac{49}{14} \\ mean=\frac{7}{2} \\ mean=3.5 \end{gathered}[/tex]We now find the median
Median is the middle number
Since the total frequency is 14
The median will be on the 7th and 8th term in ascending order
[tex]\begin{gathered} median=\frac{7th+8th}{2} \\ median=\frac{3+4}{2} \\ median=\frac{7}{2} \\ median=3.5 \end{gathered}[/tex]Lastly, we will find the interquartile range
The formula is given by
[tex]IQR=Q_3-Q_1[/tex]Where
[tex]\begin{gathered} Q_3=\frac{3}{4}(n+1)th\text{ term} \\ Q_1=\frac{1}{4}(n+1)th\text{ term} \end{gathered}[/tex]We calculate for Q1 and Q3
[tex]\begin{gathered} Q_1=\frac{1}{4}(n+1)th\text{ term} \\ \text{n is the total frequency} \\ n=14 \\ Q_1=\frac{1}{4}(14+1)th\text{ term} \\ Q_1=\frac{1}{4}(15)th\text{ term} \\ Q_1=3.75th\text{ term} \\ Q_1\text{ falls betwe}en\text{ the frequency 3 and 4 in ascending order} \\ \text{From the table above} \\ Q_1=2 \end{gathered}[/tex][tex]\begin{gathered} Q_3=\frac{3}{4}(n+1)th\text{ term} \\ Q_3=\frac{3}{4}(14+1)th\text{ term} \\ Q_3=\frac{3}{4}(15)th\text{ term} \\ Q_3=11.25th\text{ term} \\ \text{From the table above} \\ Q_3=5 \end{gathered}[/tex]Therefore, the IQR is
[tex]\begin{gathered} IQR=Q_3-Q_1 \\ IQR=5-2 \\ IQR=3 \end{gathered}[/tex]Which of the following logarithmic expressions have been evaluated correctly?
Answers
Given:
Logarithmic expressions in options.
Required:
Select correct calculated option.
Explanation:
1). ln 1 = 0
2).
[tex]log_29=3.1699250014[/tex]3)
[tex]log\frac{1}{100}=-2_[/tex]4).
[tex]log_3(-1)=NaN[/tex]5).
[tex]log_5\text{ }\frac{1}{125}=-3[/tex]Answer:
Hence, option A and E are correct.
when you do the graph part can you write on my picture, please?
Answers
Given that y = x + 3
Find the value of y when x = 1, 2, 3, 4, 5, and 6
For x = 1
y = 1 + 3
y = 4
For x = 2
y = 2 + 3
y = 5
For x = 3
y = 3 + 3
y = 6
For x = 4
y = 4 + 3
y = 7
For x = 5
y = 5 + 3
y = 8
For x = 6
y = 6 + 3
y = 9
Hence, the table can be filled as follows
x y
1 4
2 5
3 6
4 7
5 8
6 9
The next thing is to graph it on a graph
event a is the event that randomly selected students from your school is make event b is the event that randomly selected students from your school owns a bicycle which of the following do we know for certain correctly represents the probability of selecting a male students or selecting a student who owns a bicycle
Answers
The or probability in the context of this problem is represented as follows:
P(A U B).
Or probabilityThe or probability between two events A and B is the probability that at least one of the events happen.
The symbol of the or probability is given as follows:
U
In the context of this problem, the events are given as follows:
Event A: a randomly selected student is male.Event B: a randomly selected student owns a bike.Hence the probability of selecting a male students or selecting a student who owns a bicycle is represented as follows:
P(A or B) = P(A U B).
The other options are as follows:
P(A ∩ B): both male and own bike, representing the intersection operation of the events.P(A): male.P(B): own bike.Missing informationThe complete problem is given by the image at the end of the answer.
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I need this practice problem answered I will provide the answer options in another pic
Answers
The inverse of a matrix can be calculated as:
[tex]\begin{gathered} \text{When} \\ A=\begin{bmatrix}{a} & {b} & {} \\ {c} & {d} & {} \\ {} & {} & \end{bmatrix} \\ \text{Then A\textasciicircum-1 is:} \\ A^{-1}=\frac{1}{ad-bc}\begin{bmatrix}{d} & -{b} & {} \\ {-c} & {a} & {} \\ {} & {} & \end{bmatrix} \end{gathered}[/tex]Then, let's start by calculating the inverse of the given matrix:
[tex]\begin{gathered} \begin{bmatrix}{4} & {1} & {} \\ {-2} & {3} & {} \\ {} & {} & \end{bmatrix}^{-1}=\frac{1}{4\cdot3-1\cdot(-2)}\begin{bmatrix}{3} & -{1} & {} \\ {-(-2)} & {4} & {} \\ {} & {} & \end{bmatrix} \\ \begin{bmatrix}{4} & {1} & {} \\ {-2} & {3} & {} \\ {} & {} & \end{bmatrix}^{-1}=\frac{1}{14}\begin{bmatrix}{3} & -{1} & {} \\ {2} & {4} & {} \\ {} & {} & \end{bmatrix} \end{gathered}[/tex]The problem says he multiplies the left side of the coefficient matrix by the inverse matrix, thus:
[tex]\begin{gathered} \begin{bmatrix}{4} & {1} & {} \\ {-2} & {3} & {} \\ {} & {} & \end{bmatrix}^{-1}\begin{bmatrix}{4} & {1} & {} \\ {-2} & {3} & {} \\ {} & {} & \end{bmatrix}\cdot\begin{bmatrix}{x} & {} & {} \\ {y} & {} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{4} & {1} & {} \\ {-2} & {3} & {} \\ {} & {} & \end{bmatrix}^{-1}\begin{bmatrix}{2} & {} & {} \\ {-22} & {} & {} \\ {} & {} & {}\end{bmatrix} \\ \end{gathered}[/tex]*These matrices will be the options to put on the first and second boxes.
Then:
[tex]\begin{gathered} \begin{bmatrix}{x} & {} & {} \\ {y} & {} & {} \\ {} & {} & {}\end{bmatrix}=\frac{1}{14}\begin{bmatrix}{3} & -{1} & {} \\ {2} & {4} & {} \\ {} & {} & \end{bmatrix}\cdot\begin{bmatrix}{2} & {} & {} \\ {-22} & {} & {} \\ {} & {} & {}\end{bmatrix}\text{ This is for the third box} \\ \begin{bmatrix}{x} & {} & {} \\ {y} & {} & {} \\ {} & {} & {}\end{bmatrix}=\frac{1}{14}\begin{bmatrix}{3\times2+(-1)\times(-22)} & & {} \\ {2\times2+4\times(-22)} & & {} \\ {} & {} & \end{bmatrix}=\frac{1}{14}\begin{bmatrix}{28} & & {} \\ {-84} & & {} \\ {} & {} & \end{bmatrix}\text{ This is the 4th box} \\ \begin{bmatrix}{x} & {} & {} \\ {y} & {} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{28/14} & & {} \\ {-84/14} & & {} \\ {} & {} & \end{bmatrix}=\begin{bmatrix}{2} & & {} \\ {-6} & & {} \\ {} & {} & \end{bmatrix}\text{ And finally this is the last box} \end{gathered}[/tex]let f(x)=8x+5 and g(x)=9x-2. find the function.f - g(f - g) (x) =find the domain.
Answers
Answer:
(f - g)( x ) = -x + 7
Domain;
[tex](-\infty,\infty)[/tex]Explanation:
Given the below functions;
[tex]\begin{gathered} f(x)=8x+5 \\ g(x)=9x-2 \end{gathered}[/tex]To find (f - g)( x ), all we need to do is subtract g(x) from f(x) as shown below;
[tex]\begin{gathered} (f-g)\mleft(x\mright)=(8x+5)-(9x-2) \\ =8x+5-9x+2 \\ =8x-9x+5+2 \\ =-x+7 \end{gathered}[/tex]The domain of the function will be all values from negative infinity to positive infinty, written as;
[tex](-\infty,\infty)[/tex]Hello! I need some assistance with this homework question for precalculus, please?HW Q5
Answers
Explanation:
We were given the function:
[tex]g(x)=-1+4^{x-1}[/tex]We are to determine its domain, range and horizontal asymptote. This is shown below:
Domain:
[tex]\begin{gathered} g(x)=-1+4^{x-1} \\ 4^{x-1} \\ when:x=-10 \\ 4^{-10-1}=4^{-11} \\ when:x=1 \\ 4^^{1-1}=4^0=1 \\ when:x=20 \\ 4^{20-1}=4^{19} \\ \text{This shows us that the function is valid for every real number. This is written as:} \\ \left\{x|x∈R\right\} \end{gathered}[/tex]Range:
[tex]\begin{gathered} g(x)=-1+4^{x-1} \\ \begin{equation*} -1+4^{x-1} \end{equation*} \\ when:x=-10 \\ =-1+4^{-10-1}\Rightarrow-1+4^{-11} \\ =-0.9999\approx-1 \\ when:x=1 \\ =-1+4^{1-1}\Rightarrow-1+4^0\Rightarrow-1+1 \\ =0 \\ when:x=5 \\ =-1+4^{5-1}\Rightarrow-1+4^4\Rightarrow-1+256 \\ =255 \\ \text{This shows us that the lowest value of ''y'' is -1. This is written as:} \\ \left\{y|y>−1\right\} \end{gathered}[/tex]Horizontal asmyptote:
For exponential functions, the equation of the horizontal asymptote is given as:
[tex]y=-1[/tex]the length of a screwdriver is 0.75 cm is how many screws can be placed to the end to make a road that's 18 cm long show yours
Answers
Length of screwdriver = 0.75
Length of road = 18cm
Number of screws that can be placed on a road
[tex]\begin{gathered} =\text{ }\frac{18}{0.75} \\ =\text{ 24} \end{gathered}[/tex]Use the following results from a test for marijuana use, which is provided by a certain drug testing company. Among 143 subjects with positive test results, there are 24
false positive results; among 150 negative results, there are 5 false negative results. If one of the test subjects is randomly selected, find the probability that the subject
tested negative or did not use marijuana. (Hint: Construct a table.)
The probability that a randomly selected subject tested negative or did not use marijuana is.
(Do not round until the final answer. Then round to three decimal places as needed.)
Answers
The probability that the subject tested negative or did not use marijuana is 145/293.
What is probability?
Potential is described by probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events. Probability generally refers to the degree to which something is likely to occur. This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Before we can determine the probability that a certain event will occur, we must first know the total number of outcomes.
As given in the question,
Total positive results are 143 out of which 24 are false, and
total negative results are 150 out of which 5 are false.
We know that,
probability = favorable outcome/ Total outcome
so,
Total outcome = total tests
total tests = 143 + 150
total outcome = 293
and favorable outcome = true negative outcome
true negative outcome = total negative outcome - false negative outcome
true negative outcome = 150 - 5
favorable outcome = 145
Therefore, the probability is equal to 143/293
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If students only know the radius of a circle, what other measures could they determine? Explain how students would use the radius to find the other parts.
Answers
Radius of the circle : Radius is the distance from the center outwards.
With the help of radius we can determine the following terms:
1. Diameter : Diameter is the twice of radius and it is teh staright line that passes through the center. Expression for the diameter is :
[tex]\text{ Diameter= 2}\times Radius[/tex]2. Circumference: Circumference of the circle or perimeter of the circle is the measurement of the boundary of the circle. It express as:
[tex]\begin{gathered} \text{ Circumference of Circle=2}\Pi(Radius) \\ \text{ where }\Pi=3.14 \end{gathered}[/tex]3. Area of Circle: Area of a circle is the region occupied by the circle in a two-dimensional plane. It express as:
[tex]\begin{gathered} \text{ Area of Circle = }\Pi(radius)^2 \\ \text{where : }\Pi=3.14 \end{gathered}[/tex]4. Center Angle of the Sector: Central angles are subtended by an arc between those two points, and the arc length is the central angle of a circle of radius one. It express as :
[tex]\text{ Central Angle of sector=}\frac{Area\text{ of Sector}}{\Pi(radius)^2}\times360[/tex]5. Arc length : An arc of a circle is any portion of the circumference of a circle. It express as :
[tex]\text{ Arc Length = }Radius(\text{ Angle Substended by the arc from the centerof crircle)}[/tex]In the given figure the radius is AO & BO
Margie uses 36 inches of lace to make one pillow. She makes 24 pillows for the school fair. How many total inches of lace does Margie use on the pillows?
Answers
Margie used a total of 264 inches of lace for the 24 pillows
How to calculate the total inches of lace used ?
Margie used 36 inches of lace for one pillow
She needs to make 24 pillows
The total inches of lace that was used for the 24 pillows can be calculated as follows
= 36 × 24
= 864
Hence Margie used 864 inches of lace for 24 pillows
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Which answer choice shows 3.002 written in expanded form?A) 3 + 0.2B) 3 + 0.02C) 3 + 0.002D) 3+ 0.0002
Answers
SOLUTION
We want to know which answer choice shows 3.002 written in expanded form
To do this let us subtract 3.002 from 3, we have
We got 0.002
So the expanded form is
[tex]3+0.002[/tex]Hence the correct answer is option C
Two liters of soda cost $2.50 how much soda do you get per dollar? round your answer to the nearest hundredth, if necessary.
Answers
If two litters of soda cost $2.50;
Then, a dollar would buy;
[tex]\begin{gathered} =\frac{2}{2.5}\text{litres of soda} \\ =0.80\text{ litres of soda} \end{gathered}[/tex]In the diagram, RSTU ~ ABC D. Find the ratio of their perimeterA А.24BR18S36TDCThe ratio of their perimeters is
Answers
The ratio of the perimeters of two similar shapes is equal to the ratio of their corresponding sides, then, by taking the top sides of these figures we can express the following ratio
18 : 24
by dividing both numbers by 2, we get:
9 : 12
Dividing by 3:
3 : 4
Then the ratio of their perimeters equals 3 : 4
which description compass the domains of function a and function be correctly rest of the information in the picture below please answer with the answer choices
Answers
Given:
Function A: f(x) = -3x + 2
And the graph of the function B
We will compare the domains of the functions
Function A is a linear function, the domain of the linear function is all real numbers
Function B: as shown in the figure the graph starts at x = 0 and the function is graphed for all positive real numbers So, Domain is x ≥ 0
So, the answer will be the last option
The domain of function A is the set of real numbers
The domain of function B: x ≥ 0
The graph shows the relationship between pounds of grapes, g, and their cost, c.
A graph on a coordinate plane shows cost of grapes on the horizontal axis (c), numbered 2 to 6, and pounds of grapes on the vertical axis (g), numbered 1 to 4. Solid circles are at points (0, 0), (2, 1), (4, 2), (6, 3), and are connected by a solid line.
Use the graph to complete the statements.
For every dollar you spend, you can get
0.5
pounds of grapes.
For each pound of grapes, you would need $
.
Answers
For every dollar you spend, you can get 0.5 pounds of grapes.
For each pound of grapes, you would need $2.
How to interpret the graph?From the coordinates of this graph, we can reasonably infer and logically deduce that it models a straight line, shows a proportional relationship and can be represented by using a linear function.
Mathematically, a proportional relationship can be represented by the following equation:
g = kc
Where:
k is the constant of proportionality.g represent the pounds of grapes.c represent the cost of grapes in dollar.Next, we would determine the constant of proportionality (k) for the data points shown on this graph as follows:
k = g/c
k = 1/2 or 0.5
Therefore, the linear equation is given by g = 0.5c.
For the amount of dollar needed at g = 1, we have:
g = 0.5c
c = g/0.5
c = 1/0.5
c = $2.
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Corbie earns $2750 paid once a month after taxes.
James gets paid every other week for tutoring at the
local library, and his smallest paycheck in the past six
months was $280.
Their monthly rent for their home is $925 and their most
expensive month for combined utilities last year cost
$325. Their smartphones cost $180 per month. They
spend $120 per week on groceries, $45 per week on
gas,and $620 per month for their car's payment,
insurance, and maintenance savings. James spends
$600 per semester (twice a year) for college tuition.
They each give themselves a $100 per week allowance
for personal expenses such as clothes, haircuts, dining
out, and entertainment.
Calculate their prorated monthly amounts, their monthly
totals, and their cash flow.
Answers
1. Corbie and James' total prorated monthly incomes are Corbie's $2,750 and James' $606.
2. Their combined monthly totals are:
Income = $3,356.
Expenses = $3,111.
3. Their monthly net cash flow is $245.
What is the net cash flow?The net cash flow is the cash surplus after paying all operating costs.
The net cash flow for Corbie and James is the difference between their total earnings per month and their total expenses per month.
For some income and expenses, there is a proration. Since 52 weeks make up the typical year, each month is considered 4.33 weeks.
1 year = 52 weeks
1 month = 4.33 weeks (52/12)
Monthly Income:
Corbie = $2,750
James = $606 ($280 x 26/52 x 4.333)
Total income = $3,356
Monthly Expenses:
Rent = $925
Utilities = $325
Phones = $180
Groceries = $520 ($120 x 4.33)
Gas = $195 ($45 x 4.33)
Tuition = $100 ($600 x 2)/12
Incidentals = $866 (200 x 4.33)
Total expenses = $3,111
Net Cash Flow = $245 ($3,356 - $3,111)
Thus, whereas, Corbie and James earn a combined and prorated monthly income of $3,356, their total monthly expenses of $3,111 leave them with a net cash flow of $245.
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Quadrilateral TUVW is a rhombus and m∠SVU=4z+56°. What is the value of z?WTUVS26°z=°Submit
Answers
From the question, we were told:
TUVW is a rhombus
Angle SUV = 4z + 56˚
We are asked to find the value of z.
From the diagram, we can see that angle SVU is 90˚
So, to get the value of z, we equate the value of SVU to 90˚
4z + 56˚ = 90˚
subtract 56˚ from both sides:
4z + 56 - 56 = 90 - 56
4z = 34
divide both sides by 4 to make z the subject of formula:
z = 34/4
z = 8.5
Which two ratios are NOT equal? 1:6 and 3:18 OB. 2:14 and 3:42 OC. 12:6 and 2:1 OD 3:11 and 6:22
Answers
Let's check the ratios:
[tex]\begin{gathered} \frac{1}{6} \\ \text{and} \\ \frac{3}{18} \\ \end{gathered}[/tex]First one is already reduced. Let's reduce the 2nd fraction by dividing top and bottom by 3, so
[tex]\frac{3}{18}=\frac{1}{6}[/tex]So, they are equal.
Next ratio:
[tex]\begin{gathered} \frac{2}{14}\text{and}\frac{3}{42} \\ \end{gathered}[/tex]Let's divide both top and bottom by 2 (1st fraction) and top and bottom by (3) in 2nd fraction:
[tex]\begin{gathered} \frac{2}{14}=\frac{1}{7} \\ \text{and} \\ \frac{3}{42}=\frac{1}{14} \end{gathered}[/tex]They aren't equal. So, we have already found our answer.
OB. 2:14 and 3:42 --- is our answer.
Given A(-9, -12), B(-2, 2), C(x, 6).and D(-5, -2), find the value ofx so that AB || CD
Answers
1) Given these line segments, let's find the slope of them. Let's begin with AB
[tex]m=\frac{2-(-12)}{-2-(-9)}=\frac{14}{-2+9}=\frac{14}{7}=2[/tex]2) Parallel lines have the same slope, so let's set this slope formula so that we can get the slope m=2. Bearing in mind CD:
[tex]\begin{gathered} 2=\frac{-2-6}{-5-x} \\ 2=\frac{-8}{-5-x} \\ 2(-5-x)=-8 \\ -10-2x=-8 \\ -2x=-8+10 \\ -2x=2 \\ x=-1 \end{gathered}[/tex]Thus, x=-1
Find the slope and the equation of the line having the points (0, 2) and (5, 5)
Answers
Answer:
The slope is 3/5 and the equation is:
[tex]y=\frac{3}{5}x+2[/tex]Explanation:
Given the points (0,2) and (5, 5)
The slope of a line is the ratio of the difference between the y coordinates to the x coordinates. The x coordinates are 0 and 5, the y coordinates are 2 and 5.
[tex]\begin{gathered} m=\frac{5-2}{5-0} \\ \\ =\frac{3}{5} \end{gathered}[/tex]The equation of a straight line is given as:
y = mx + b
Where m is the slope and b is the y-intercept
Using any of the given points, we can find b
Use (0, 2), with x = 0, y = 2
2 = (3/5)(0) + b
b = 2
Now the equation is:
[tex]y=\frac{3}{5}x+2[/tex]During a baseball game, Diego thought his team would get 4 runs, and they actually got 7 runs. What was Diego's percent error? Make sure to include a percent sign. (Round to two decimal places)
Answers
Answer:
11 percent
Step-by-step explanation:
No idea to explain
