A) What does the point (1,8) represent in the context of the situation? B) Is the amount of money proportional to the number of hours worked? C) Write an equation that represents this situation? D) What will be Amber’s Wages after 6 hours worked?
Answers
Answer:
A) Amber's wages for 1 hour is $8.
B) Yes
C) y = 8x
D)
Explanation:
A) Looking at the graph, we can deduce that the point (1, 8) shows how much Amber makes in one hour. So in 1 hour, Amber makes $8.
B)To determine whether the amount of money is proportional to the number of hours worked, we have to look at the graph and see if it starts from the origin (0, 0), if it does then we can conclude that they are proportional.
Since the graph starts from the origin (0, 0), then the amount of money is proportional to the number of hours worked.
C) The slope-intercept equation of a line is given as;
[tex]y=mx+b[/tex]where m = slope of the line
b = y-intercept of the line
So let's go ahead and determine the slope of the line at points (1, 8) and (2, 16) using the below formula;
[tex]m=\frac{y_2-y_1_{}_{}_{}}{x_2-x_1_{}}=\frac{16-8}{2-1}=\frac{8}{1}=8[/tex]Since the line starts from the origin, therefore the y-intercept, b, is zero.
Since m = 8 and b = 0, the equation can then be written as;
[tex]\begin{gathered} y=8x+0 \\ y=8x \end{gathered}[/tex]D
Related Questions
What is the standard deviation of the data?Some teenagers collected trash for a beach cleanup.The data for the number of pounds of trash collected byeach teenager are shown below.26, 26, 21, 22, 20, 25, 35O pounds4.66 pounds5.03 poundso 25.33 pounds
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Write inequalities to represent the situation below.Latoya exercises no less than 50 minutes per day.Use t to represent Latoya's amount of exercise (in minutes per day).(Thank you for the help!)
Answers
To answer this question, we have that:
1. Latoya exercises no less than 50 minutes per day.
In this case, we can say that Latoya exercises more than 50 minutes per day.
Therefore, if we have that t represents Latoya's amount of exercise - in minutes per day, we can express this using inequality as follows:
[tex]t>50[/tex]In summary, we can represent the situation as:
[tex]t>50[/tex]One gram is approximately 2.2 x 10-pounds. Which of the following represents this number in standard notation? OA. 0.0022 OB. 0.022 OC. 2200 OD. 0.00022
Answers
One gram is approximately 2.2 x 10^-3
10^-3 = 1/1000
= 0.001
= 2.2 x 0.001
= 0.0022
The answer is option A
An orange has about I cup of juice. How many oranges are needed to make 2 cups of juice?
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An orange has about 1/4 cup of juice. To find how many oranges are needed to make 2 1/2 cups of juice, we can use the next proportion
[tex]\frac{\frac{1}{4}\text{cup}}{2\frac{1}{2}\text{ cup}}=\frac{1\text{ orange}}{x\text{ oranges}}[/tex]Solving for x:
[tex]undefined[/tex]help me please I want to learn how to solve this
Answers
SOLUTION
In this question, we are meant to find the slope of the line represented
by 5x - 12 y = 24.
Re-arranging the equation, we have: 12 y = 5x - 24
Dividing both sides by 12,
[tex]\begin{gathered} y\text{ = }\frac{1}{12}(\text{ 5x -24 )} \\ y\text{ = }\frac{5}{12}x\text{ - 2} \\ \text{CONCUSION: The slope of the line is }\frac{5}{12}\text{ ------OPTION J} \end{gathered}[/tex]Jessica is the secretary of the Hillside Players.They are going to put on a show at the village hall.Jessica needs to arrange 4dates in October for rehearsals
Answers
ANSWER :
EXPLANATION :
a
The dot plot shows how many customers purchased different numbers of shirts at a sale last weekend.
Answers
The interquartile range IQR of a dataset is the difference between the upper and lower quartiles, Q3 and Q1
The median of the whole dataset is Q2 and corresponds to the value x=3.5
The value of Q1 is the median of the lower 3 values: Q1=2
The value of Q3 is the median of the upper 3 values: Q3=5
The IQR is: 5 - 2 = 3
One month Chris rented 8 movies and 4 video games for a total of 49$.The next month he rented 3 movies and 2 video games for a total of 21$.Find the rental cost for each movie and each video game.
Answers
Given
One month Chris rented 8 movies and 4 video games for a total of 49$.The next month he rented 3 movies and 2 video games for a total of 21$. Find the rental cost for each movie and each video game.
Solution
Step 1
Let m represent the movies
And let v represent the video
Therefore,
[tex]\begin{gathered} 8m+4v=\text{ \$49}\ldots Equation\text{ 1} \\ 3m+2v=\text{ \$ 21 }\ldots Equation\text{ 2} \end{gathered}[/tex]Step 2
If you solved the following system by substitution, which of these could be yourcombined equation?y = 3x - 44x + 3y = 1
Answers
To solve the given system, we have to combine the equations
[tex]\begin{gathered} 4x+3y=1 \\ 4x+3(3x-4)=1 \\ 4x+9x-12=1 \\ 13x=12+1 \\ 13x=13 \\ x=\frac{13}{13} \\ x=1 \end{gathered}[/tex]Then, we find y
[tex]y=3x-4=3\cdot1-4=3-4=-1[/tex]Hence, the solutions (1,-1,). C is the answer.Which of the follwoing shows the area of circle with a diameter of 8 km? a. 16 km2 50.27km2 X b. 4tkm? ~ 12.57km? c.21km? ~ 6.28km? d. Akm? ~ 3.14km2
Answers
The formula of the area of a circle is
[tex]A=\pi r^2[/tex]where r is the radius
in this case, we have the length of the diameter, the diameter is twice the radius
d= diameter
d=2r
therefore
r=d/2
r=8/2
r=4
we substitute the value of the radius in the formula
[tex]A=\pi r^2=\pi(4)^2=16\pi=50.27\operatorname{km}^2[/tex]the area of a circle with a diameter of 8km is 16pi km^2 or 50.27km^2
A boutique sells t-shirts for $30. They pay $12.50 for each shirt and spend $740 for the right to sell the brand in their store. How many t-shirts do they have to sell to break even?
Answers
First let's find the profit for each t-shirt, by subtracting the selling price and the buying price:
[tex]30-12.5=17.5[/tex]So they have a profit of $17.5 per t-shirt sold.
Now, to find the number of t-shirts they have to sell to break even, we just need to divide the right cost of $740 by the profit value of one t-shirt:
[tex]\frac{740}{17.5}=42.29[/tex]So they need to sell approximately 43 t-shirts to break even.
If I have 2 and a 1/2 bags of mortar
or every 100 cement blocks how many bags of water Mason needed for 350 blocks
Answers
The number of bags for 350 blocks is 8.75 bags
How to determine the number of bags for 350 blocks?From the question, we have the following parameters that can be used in our computation:
Bags of mortal = 2 and a 1/2 bags
Number of cements blocks = 100 blocks
The above parameters can be represented using the following ratio
Ratio = Bags of mortal : Number of cements blocks
Substitute the known values in the above equation, so, we have the following representation
Bags of mortal : Number of cements blocks = 2 and a 1/2 bags : 100 blocks
When the number of blocks is 350, we have the following equation
Bags of mortal : 350 = 2 and a 1/2 bags : 100 blocks
Express the ratio as fraction
Bags of mortal/350 = 2.5/100
Multiply both sides by 350
Bags of mortal = 350 * 2.5/100
Evaluate the products
Bags of mortal = 8.75
Hence, the number of bags is 8.75
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solve for x:
7x=6+5 (3x+3)-x
Answers
Answer: x= -3
Step-by-step explanation:
7x = 6+ 15x + 15 - x
7x = 21 + 14x
-7x = 21
x= -3
Graph two full periods, highlighting the first period using bold marking and analyze each function.Y = 2 sin (1/2 (x + pi/2) ) + 1
Answers
Given
[tex]y=2\sin(\frac{1}{2}(x+\frac{\pi}{2}))+1[/tex]
Procedure
Period: 4pi
Interval length: In the graph 2 periods 8pi
Phase shift: -pi/2
1st Per. begins: -pi/2
1st Per. ends: 7pi/2
Amplitude: 2
Domain:
(-∞, ∞)
Range:
[-1,3]
y-intercep:
(0,2.414)
x-intercept:
[tex]x=\frac{11\pi}{6}+4\pi n,\frac{19\pi}{6}+4\pi n,\text{ for any integer of n }[/tex]reduce the radical of 200
Answers
At a particular restaurant, each mozzarella stick has 100 calories and each slider has
200 calories. A combination meal with mozzarella sticks and sliders is shown to have
1500 total calories and 9 more mozzarella sticks than sliders. Determine the number
of mozzarella sticks in the combination meal and the number of sliders in the
combination meal.
There are
mozzarella sticks and
sliders in the combination meal.
Answers
The 1,500 calories in the combination meal and the amount of calories per mozzarella stick and per each slider gives an equation with the following solution;
There are 11 mozzarella sticks and 2 sliders in the combination meal.
What is a mathematical equation?An equation in mathematics is a statement that two mathematical expressions are equal.
The number of calories in each mozzarella stick = 100
Number of calories in each slider = 200
Number of calories in the combination meal = 1,500
Number of mozzarella sticks in the combination meal = 9 + The number of sliders
Let s represent the number of sliders in the combination meal, we have;
Number of mozzarella in the combination meal = s + 9
The equation that gives the amount of calories in the meal is therefore;
200·s + 100·(s + 9) = 1,500
200·s + 100·s + 900 = 1,500
300·s = 1,500 - 900 = 600
s = 600 ÷ 300 = 2
The number of sliders in the combination meal, s = 2
The number of mozzarella in the meal = 2 + 9 = 11
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The data set below provides the monthly rent (in dollars) paid by 7 tenants.990, 879, 940, 1010,950, 920, 1430Suppose the rent for one of the tenants changes from $1430 to $1115.What is the mean before the rent change?What is the mean after the change?
Answers
To solve this question, we need to find the mean for both cases. The mean is given by summing the given values and then dividing them by the number of values (or given cases).
We have that, before the rent chance, we have the following monthly rent (in dollars):
990, 879, 940, 1010,950, 920, 1430
There are seven (7) values. Then, the mean, in this case, is:
[tex]m_{\text{before}}=\frac{990+879+940+1010+950+920+1430}{7}=\frac{7119}{7}\Rightarrow m=1017[/tex]Therefore, the mean, in this case, is equal to $1017.
Now, we have that the rent change for the one with $1430 to $1115, now the values are:
990, 879, 940, 1010,950, 920, 1115.
We can proceed as before to obtain the mean:
[tex]m_{\text{after}}=\frac{990+879+940+1010+950+920+1115}{7}=\frac{6804}{7}\Rightarrow m_{after}=972[/tex]Thus, the mean after the change is equal to $972.
In summary, we have that:
• The mean before the rent change is equal to $1017
,• The mean after the rent change is equal to $972.
Determine the amplitude, period, and phase shift for y=1/3tan (0 +30) and use them to plot the graph of the function.
Answers
Given: The function below
[tex]y=\frac{1}{3}tan(\theta+30^0)[/tex]To Determine: The amplitude, the period, and the phase shift
Solution
The graph of the function is as shown below
The general equation of a tangent function is
[tex]f(x)=Atan(Bx+C)+D[/tex]Where
[tex]\begin{gathered} A=Amplitude \\ Period=\frac{\pi}{B} \\ Phase-shift=-\frac{C}{B} \\ Vertical-shift=D \end{gathered}[/tex]Let us compare the general form to the given
[tex]\begin{gathered} y=\frac{1}{3}tan(\theta+30^0) \\ f(x)=Atan(B\theta+C)+D \\ A=\frac{1}{3} \\ B=1 \\ C=30^0 \\ D=0 \end{gathered}[/tex]Therefore
[tex]\begin{gathered} Amplitude=\frac{1}{3} \\ Period=\frac{\pi}{B}=\frac{180^0}{1}=180^0 \\ Phase-shift=-\frac{C}{B}=-\frac{30^0}{1}=-30^0 \end{gathered}[/tex]Hence, the correct option is as shown below
47 Dominic used the equation below to find d, the amount in dollars he would spend on gasolineto drive a distance of m miles.d =(3.5)Based on this equation, how much would Dominic spend on gasoline to drive a distance of180 miles?A $25.203.628B $21.00 - 2.94C $24.50 -343: 3.02D $28.00
Answers
Answer
Explanation
The equation that
need help asappppppp
Answers
Here, we want to get the length of the ladder
The kind of triangle we have is a right triangle for which obeys the Pythagoras' theorem
According to the theorem, the square of the hypotenuse equals the sum of the squares of the two other sides
The length of the ladder marked as h is the hypotenuse
Thus, we have it that;
[tex]\begin{gathered} h^2=9^2+7^2 \\ h^2\text{ = 81 + 49} \\ h^2\text{ = 130} \\ h\text{ = }\sqrt[]{130} \\ h\text{ = 11.40 meters} \end{gathered}[/tex]a. If Links printing store will make a 150 copies for the cost of $15.00, then what is theunit rate of price per copy?
Answers
ANSWER
$0.10
EXPLANATION
We have that 150 copies are made for a total cost of $15.00
The unit rate of price per copy is the price of each copy of the printing.
To find the unit rate of price per copy, we have to divide the total price by the total number of copies.
So, we have:
[tex]\frac{15}{150}\text{ = \$0.10}[/tex]This means that the unit rate of price per copy is $0.10
which would it be? …….
Answers
Answer:
A
Step-by-step explanation:
for the relationship to be a function, then each value from the input must map to exactly one unique value in the output.
This is the case here si represents a function.
Find the infinite sum of the geometric sequence with a=3,r=3/6 if it exists.S∞=
Answers
ANSWER
[tex]S_{\infty}=6[/tex]EXPLANATION
Given:
1. First term (a) = 3
2. Common ration (r) = 3/6
Desired Outcome:
Infinite sum of the geometric sequence.
The formula to calculate the infinite sum of the geometric sequence
[tex]S_{\infty}=\frac{a(1-r^n)}{1-r}[/tex]Now, as n approaches infinity,
[tex]1-r^n\text{ approaches 1}[/tex]So,
[tex]\frac{a(1-r^n)}{1-r}\text{ approaches }\frac{a}{1-r}[/tex]Therefore,
[tex]S_{\infty}=\frac{a}{1-r}[/tex]Substitute the values
[tex]\begin{gathered} S_{\infty}=\frac{3}{1-\frac{3}{6}} \\ S_{\infty}=\frac{3}{1-\frac{1}{2}} \\ S_{\infty}=\frac{3}{\frac{1}{2}} \\ S_{\infty}=6 \end{gathered}[/tex]Hence, the infinite sum of the geometric sequence is 6.
Rotation of 270° (x,y) or (a,b) becomes
Answers
A totation of 270º will chncge the sign of the x and y coordinate so the condinates will change:
[tex]\begin{gathered} (x,y)\to(-x,-y) \\ (a,b)\to(-a,-b) \end{gathered}[/tex]A number decreased by 7 is less than -6. Find the number.
Answers
Answer:
The number is less than 1.
[tex]x<1[/tex]Explanation:
Let x represent the number.
When the number is decresed by 7, it becomes;
[tex]x-7[/tex]From the question, When the number is decresed by 7 it is less than -6.
So;
[tex]x-7<-6[/tex]Solving the inequality by adding 7 to both sides of the equation. we have;
[tex]\begin{gathered} x-7+7<-6+7 \\ x<1 \end{gathered}[/tex]Therefore, the number is less than 1.
[tex]x<1[/tex]I need some help please Find the inverse function of the given function.1. F(x)= x^2-4/2x^2
Answers
to solve this problem, we can follow some steps
step 1
replace f(x) with y
[tex]\begin{gathered} f(x)=\frac{x^2-4}{2x^2} \\ y=\frac{x^2-4}{2x^2} \end{gathered}[/tex]step 2
replace every x with a y and every y with an x
[tex]\begin{gathered} x=\frac{y^2-4}{2y^2} \\ \end{gathered}[/tex]step 3
solve for y
[tex]\begin{gathered} x=\frac{y^2-4}{2y^2} \\ \text{cross multiply both sides} \\ 2y^2\times x=y^2-4^{} \\ 2y^2x=y^2-4 \\ \text{collect like terms} \\ 2y^2x-y^2=-4 \\ \text{factorize y}^2 \\ y^2(2x-1)=-4 \\ \text{divide both sides by 2x - 1} \\ \frac{y^2(2x-1)}{(2x-1)}=-\frac{4}{(2x-1)} \\ y^2=-\frac{4}{2x-1} \\ \text{take the square root of both sides} \\ y=-\sqrt[]{\frac{4}{2x-1}} \end{gathered}[/tex]therefore the inverse of f(x) is
[tex]f^{-1}(x)=-\sqrt[]{\frac{4}{2x-1}}[/tex]Can anyone help me with this a 7 more problem
Answers
We are given the following statement.
If a number is an integer, then it is either positve or negative.
In the above statement, the 1st part is the condition and the 2nd part is conclusion.
Condition = a number is an integer
Conclusion = it is either positve or negative
Therefore, the conclusion of the conditional is option B.
A number is either positive or negative.
hello can u help me please5.Admission to the Basketball Hall of Fame in Springfield is $5.00 per student. A group of students bought admission tickets. One student spent an extra $9.00 for a poster. The total amount they spent was $34.00. How many students were in the group?a.4b.5c.6d.7
Answers
Given:
The price per student for the admission, m=$5.
Extra amount spent by a student, c=$ 9.
Total amount spent, T=$34.
Let x be the number of students. Then, the expression for the total amount is,
[tex]T=mx+c[/tex]Substitute values and solve for x.
[tex]\begin{gathered} 34=5x+9 \\ 34-9=5x \\ 25=5x \\ x=\frac{25}{5} \\ x=5 \end{gathered}[/tex]Therefore, the number of students is 5.
Option (b) is correct.
Your favorite music artist is inside Best Buy signing autographs. If you are at the back of a single fileline that is 2 miles out the door, how many people are ahead of you? Each person takes up 18 inches.
Answers
there are 7372 people ahead of you
The first thing we will do is state the parameters we are given:
Your location is 2miles from the door.
Each person takes 18inches.
To know the number of people ahead, we will find how many inches make up a mile.
1 mile = 66360inches
[tex]\begin{gathered} 2\text{ miles = 2}\times66360\text{ } \\ =\text{ 132720 inches} \end{gathered}[/tex]Since 1 person = 18inches, the number of persons on that line would be:
[tex]\begin{gathered} =\text{ }\frac{132720}{18} \\ =\text{ 7373 approxi}mately \end{gathered}[/tex]There are 7373 people on the line.
The number of people ahead of you = 7373-1 = 7372
But, there are 7372 people ahead of you
Among all of the pairs of numbers whose difference is 12, the smallest product is
Answers
We have two numbers x and y such that their difference is 12:
[tex]\begin{gathered} x-y=12 \\ \Rightarrow x=12+y \end{gathered}[/tex]Now, we take the product of them:
[tex]x\cdot y=(12+y)\cdot y=y^2+12y[/tex]The smallest result we can get is 0 (ignoring the negative numbers, because the meaning of "small" implies an absolute value). Looking at the expression above, it is 0 for y = 0. If y = 0 then x = 12, and the difference is:
[tex]x-y=12-0=12[/tex]And their product is:
[tex]x\cdot y=12\cdot0=0[/tex]