Scenario 1: Cameron works at a local grocery store after school. He is paid $8 for each hour he works.
Scenario 2: At a local bakery, one box of donuts costs $5. Two boxes of donuts cost $10.
Consider the two scenarios given above. Can you write an equation to represent each situation? What would the graphs of these equations look like? Can you think of a situation that would result in a similar equation?
Answer:
1: Linear
2: Linear
Step-by-step explanation:
Scenario 1:
Equation: y=8x (where x represents # of hours worked)
The graph would be linear.
Scenario2:
Equation: y=5x (where x is the # of boxes of donuts purchased)
The graph would be linear. ( I assumed that each box is $5 since 5/1=10/2 )
A similar situation could be: In an art shop, crayons are sold. It costs $7 for 1 box of crayons.
- The graph would be linear, and it would be constant as long as the price for each box of crayons is not changed. Equation is: y=7x
I'm not sure if this is exactly what the last question asked, pretty sure this would be an okay example.
HELP!!!!QUICK!!!!!!!!!!!
Answer:
= – 5 – 7
Step-by-step explanation:
3 – 8 = – 5 + 4 – 5 = – 1 –1 – 6 = –7= –5 – 7
factorise completely
2x²+8+6
Hi there,
please see below for solution steps :
‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
⨠ add 8 and 6
[tex]\sf{2x^2+14}[/tex]
⨠ factor the 2 out
[tex]\sf{2(x^2+7)}[/tex]
Since we cannot simplify this more, we know that we've simplified completely. [tex]\small\pmb{\sf{Frozen \ melody}}[/tex]
‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
Ida's rent increased by 5%. the increase was $59. what was the original amount of ida's rent?
The original amount of ida's rent is $56.
How do you find the original price after an increase?First consider the unknown original amount as 'x'. To find the increase or decrease, multiply the rate by the original amount 'x'. To find the final amount, add or subtract the increase or decrease to the original amount 'x' and equate this to given final amount. Solve the equation and find the original amount 'x'.
Let the original amount be x. This amount increase by 5% after increasing the amount is $59.
[tex]x+x(\frac{5}{100})=59\\\\[/tex]
[tex]x+x(\frac{1}{20})=59\\\\[/tex]
[tex]\frac{21x}{20}[/tex] = 59
x = $56.19
Hence, The original amount be x =$56.19.
To learn more about the original amount from the given link:
https://brainly.com/question/25793394
#SPJ4
What is the value of x to the nearest tenth? The figure is not drawn to scale
Answer:
x=10.5
Step-by-step explanation:
if the two triangles were ratios it would be like
19.3:7.2 to x:3.9
so 75.27 = 7.2x
whcih is 10.45 which is approximately 10.5
HELP PLS WHAT IS X
Darn
Answer:
x = 55°
Step-by-step explanation:
x , 35° , 90° lie on a straight line and sum to 180° , that is
x + 35° + 90° = 180°
x + 125° = 180° ( subtract 125° from both sides )
x = 55°
I have a list of five numbers, where the first number is 1 and the fifth number is 5. Each of the other numbers is equal to one more than the average of its two neighbors. What is the sum of all five numbers in the list?
The sum of all five numbers in the list is 25.
According to the question,
The first number on my list of five numbers is 1, and the fifth is 5. The other figures are all one more than their two nearest neighbors' averages.
Let the list of numbers be 1,x,y,z,5.
As each of the other numbers is equal to one more than the average of its two neighbors.
x=(1+y)/2+1
2x=3+y -(1)
Similarly,
y=(x+z)/2+1
2y=x+z+2 -(2)
z=(y+5)/2+1
2z=y+7 -(3)
Multiply equation (2) by 2 and then substitute equations (1) and (3),
4y=3+y+y+7+4
4y=2y+14
2y=14
y=14/2
y=7
From equation (1),
2x=3+7
2x=10
x=5
From equation (3),
2z=7+7
2z=14
z=14/2
z=7
The list is: 1,5,7,7,5
Sum of the numbers of list = 1+5+7+7+5 = 25
Learn more about sum here:
https://brainly.com/question/17695139
#SPJ1
5 yd
5 yd
8 yd
5 yd
14 yd
3 yd
9 yd
6 yd
Pleasee help rn
A force of 3 pounds is required to hold a spring stretched 0.6 feet beyond its natural length. how much work (in foot-pounds) is done in stretching the spring from its natural length to 0.7 feet beyond its natural length? answer exactly or round to 2 decimal places.
The work done (in foot-pounds) in stretching the spring from its natural length to 0.7 feet beyond its natural length is 1.23 foot-pound
Data obtained from the questionFrom the question given above, the following data were obtained:
Force (F) = 3 poundsExtension (e) = 0.6 feetWork done (Wd) =?How to determine the spring constantForce (F) = 3 poundsExtension (e) = 0.6 feetSpring constant (K) =?F = Ke
Divide both sides by e
K = F/ e
K = 3 / 0.6
K = 5 pound/foot
Thus, the spring constant of the spring is 5 pound/foot
How to determine the work doneSpring constant (K) = 5 pound/footExtention (e) = 0.7 feetWork done (Wd) =?Wd = ½Ke²
Wd = ½ × 5 × 0.7²
Wd = 2.5 × 0.49
Wd = 1.23 foot-pound
Therefore, the work done in stretching the spring 0.7 feet is 1.23 foot-pound
Learn more about spring constant:
https://brainly.com/question/9199238
#SPJ1
A construction worker is pouring concrete stairs. The first step requires 1.7 cubic feet of concrete, and the first 4 steps require a total of 17 cubic feet. If the steps follow an arithmetic series, how much concrete is required for the first 12 steps
Based on the given parameters of a = 1.7 cubic feet and concrete for first 4 steps as 17 cubic feet, the concrete is required for the first 12 steps is 132.6 cubic feet
Arithmetic progressionFirst term, a = 1.7 cubic feetSum of first four terms = 17 cubic feetSn = n/2 {2a + (n - 1) d}
17 = 4/2{2×1.7 + (4 - 1)d}
17 = 2{3.4 + (3)d}
17 = 2(3.4 + 3d)
17 = 6.8 + 6d
17 - 6.8 = 6d
10.2 = 6d
d = 10.2/6
Common difference, d = 1.7Concrete required for first 12 steps;
Sn = n/2 {2a + (n - 1) d}
= 12/2{2×1.7 + (12-1)1.7}
= 6{3.4 + (11) 1.7}
= 6(3.4 + 18.7)
= 6(22.1)
= 132.6
Concrete required for first 12 steps = 132.6 cubic feet
Learn more about sum of arithmetic progression:
https://brainly.com/question/24205483
#SPJ1
Answer:
132.6 cubic feet
Step-by-step explanation:
A newspaper started an online version of its paper 14 years ago. In a recent presentation to stockholders, the lead marketing executive states that the revenues for online ads have more than doubled that of the revenues for printed ads since starting the online version of the paper. Use the graph below to justify the lead executive’s statement and to determine the approximate year that the two ad revenues were equal.
The approximate year at which two revenues were equal is; 7.5 years
How to interpret Revenue Graphs?From the graph attached, we see that in the year 10, the revenue for printed ads was 2 million dollars & 3 million dollars for printed ads and online ads revenue respectively.
Thus, printed ad. Revenue line equation is;
(y - 2) = (3 - 2)(x - 10)/(0 - 10)
y - 2 = (x - 10)/-10
x - 10 = -10(y - 2)
x - 10 = -10y + 20
x - 10 = -10y + 20
x + 10y = 30 -----(1)
At x = 12 years from the graph, we have;
12 + 10y = 30
10y = 18
y = 1.8
Thus, online ad. Revenue line equation is;
(y - 0) = ((3 - 0)/(10 - 0))(x - 0)
y = 3x/10
10y = 3x
10y - 3x = 0 -----(2)
At x = 12, we have;
10y = 3*12
10y = 36
y = 3.6
In year '12' the online ad revenue got doubled as that of printed ad revenue and afterward more than doubled.
B) The approximate year at which two revenues were equal is gotten by solving equation 1 and 2 simultaneously to get;
x = 7.5
Read more about Revenue Graphs at; https://brainly.com/question/4205637
#SPJ1
What form of deductive reasoning is used in the given argument? a number ends in , then it is divisible by 10. a number is divisible by 10, then it is divisible by 5 a number ends in , then it is divisible by law of detachment . law of syllogism law of contrapositive . Identification of counterexample
The form of deductive reasoning used in the given argument is; Law of Syllogism
How to identify the Logic Law used?The argument we are given is;
If a number ends in 0, then it is divisible by 10.
If a number is divisible by 10, then it is divisible by 5.
If a number ends in 0, then it is divisible by 5.
The law used for the deductive reasoning in the given argument is called Law of Syllogism. This is because this law of mathematical logic states that;
If the following two statements are true:
(1) If p , then q .
(2) If q , then r .
Then we can derive a third true statement:
(3) If p , then r .
Read more about Logic Laws at; https://brainly.com/question/13419663
#SPJ1
What is the area of the triangle shown below?
Answer: the area of the triangle is 5.
Step-by-step explanation:
[tex]A(0;0) \ \ \ \ B(1;3) \ \ \ \ C(4;2) \ \ \ \ S_{ABC}=?\\Use \ the\ formula:\\\displaystyle\\\boxed{S=\frac{1}{2}*|[(x_A-x_C)*(y_B-y_C)-(x_B-x_C)*(y_A-y_c)] |}\\x_A=0\ \ \ \ x_B=1\ \ \ \ x_C=4\ \ \ \ y_A=0\ \ \ \ \ y_B=3\ \ \ \ \ y_C=2.\\S=\frac{1}{2}*|[(0-4)*(3-2)-(1-4)*(0-2)]|\\S=\frac{1}{2}*| [(-4)*1-(-3)*(-2)]|=\\ S=\frac{1}{2}*| (-4-6)|\\S=\frac{1}{2}*|(-10)|\\S= \frac{1}{2} *10\\S=5.[/tex]
What is the sign of b/c
Answer:
Negative.
Step-by-step explanation:
b is above zero. So, it is positive.
c is below zero. So, it is negative.
A positive divided by negative number results in negative.
Answer:
B. negative
Step-by-step explanation:
-2 is negative. That's why.
Statistical analyses are least likely to be found in a. applied research b. basic research c. field research d. qualitative research
Statistical analyses are least likely to be found in a (D) qualitative research.
What is qualitative research?Data from first-hand observation, interviews, questionnaires (on which participants write descriptively), focus groups, participant-observation, recordings recorded in natural settings, documents, case studies, and artifacts are used in qualitative research. The information is mostly nonnumerical. Ethnography, grounded theory, discourse analysis, and interpretative phenomenological analysis are examples of qualitative approaches. Sociology, anthropology, political science, psychology, social work, and educational research have all used qualitative research methods. Qualitative researchers investigate people's perceptions of their social reality.A qualitative study is unlikely to contain statistical analyses.Therefore, statistical analyses are least likely to be found in a (D) qualitative research.
Know more about qualitative research here:
https://brainly.com/question/24492737
#SPJ4
A store has a 40 percent off sale on headphones. With this discount, the price of one pair of headphones is $36. What is the original price of the pair of headphones
Answer:
Discount =40\%
Selling price of headphone =\$36
Solution --
we know that,
MP=SP * 100/(100-D\%)
putting values now we get,
MP = 36 * 100 / 60=60$
so, initial price of Headphone was =$60
exponential growth and decay real-world word problems
The examples of exponential growth include bacteria population growth and compound interest and a real life example of exponential decay is radioactive decay.
What is exponential growth?Exponential growth is the pattern of data that shows sharper increases over time. Savings accounts with a compounding interest rate can show exponential growth.
There are many real-life examples of exponential decay. An example, is thatsuppose that the population of a city was 100,000 in 1980. Then every year after that, the population has decreased by 3% as a result of heavy pollution. This is an example of exponential decay.
One of the best examples of exponential growth is the observed in bacteria. It takes bacteria roughly an hour to be able to reproduce through prokaryotic fission. In this case, if we placed 100 bacteria in an environment and recorded the population size each hour, we would observe an exponential growth.
Learn more about exponential growth on:
https://brainly.com/question/4172151
#SPJ1
1. How many quarters are in 12 1/4
2. How many ninths are in 6 1/9
3. How many eighths are in 5 3/4
A=
B=
What are the coordinates for a and b?
Help me please asap thanks so much
Answer:
A = (0, b)
B = (a, b)
Step-by-step explanation:
A is straight up from the origin and is the same height as b so it's (0, b)
B is straight up from C so the x is the same so it's (a, b)
Please help and explain.
Answer:
B
Step-by-step explanation:
It's B
Answer:
Option B
Step-by-step explanation:
The equation is:
[tex]y=10-2x[/tex]
when x=2
[tex]y=10-2(2)010-4=6[/tex]
When x = 3
[tex]y=10-2(3)=10-6=4[/tex]
When x=4
[tex]y=10-2(4)=10-8=2[/tex]
Hope this helps
The odds of rolling a die and getting an even number is 50%. Write out the success set and the sample set to use the definition of probability to show that this is true.
Answer:
It gets more complicated with a six-sided die. In this case if you roll the die, there are 6 possible outcomes (1, 2, 3, 4, 5 or 6). Can you figure out what the theoretical probability for each number is? It is 1/6 or 0.17 (or 17 percent).
divide $800 between kofi and kweku so that kofi gets three times what kweku gets
Answer:
600 and 200
Step-by-step explanation:
kofi : kweku is 3 :1
so Kofi gets 3 out of ( 3 +1) = 3/4 of 800 = 3/4 * 800 = 600
kweku get s the rest 800- 600 = 200
Archeologists discovered a relic dating to the year 107 B.C. How old would this relic have been at the turn of the 20th century?
Step-by-step explanation:
The turn of the 20th century = 1900
So it is 1900 + 107 years ago, hence, 2007
I really need help ASAP! thx
Let f(z)=z-8 and g(z)=4z-9
Find (f+g)(2)
Answer:
(f +g)(2) = -7
Step-by-step explanation:
Functions are added by adding their values.
Application(f +g)(2) = f(2) +g(2)
= (2 -8) +(4(2) -9) . . . . . evaluate f and g with z=2
= -6 +(-1)
(f +g)(2) = -7
What is a31 of the
arithmetic sequence for
which a5 = 12.4 and
ag = : 22.4?
The value of a₃₁ of the arithmetic sequence exists 77.4.
How to find the value of a₃₁ of the arithmetic sequence?Given: a₅ = 12.4 and a₉ = : 22.4
For the arithmetic sequence a₁, a₂, a₃, ..., the n-th term exists
where d = common difference
a₅ = 12.4,
a₁ + 4d = 12.4 .........(1)
Because a₉ = 22.4,
a₁ + 8d = 22.4 .........(2)
Subtract (1) from (2), we get
a₁ + 8d - (a₁ + 4d) = 22.4 - 12.4
4d = 10
Dividing throughout by 4, we get
d = 2.5
From (1), we get
a₁ = 12.4 - 4 [tex]*[/tex] 2.5 = 2.4
a₃₁ = 2.4 + 30 [tex]*[/tex] 2.5 = 77.4
Therefore, the correct answer is a₃₁ = 77.4
To learn more about the arithmetic sequence refer to; https://brainly.com/question/6561461
#SPJ9
Please help quick
[tex]y=\frac{-1}{2\sqrt{x^{3} } }[/tex]
can you put step-by-step no verbal explanation needed how I can get to
[tex]y=\frac{-2}{x\sqrt{x} }[/tex]
The equation y=[tex]-1/2\sqrt{x^{3} }[/tex] does not give result to y=-2/[tex]x\sqrt{x}[/tex].
Given two equations y=[tex]-1/2\sqrt{x^{3} }[/tex] and y=-2/[tex]x\sqrt{x}[/tex].
We are required to find that how the first equation will result in second equation.
Equation is like a relationship between two or more variables that are expressed in equal to form.Equation of two variables look like ax+by=c. It may be a linear equation,cubic or quadratic equation or many more depending on the power if variable.
Taking the first equation.
y=[tex]-1/2\sqrt{x^{3} }[/tex]
Interchange the power of x.
y=-1/2[tex]\sqrt{x} ^{3}[/tex]
Now multiply [tex]\sqrt{x}[/tex] three times.
y=-1/2[tex]\sqrt{x} \sqrt{x} \sqrt{x}[/tex]
Now [tex]\sqrt{x} \sqrt{x}[/tex] will result in x.
y=-1/2x[tex]\sqrt{x}[/tex]
You can see our result is not matching the second equation.
Hence the equation y=[tex]-1/2\sqrt{x^{3} }[/tex] does not give result to y=-2/[tex]x\sqrt{x}[/tex].
Learn more about equations at https://brainly.com/question/2972832
#SPJ1
For this item, a non-integer answer should be entered as a fraction using / as the fraction bar.
Simplify the numerical expression.
The expression has a value equal to
The numerical expression, 2/3 ÷ 2⁴ + (3/4 + 1/6) ÷ 1/3 = 67/24 on simplification using the BODMAS rule.
In the question, we are asked to simplify the numerical expression:
2/3 ÷ 2⁴ + (3/4 + 1/6) ÷ 1/3.
To simplify the expression, we will follow the BODMAS rule, where B means Brackets, O means Of, D means Divide, M means Multiplication, A means Addition, and S means Subtraction.
2/3 ÷ 2⁴ + (3/4 + 1/6) ÷ 1/3
= 2/3 ÷ 16 + (3/4 + 1/6) ÷ 1/3 {Solving 2⁴ = 16, before proceeding BODMAS}.
= 2/3 ÷ 16 + ((9+2)/12) ÷ 1/3 {Solving Brackets by taking LCM}
= 2/3 ÷ 16 + 11/12 ÷ 1/3 {Simplifying}
= 2/3 * 1/16 + 11/12 * 3/1 {Solving divisions by taking reciprocals}
= 1/24 + 11/4 {Multiplying}
= (1 + 66)/24 {Adding using LCM}
= 67/24 {Simplifying}.
Thus, the numerical expression, 2/3 ÷ 2⁴ + (3/4 + 1/6) ÷ 1/3 = 67/24 on simplification using the BODMAS rule.
Learn more about the simplification of numerical expression at
https://brainly.com/question/17205434
#SPJ1
The provided question is incomplete. The complete question is:
"Type the correct answer in the box. Use numerals instead of words. For this item, a non-integer answer should be entered as a fraction using / as the fraction bar.
Simplify the numerical expression.
2/3 ÷ 2⁴ + (3/4 + 1/6) ÷ 1/3
The expression has a value equal to."
Evaluate the following integral (Calculus 2) Please show step by step explanation!
Answer:
[tex]\displaystyle \int \dfrac{\ln x}{x^8}\:\:\text{d}x=-\dfrac{\ln x}{7x^7}- \dfrac{1}{49x^7}+\text{C}[/tex]
Step-by-step explanation:
Fundamental Theorem of Calculus
[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]
If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.
Given integral:
[tex]\displaystyle \int \dfrac{\ln x}{x^8}\:\:\text{d}x[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{1}{a^n}=a^{-n}[/tex]
[tex]\implies \displaystyle \int x^{-8}\ln x\:\:\text{d}x[/tex]
[tex]\boxed{\begin{minipage}{4.8 cm}\underline{Integration by parts} \\\\$\displaystyle \int u \dfrac{\text{d}v}{\text{d}x}\:\text{d}x=uv-\int v\: \dfrac{\text{d}u}{\text{d}x}\:\text{d}x$ \\ \end{minipage}}[/tex]
Using Integration by parts:
[tex]\textsf{Let }u=\ln x \implies \dfrac{\text{d}u}{\text{d}x}=\dfrac{1}{x}[/tex]
[tex]\textsf{Let }\dfrac{\text{d}v}{\text{d}x}=x^{-8} \implies v=-\dfrac{1}{7}x^{-8+1}=-\dfrac{1}{7}x^{-7}=-\dfrac{1}{7x^7}[/tex]
Therefore:
[tex]\begin{aligned}\displaystyle \int u \dfrac{dv}{dx}\:dx & =uv-\int v\: \dfrac{du}{dx}\:dx\\\\\implies \displaystyle \int x^{-8}\ln x\:\:\text{d}x & = -\dfrac{1}{7x^7}\ln x- \int -\dfrac{1}{7x^7} \cdot \dfrac{1}{x}\:\:\text{d}x\\\\& = -\dfrac{\ln x}{7x^7}+ \int \dfrac{1}{7x^8}\:\:\text{d}x\\\\& = -\dfrac{\ln x}{7x^7}+ \int \dfrac{1}{7}x^{-8}\:\:\text{d}x\\\\& = -\dfrac{\ln x}{7x^7}-\dfrac{1}{7 \cdot 7}x^{-8+1}+\text{C}\\\\& = -\dfrac{\ln x}{7x^7}- \dfrac{1}{49x^7}+\text{C}\end{aligned}[/tex]
[tex]\boxed{\begin{minipage}{4 cm}\underline{Differentiating $\ln x$}\\\\If $y=\ln x$, then $\dfrac{\text{d}y}{\text{d}x}=\dfrac{1}{x}$\\\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex]
Learn more about integration here:
https://brainly.com/question/27988986
https://brainly.com/question/27805589
Substitute [tex]y=\ln(x) \iff e^y = x[/tex] and [tex]dy=\frac{dx}x[/tex] to get
[tex]\displaystyle \int \frac{\ln(x)}{x^8} \, dx = \int ye^{-7y} \, dy[/tex]
Integrate by parts with
[tex]u = y \implies du = dy[/tex]
[tex]dv = e^{-7y} \, dy \implies v = -\dfrac17 e^{-7y}[/tex]
Then
[tex]\displaystyle \int u\,dv = uv - \int v\,du \\\\ \implies \int y e^{-7y} \, dy = -\dfrac17 ye^{-7y} + \frac17 \int e^{-7y} \, dy + C \\\\ ~~~~~~~~~~~~ = -\frac17 ye^{-7y} - \frac1{49} e^{-7y} + C \\\\ ~~~~~~~~~~~~ = \boxed{-\frac{\ln(x)}{7x^7} - \frac1{49x^7} + C}[/tex]
The first quartile of the dataset {1, 2, 3, 4, 5, 6} is _______. (give your answer as a whole number.
The first quartile of the dataset {1, 2, 3, 4, 5, 6} is 2.
Given data set: {1,2,3,4,5,6}
Median of the given data set =3.5
The data set can be split into 2 parts as, {1,2,3} and {4,5,6}. The first quartile is calculated by simply finding the median of the first part of the data set.
Thus, the first quartile is 2.
The quarter divides the distribution into four groups and calculates the range of values above and below the mean.
A quartile separates the dataset into four categories by dividing the data into three points: the lowest, median, and upper quartiles.
The interquartile range, a measurement of variation around the median, is calculated using quartiles.
Learn more about quartiles here:
https://brainly.com/question/10005803
#SPJ4
Figure A is a scalr image of figur B. Figure A maps to Figure B with scale factor of 2/3. what is tge value of x?
Answer:
7
Step-by-step explanation:
You take the corresponding side that you know which is 10.5 and you multiply that by your scale factor of 2/3.
Another name for 10.5 is 10 [tex]\frac{1}{2}[/tex] and that can be changed to [tex]\frac{21}{2}[/tex]
([tex]\frac{21}{2}[/tex])([tex]\frac{2}{3}[/tex]) The two's cancel out and we are left with [tex]\frac{21}{3}[/tex] Which is the same as 7.