Answers
We are asked to determine the unit price of two different packages. The unit price is determined by dividing the price of an item over the quantity used to measure that item at the given price. In this case, the unit of measure is "ounce", therefore, we need to determine the price per ounce. The first unit price is determined by dividing the price of $3.19 for 11.5 ounces, like this:
[tex]P_1=\frac{3.19\text{ dollars}}{11.5\text{ ounces}}=0.28\text{ dollar/ounce}[/tex]Since we are told to round to the nearest cent we take the first two digits after the decimal point and we add 1 to the second digit if the third digit is equal to or greater than 5.
Now we use the same procedure to determine the second unit price:
[tex]P_2=\frac{7.98\text{ dollars}}{30.6\text{ ounces}}=0.26\text{ dollar/ounce}[/tex]Since the unit price for the 30.6 ounces package is less than the price for the 11.5 ounces package this means that the second package is a better buy.
Related Questions
Find the distance between the two points: (8, 3) and (-2, 6). Round your answer to 2 decimal places.
Answers
To find the distance between two points we have to use the following formula:
[tex]d=\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]Where d is the distance, x2 and x1 are the x coordinates of the points and y2 and y1 are the y coordinates of the points:
[tex]\begin{gathered} d=\sqrt{(8-(-2))^2+(3-6)^2} \\ d=\sqrt{(10)^2+(-6)^2\frac{}{}} \\ d=\sqrt{100+36} \\ d=\sqrt{136} \\ d=11.66 \end{gathered}[/tex]It means that the distance between these two points is 11.66.
cual es la suma y resta de este monomio: 8a - 10a + 14a.
Answers
En el monomio:
[tex]8a-10a+14a[/tex]Al ser terminos semejantes (todos tienen la misma variable "a") los terminos que se restan son 8a-10a= -2a, a este resultado se le suma 14a:
[tex]\begin{gathered} =-2a+14a \\ =12a \end{gathered}[/tex]Entonces, el monomio es 12aFind the sum and enter it in the box below. Enter your answer as a polynomialin descending order, and use the caret() for exponents. For example, youwould write 4x as 4x^2.(x8 - x) + (3x + 2)
Answers
(x^8-x)+(3x^8+2) = (opperating like terms:)
x^8+3x^8-x+2 =
4x^8-x+2
The answer will be 4x^8-x+2
I need help finding out the answer to this problem! I tried solving it but it just gave me a point on a graph, not just 1 number.....
y-65=-(x-22) 4x-y=23
Answers
Answer:
(22, 65)
x = 22, y = 65
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}y-65=-(x-22)\\ 4x-y=23\end{cases}[/tex]
Rearrange the first equation to make y the subject:
[tex]\implies y-65=-(x-22)[/tex]
[tex]\implies y-65=-x+22[/tex]
[tex]\implies y-65+65=-x+22+65[/tex]
[tex]\implies y=-x+87[/tex]
Substitute the rearranged equation into the second equation and solve for x:
[tex]\implies 4x-y=23[/tex]
[tex]\implies 4x-(-x+87)=23[/tex]
[tex]\implies 4x+x-87=23[/tex]
[tex]\implies 5x-87=23[/tex]
[tex]\implies 5x-87+87=23+87[/tex]
[tex]\implies 5x=110[/tex]
[tex]\implies \dfrac{5x}{5}=\dfrac{110}{5}[/tex]
[tex]\implies x=22[/tex]
Substitute the found value of x into the rearranged first equation and solve for y:
[tex]\implies y=-x+87[/tex]
[tex]\implies y=-22+87[/tex]
[tex]\implies y=65[/tex]
Therefore, the solution to the system of equations is:
[tex]x = 22, \quad y = 65[/tex]The solution in (x, y) form is (22, 65).
Note: If the question requires only one number as the answer, it is likely that it wants only the x-value of the solution, which in this case is x = 22.
The solution to the system of equations are (x,y) 22 and 65 respectively.
What is an equation?A system of equations is a group of two or more equations with the same variables. A solution to a system of equations is the values of the variables that make all of the equations in the system true.
Rearranging the first equation which is y - 65 = -(x - 22) will be y = -x + 87.
Substitute the rearranged equation into the second equation and then solve for x.
4x - y = 23
4x - (-x + 87) = -23
Collect like terms
5x = 110
Divide
x = 110 / 5
x = 23
Since y = -x + 87.
y = -22 + 87
y = 65
Learn more on system of equations here;
https://brainly.com/question/13729904
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I need an answer and explanation about how it corrects the misconceptions the artist had
Answers
The artist thought a decrease of 14% over the original tile 50 x 50, that's why she thought 49 x 49 was wrong.
But when she calculated she correctly calculated a decrease by 14% over the 57 x 57 tile that's how she had the same results.
1) Since the ceramic artist is aware that clay shrinks by 14% then the calculation should be:
[tex]50\cdot(1+0.14)=57[/tex]2) So since the dimensions will shrink it, then this artist correctly calculated the new tile to 57 x 57 (since squares have the same length and width)
2.2) When the clay was in the oven, it shrank following this equation (minus 14%):
[tex]57\times(1-0.14)=57\times(0.86)=49.02[/tex]She thought that there was an error, probably because she calculated
a decrease of 14% of that original tile would yield a 43 x 43 tile, instead
of 57 x 57 Because: 50x ( 1-0.14)= 43.
3) Hence, the answer is:
The artist calculated a decrease of 14% over the original tile 50 x 50, that's
why she thought 49 x 49 was wrong.
Triangle B is rotated 180° about the origin. Which triangle shows the image?
Answers
A 180 degree rotation transform the points like:
The triangle that correspond to a rotation of 180 degrees of the Triangle B is Triangle D.
If we look at the vertices and transform them one by one, we would get the vertices of triangle D.
Answer: Triangle D.
The shapes below have congruent perimeters. Find the value of x.
Answers
Step-by-step explanation:
that is a strange way to express to situation.
what they mean here is that the perimeters are of identical lengths.
other than the total length the perimeters have nothing in common. therefore, I would have never used the word "congruent" for that. if that would have been the answer to a question like "what statement describes the relationship between the 2 perimeters ?", I would have flagged this as wrong.
anyway, so, the perimeters are of equal length. that means
x + 6 + x + 3 + x + 9 = 2(x + 4) + 2(x + 1)
3x + 18 = 2x + 8 + 2x + 2 = 4x + 10
3x + 8 = 4x
8 = x
Find the area. Leave answer in terms of pi.A) 91 kmC) 647 kmB) 167 kmD) 257 km
Answers
The figure we have is a circle and we need to find its area.
To find the area of any circle we use the following formula:
[tex]A=\pi r^2[/tex]Where A is the area, and r is the radius of the circle.
Step 1. Identify the radius of the circle.
The radius is a line that goes from the center of the circle to a point in the circumference. In this case, the radius is shown in red in the following diagram:
Thus:
[tex]r=5kn[/tex]Step 2. Once we know the radius, we can substitute its value into the area formula:
[tex]A=\pi r^2[/tex]substituting r=5km:
[tex]A=\pi(5km)^2[/tex]And we solve the operations since 5^2 is equal to 25:
[tex]A=25\pi km^2[/tex]The indications are to leave the answer in terms of pi, which means that we don't substitute the value of pi in the answer, thus, that is the final answer.
Answer:
[tex]D)\text{ }25\pi km^2[/tex]The expected number y (in millions) of employed registered nurses x years after 2012 is given by the equation y=0.83x +2.71.a) Find the slope of this equation. Explain what this slope signifies.b) Find the y-intercept of the equation. Explain what this y-intercept signifies.c) Use the equation to predict the number of employed registered nurses 2027.(Type integers or decimals.)OA. The slope of the equation is which signifies that in 2012 there were approximately million employed registered nurses.B. The slope of the equation is which signifies that each year the number of employed registered nurses will increase byOC. The slope of the equation is, which signifies that each year the number of employed registered nurses will decrease byb) Select the correct choice below and fill in the answer boxes to complete your choice.(Type an ordered pair. Type an integer or a decimal.)A. The y-intercept isB. The y-intercept isC. The y-intercept isc) The predicted number of employed registered nurses in 2027 is million.which signifies that each year the number of employed registered nurses will decrease bywhich signifies that each year the number of employed registered nurses will increase bywhich signifies that in 2012 there were approximately million employed registered nurses.million.million.million.million.
Answers
Given: The equation relating the expected number of employed registered nurses and the number of years after 2012 is
[tex]y=0.83x+2.71[/tex]To Determine: The slope
Solution
Given the general equation of a line in slope-intercept form
[tex]\begin{gathered} y=mx+c \\ m=slope \\ c=y-intercept \end{gathered}[/tex]Let us compare the given equation to the general equation of a line in slope-intercept form as shown above
[tex]\begin{gathered} y=mx+c \\ y=0.83x+2.71 \\ slope=m=0.83 \\ y-intercept=c=2.71 \end{gathered}[/tex]The total number of years from 2012 to 2027 is
[tex]\begin{gathered} x=2027-2012 \\ x=15 \end{gathered}[/tex][tex]\begin{gathered} y=0.83x+2.71 \\ y=0.83(15)+2.71 \\ y=12.45+2.71 \\ y=15.16 \end{gathered}[/tex]Hence:
(a) The slope is 0.83, which signifies that each year the number of employed registered nurses will increase by 0.83 million, OPTION B
(b) The y-intercept is 2.71, which signifies that in 2012 there were approximately 2.71 million employed registered nurses, OPTION C
(c) The predicted number of employed number of registered nurses in 2027 is 15.16 million
Question 8 of 40The cost of renting a bicycle is $9 for the first hour plus another $4 for eachadditional hour. Which of the following represents this situation, where Cisthe total cost of renting a bicycle for h hours?O A. C= 9h+4O C. C = 13hOD. C= 4h+9SUBMITB. C= 4(h-1) +9°
Answers
Based on the given information, for 1 hour the cost is $9, for additional hours each hour cost $4. For example, for 2 hours, the cost is $4 + $9 = $13 and for 3 hours is $4 + $4 + $9 = $17.
Based on the previous calculation, you can conclude that following expression represent the given situation.
C = 4(h - 1) + 9
Hence, the answer is option B.
Please show me how to solve/graph this Algebra 2 problem step by step, thank you!
Answers
Explanation:
Step 1. We have a piecewise function defined for certain x value intervals.
for x values between -4 and -1, the definition is:
[tex]f(x)=x+6,\text{ for }-4And for the x values between -1 and 5, the definition is:[tex]f(x)=-2x+7,\text{ for }-1Step 2. We need to graph the function, for that, we start with the definition for x values between -4 and -1[tex]\begin{equation*} f(x)=x+6 \end{equation*}[/tex]To graph this, we compare it with the general line function
[tex]f(x)=mx+b[/tex]where m is the slope (the rate of change of the line) and b is the y-intercept. In this case, for f(x)=x+6, the slope is m=1, and the y-intercept is 6, if we were to graph this line in the whole plane, it would look as follows:
But since this is just the definition of the function for the values between -4 and -1, the result is:
Step 3. Now we consider the second definition of the function:
[tex]\begin{equation*} f(x)=-2x+7 \end{equation*}[/tex]Comparing it with the general line function
[tex]f(x)=mx+b[/tex]where m is the slope (the rate of change of the line) and b is the y-intercept.
Here in f(x)=-2x+7, the slope is m=-2, and the y-intercept is b=7, which means that the line is decreasing at a rate of -2, and that it crosses the y-axis at 7.
If we were to graph this line in the whole plane, it will look as follows (in blue):
But since that is the definition of the function only for the interval from -1 to 5, we only consider the line for that specific x-interval, we represent the point at -1 with an open circle and at 5 with a filled circle to represent that 5 is included in the segment:
Answer:
20 over 25 equals 60 over 75 true or false
Answers
20 over 25 equals 60 over 75 true or false
we have
20/25=60/75
Multiply the left side by 3/3
(3/3)(20/25)=60/75
so
60/75=60/75
therefore
answer is truewhat does the point (1,5) represent
Answers
The point (1,5) is:
Like it is shown this means that we have to move one unit in the right direction and 5 units up.
This question: 1point(s) possibleThe recommended dosage of a drug for pediatric patients is 200 mg per kilogram of a patient's weight. If John weighs 80 lb, how much of the drug should he receive?Use the fact that 1 lb =0.45 kgJohn should receive about milligrams of the drug.(Round to the nearest milligram as needed.)
Answers
SOLUTION:
Case: Proportions
Method:
The recommended dosage of a drug for pediatric patients is 200 mg per kilogram
We calculate John's weight in kg
Since
[tex]\begin{gathered} 1lb\equiv0.45kg \\ 80lb=80\times0.45 \\ =36kg \end{gathered}[/tex]Next, the drug should he receive
[tex]\begin{gathered} 200mg\text{ }per\text{ }kg \\ \therefore36kg\rightarrow36\times200 \\ =7200mg \end{gathered}[/tex]Final an
Please solve this and it also says show work, I really need help!
Answers
Explanation
Given that 12 players chose a bottle of water which is 3/4 of the total number of players (p). The equation to determine p can be seen below
We can create the equation below;
[tex]\begin{gathered} \frac{3}{4}\text{ of p =12} \\ \frac{3}{4}\times P=12 \\ Cross\text{ multiply} \\ 3p=12\times4 \\ Divide\text{ both sides by 3} \\ p=\frac{12\times4}{3} \\ p=4\times4 \\ p=16 \end{gathered}[/tex]Answer: The total number of players at the baseball game is 16
Solve on the interval [0, 2pi):3 sec x - 2 = 13 sec x =3secx= 1cos = -1Is it 0?
Answers
3 sec x - 2 = 1
Add 2 to both sides
3 sec x = 1+ 2
3 sec x = 3
divide both sides by 3
sec x = 3/3
sec x = 1
[tex]\begin{gathered} \text{ sec x = 1} \\ x=sec^{-1}1 \\ x\text{ = 0 } \\ \text{and also, the interval is \lbrack{}0, 2}\pi\rbrack \\ x\text{ = 2}\pi \\ \text{The answer is x = 0 and x = 2}\pi \end{gathered}[/tex]Wendy is a waitress and has $15,000 toinvest, and wishes to gain $4,200 in interestover the next eight years. Approximatelywhat is the minimum simple interest rateWendy needs to reach her goal?
Answers
The formula for determining simple interest is expressed as
I = PRT/100
where
I = interest earned
R = interest rate
T = number of years
P = principal or amount invested
From the information given,
P = 15000
I = 4200
T = 8
Thus, we have
4200 = (15000 x R x 8)/100
4200 = 1200R
R = 4200/1200
R = 3.5
The required interest rate is 3.5%
Solve using substitution methody= -5x + 2y= -10x + 7
Answers
ANSWER
(1, -3)
EXPLANATION
Since we have y in function of x in both equations, we can replace the first equation into the second and solve for x:
[tex]\begin{gathered} -5x+2=-10x+7 \\ -5x+10x=7-2 \\ 5x=5 \\ x=1 \end{gathered}[/tex]And then replace x = 1 into one of the equations to find the value of y:
[tex]\begin{gathered} y=-5x+2 \\ y=-5\cdot1+2 \\ y=-5+2 \\ y=-3 \end{gathered}[/tex]The solution is (1, -3)
solve the equation for y7x + 4y = 8
Answers
To solve the equation for a variable we need to isolate the variable on the left side of the equation. The expression is:
[tex]7x+4y=8[/tex]To start we need to subtract by "7x" on both sides of the equation.
[tex]\begin{gathered} 7x+4y-7x=8-7x \\ 4y=8-7x \end{gathered}[/tex]We then need to divide both sides by 4.
[tex]\begin{gathered} \frac{4y}{4}=\frac{8-7x}{4} \\ y=\frac{8-7x}{4} \end{gathered}[/tex]= help please!!
ODECIMALS
Ordering decimals
Order these numbers from least to greatest.
1.85, 1.7, 1.805, 1.7051
Answers
Answer:
1.7, 1.7051, 1.805, 1.85
Step-by-step explanation:
Which situation can be modeled by the equation y= 3x + 25? Select one: A rental car costs $25 per day plus a $3 charge for cleaning. A rental car costs a one-time fee of $25 plus $3 for each hour. A rental car costs a one-time fee of $25 plus an additional $3 charge for processing. A rental car costs $25 per day plus $3 per gallon of fuel needed upon return to fill the tank.
Answers
Here, given the linear equation, we want to select which of the options can correctly be modeled by the given equation
As we can see from the equation, the cost $25 represents a fixed cost, while 3 multiplied by x is based on a certain recurring amount
Thus, we can have our answer here as;
A rental car costs a one-time fee of $25 plus $3 for each hour
The $25 is the fixed cost, while the other amount that adds to it is dependent on the number of hours for which the car was driven
a. if a circle has a circumference of 8π cm, what is it's area? b. If a circle of radius r, and a square with a side length b have equal areas, express r in terms of b.
Answers
Given:
(a) Circumference of a circle is
[tex]8\pi[/tex]To find: Area of circle
Circumference of circle is given as:
[tex]\text{circumference}=2\pi r=8\pi[/tex]where, r is radius of circle
On solving,
[tex]\begin{gathered} 2\pi r=8\pi \\ r=4 \end{gathered}[/tex]Area of circle is given by formula:
[tex]\begin{gathered} \text{area=}\pi\times r^2^{} \\ =\pi\times4^2 \\ =16\pi \end{gathered}[/tex]Hence, area of circle is :
[tex]=16\pi\text{ squares cm}[/tex](b) Radius of circle is given 'r' and square of length is given 'b'
and they have equal areas.
To find: r in terms of b.
According to the question,
Area of circle= Area of square
[tex]\begin{gathered} \pi\times r^2=b^2 \\ r^2=\frac{b^2}{\pi} \\ r=\sqrt[]{\frac{b^2}{\pi}} \\ =\frac{b}{\sqrt[]{\pi}} \end{gathered}[/tex]Hence,
[tex]r=\frac{b}{\sqrt[]{\pi}}[/tex]Can some help me answer this
Answers
Seeing that my graph cuts the y axis from the table at -2, the only graph that cuts at -2 is graph b.
Find -48a divided by 8 when a=1 write your answer in simplest form
Answers
-48a÷ 8 can be written as,
[tex]\frac{-48a}{8}[/tex]Put a=1 in the above exprression and solve.
[tex]\frac{-48\times1}{8}=-6[/tex]Therefore, the solution is -6.
where would the shape be located after a translation of 5 units to the right
Answers
First we determine the coordinates of the points of the shape:
p1 (-2, 4)
p2 (-2, 1)
p3 (-4, 3)
p4 (-4, 4)
After that, we add +5 to the x components, getting the following:
P1' (3, 4)
P2' (3, 1)
P3' (1, 3)
P4' (1, 4)
Answer the questions below about the quadratic function. g(x) = 3x ^ 2 - 6x + 5
Answers
In order to find a critical value (maximum or minimum) we need to compute the first derivative, which is given by
[tex]\frac{d}{dx}g(x)=6x-6[/tex]Then, a critical value ocurrs when
[tex]\frac{d}{dx}g(x)=0[/tex]which implies that
[tex]6x-6=0[/tex]So by adding 6 to both side, we have
[tex]\begin{gathered} 6x=6 \\ then \\ x=\frac{6}{6} \\ x=1 \end{gathered}[/tex]Therefore, there is a maximum or minimum at x=1.
In order to see if the point represents a maximum or minimum, we need to find the second derivative of our function, which is given by
[tex]\frac{d^2}{dx^2}g(x)=6[/tex]We have that if the second derivative is positive, the point represents a minimum and if it is negative, the point represents a maximum. In our case, since the second derivative is greater than zero (positive number) there is a minimum point at x=1. Then, by substituting this values into the function, we get
[tex]\begin{gathered} g(1)=3(1^2)-6(1)+5 \\ g(1)=3-6+5 \\ g(1)=2 \end{gathered}[/tex]so the minimum point is located at (1,2).
Therefore, with the above information, the answers are:
Does the function have a minimum or maximum values? Answer: Minimum
Where does the minimum or maximum value occur? Answer: x=1
Whats is the funtion's minimum or maximum values? Answer: 2
Find the sum of the interior angles of the shape. Use the remaining angles to solve for x. Polygons Help118105759130Sum of interior angles =degreesdegrees
Answers
Answer:
x = 112
Explanation:
The figure given is a pentagon; therefore, the sum of interior angles must add up to 540 degrees.
This means
[tex]105^o+118^o+75^o+130^o+x=540^o[/tex]Adding the angles on the left-hand side gives
[tex]428^o+x=540^o[/tex]Finally, subtracting 428 from both sides gives
[tex]428^o+x-428^o=540^o-428^o[/tex][tex]x=540^o-428^o[/tex][tex]x=112^o[/tex]which is our answer!
a business has $5000 in cash, but then it pays $500 cash to make a purchase. after the transaction is posted, what is the balance in the Cash T-account a. $500 credit balanceb. $500 debit balancec.$4500 credit balanced. $4500 debit balance
Answers
The initial amount of cash, P=$5000.
The amount paid for purchase, C=$500.
The balance amount after paying for a purchase is,
[tex]\begin{gathered} B=P-C \\ =5000-500 \\ =4500 \end{gathered}[/tex]Therefore, the credit balance is $4500.
Hence, option c is correct.
find the of change of the distance D from the origin of a point moving on the graph off …dx/dt= 9 units per second. Write the exact answer do not round
Answers
Given:
D is start origin that mean (0,0) moving with graph :
[tex]f(x)=x^2[/tex]It move x then y is
[tex]\begin{gathered} f(x)=x^2 \\ y=x^2 \end{gathered}[/tex]Point is (2,4)
Distance is:
[tex]D=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2_{}}[/tex]Where,
[tex]\begin{gathered} x_2=x \\ x_1=0 \\ y_2=x^2 \\ y_1=0 \end{gathered}[/tex]So distance is:
[tex]\begin{gathered} D=\sqrt[]{(x-0)^2+(x^2-0)^2} \\ D=\sqrt[]{x^2+x^4} \end{gathered}[/tex][tex]\begin{gathered} \frac{dD}{\differentialDt t}=\frac{d(\sqrt[]{x^2+x^4})}{\differentialDt t} \\ =\frac{1}{2\sqrt[]{x^2+x^4}}(2x+4x^3)\frac{dx}{\differentialDt t} \end{gathered}[/tex][tex]\begin{gathered} \text{when x=2} \\ \frac{dx}{\differentialDt t}=9 \end{gathered}[/tex][tex]\begin{gathered} =\frac{1}{2\sqrt[]{(2^2+2^4)}}((2\times2)+(4\times2^3))\times9 \\ =\frac{324}{6.92820} \\ =46.7653 \end{gathered}[/tex]Solve the inequality for x: x−1x−2≥0
Answers
Given:
Inequality is
[tex]\frac{x-1}{x-2}\ge0[/tex]Required:
Solve the inequality.
Explanation:
We have inequality greater than or equal to zero.
So, this can happen only when both numerator and denominator positive or negative.
Fraction will be positive when x less than or equal 1 and when x greater than 2.
So, it is
[tex](-\infty,1]or(2,\infty)[/tex]Answer:
Hence, option B is correct.