the graph shows that school's profit P for selling x lunches on one day.The school wants to change the price for lunch so that when it sells more than 30 lunches in one day, it begins to make a profit.How much would the school need to charge for each lunch situation?
Answers
Find the slope of the line. That will give us the present price for each lunch.
Use the points (0,-150) and (50,0):
[tex]\begin{gathered} m=\frac{0--150}{50-0} \\ \Rightarrow m=3 \end{gathered}[/tex]Then, the current profit equation is given by:
[tex]y=3x-150[/tex]We want to change the price of each lunch so that the point (30,0) belongs to the graph (that means that when selling 30 lunches, it begins to make profit).
Let M be the new price. Then:
[tex]\begin{gathered} 0=30M-150 \\ \Rightarrow30M=150 \\ \Rightarrow M=\frac{150}{30} \\ \therefore M=5 \end{gathered}[/tex]Therefore, the school should charge 5 dollars for each lunch.
Related Questions
-7.9 cm 26.2 cm 6.2 cm 19.1 cm 2.8 cm The perimeter of the figure is (Type a whole number or a decal.) .
Answers
ANSWER
The perimeter is 81.5 cm
EXPLANATION
The perimeter of any polygon is the sum of the length of its sides. The perimeter of this figure is:
[tex]P=7.9+26.2+6.2+22.8+18.4=81.5\operatorname{cm}[/tex]A resident is to receive 2 ounces of liquid . You know 30 ccs equals one ounce . How many ccs of the liquid will you give to ensure the resident receives 2 ounces
Answers
From the statement of the question, we know that 1 ounce and 30ccs are equivalent, we represent that with the following equation:
[tex]1\text{ounce}=30\text{ccs.}[/tex]Now, 2 ounces is double of 1 ounce, because 1 ounce is 30 ccs, 2 ounces must be 60ccs, the double of 30ccs.
[tex]2\text{ounces}=2\cdot1\text{ounce}=2\cdot30\text{ccs}=60\text{ccs.}[/tex]So if we want to ensure that the resident will receive 2 ounces of liquid, we must give him 60ccs.
Answer: we must give him 60ccs of liquid.
Which relation represents a function sample A or sample B
Answers
Sample A is a function because we don't have 2 values of x that are the same
Sample B is not a function, because it fails the vertical line test (x = 4 and y =1 also x=4 and y = 10) (4, 1) and (4, 10)
Hence the correct option is ; sample A
Solving a trigonometric equation involving an angle multiplied by a constant
Answers
In these questions, we need to follow the steps:
1 - solve for the trigonometric function
2 - Use the unit circle or a calculator to find which angles between 0 and 2π gives that results.
3 - Complete these angles with the complete round repetition, by adding
[tex]2k\pi,k\in\Z[/tex]4 - these solutions are equal to the part inside the trigonometric function, so equalize the part inside with the expression and solve for x to get the solutions.
1 - To solve, we just use algebraic operations:
[tex]\begin{gathered} \sqrt[]{3}\tan (3x)+1=0 \\ \sqrt[]{3}\tan (3x)=-1 \\ \tan (3x)=-\frac{1}{\sqrt[]{3}} \\ \tan (3x)=-\frac{\sqrt[]{3}}{3} \end{gathered}[/tex]2 - From the unit circle, we can see that we will have one solution from the 2nd quadrant and one from the 4th quadrant:
The value for the angle that give positive
[tex]+\frac{\sqrt[]{3}}{3}[/tex]is known to be 30°, which is the same as π/6, so by symmetry, we can see that the angles that have a tangent of
[tex]-\frac{\sqrt[]{3}}{3}[/tex]Are:
[tex]\begin{gathered} \theta_1=\pi-\frac{\pi}{6}=\frac{5\pi}{6} \\ \theta_2=2\pi-\frac{\pi}{6}=\frac{11\pi}{6} \end{gathered}[/tex]3 - to consider all the solutions, we need to consider the possibility of more turn around the unit circle, so:
[tex]\begin{gathered} \theta=\frac{5\pi}{6}+2k\pi,k\in\Z \\ or \\ \theta=\frac{11\pi}{6}+2k\pi,k\in\Z \end{gathered}[/tex]Since 5π/6 and 11π/6 are π radians apart, we can put them together into one expression:
[tex]\theta=\frac{5\pi}{6}+k\pi,k\in\Z[/tex]4 - Now, we need to solve for x, because these solutions are for all the interior of the tangent function, so:
[tex]\begin{gathered} 3x=\theta \\ 3x=\frac{5\pi}{6}+k\pi,k\in\Z \\ x=\frac{5\pi}{18}+\frac{k\pi}{3},k\in\Z \end{gathered}[/tex]So, the solutions are:
[tex]x=\frac{5\pi}{18}+\frac{k\pi}{3},k\in\Z[/tex]Use the Distributive Property
solve the equation.
- 6(x + 3) = 30
Answers
Using the Distributive Property of multiplication, the equation - 6(x + 3) = 30 is solved as x = -8.
What is the distributive property of multiplication?The distributive property of multiplication shows that a mathematical expression in the form of a(b + c) is also equal to ab + ac.
The distributive property applies to either addition or subtraction in multiplication.
- 6(x + 3) = 30
-6x - 18 = 30
-6x = 48
x = -8
Thus, x = -8 is the solution to the equation - 6(x + 3) = 30.
Learn more about the distributive property at https://brainly.com/question/4077386
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For a winter-themed Valentine's Day party, Mr. Rivera made 12 cups of hot chocolate. Does he have enough hot chocolate to give 26 kids 1/2 of a cup each?
Answers
Multiply the number of kids by the number of cups for each kid. This is 26 times 1/2.
[tex]26\cdot\frac{1}{2}=\frac{26}{2}=13[/tex]It means 13 cups are needed to give each of the 26 kids 1/2 of a cup of chocolate.
Mr. Rivera does not have enough hot chocolate to give 26 kids 1/2 of a cup of chocolate.
a rectangle has the perimeter of 116 cm and its length is 1cm more than twice its width. I got 39L and 19w but I'm having problems setting up the problems
Answers
To answer this question, we can proceed as follows:
1. We have that the perimeter of the rectangle is equal to 116cm, then, we have:
[tex]w+l+w+l=116\Rightarrow2w+2l=116[/tex]We know that a rectangle is a parallelogram. Then, its opposite sides are congruent.
2. We have that the length of the rectangle is 1 cm more than twice its width. We can translate this, algebraically, as follows:
[tex]l=2w+1[/tex]Now, to find the measures of the length and the width of the rectangle, we can substitute this last formula into the first one, as follows:
[tex]2w+2(2w+1)=116[/tex]We need to apply the distributive property to find w:
[tex]2w+4w+2=116[/tex]Adding like terms:
[tex]6w+2=116[/tex]Subtracting 2 to both sides of the equation, and then dividing by 6:
[tex]6w+2-2=116-2\Rightarrow6w=114\Rightarrow\frac{6w}{6}=\frac{114}{6}\Rightarrow w=19[/tex]Then, the width of the rectangle is equal to 19cm. The measure of the length can be calculated using either equation above. Let us use the first equation:
[tex]2w+2l=116\Rightarrow2\cdot19+2l=116\Rightarrow38+2l=116[/tex]Then, using similar properties as before, we have:
[tex]38-38+2l=116-38\Rightarrow2l=78\Rightarrow\frac{2l}{2}=\frac{78}{2}\Rightarrow l=39[/tex]In summary, we have that the measures of the length and width of this rectangle are:
• Width, ,(w) =, 19cm
,• Legth (l) = ,39cm
Need help with this exercise. It’s from a review the real test is next week need more explanation so I already know what to do on the test.
Answers
ANSWER
Options 1 and 4
EXPLANATION
First, let us find the length of the third side of the right triangle. To do this apply the Pythagoras theorem.
Let the length of the third side of the triangle be x.
It implies that:
[tex]\begin{gathered} x^2+8^2=17^2 \\ x^2=17^2-8^2 \\ x^2=289-64=225 \\ x=\sqrt[]{225} \\ x=15 \end{gathered}[/tex]Now, we can find the value of sinA, tanA, and sinC.
According to trigonometric ratios, SOHCAHTOA, we have that:
[tex]\begin{gathered} \sin A=\frac{\text{opposite}}{\text{hypotenuse}} \\ \tan A=\frac{\text{opposite}}{\text{adjacent}} \\ \sin C=\frac{\text{opposite}}{\text{hypotenuse}} \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} \sin A=\frac{15}{17} \\ \tan A=\frac{15}{8} \\ \sin C=\frac{8}{17} \end{gathered}[/tex]Hence, the correct options are options 1 and 4.
Team A, B, and C are competing in a basketball tournament. The probability of team A winning is 0.2, the probability of team B winning is 0.45, and the probability of team C winning is 0.35. Anna can join either team A or team B. Elina can join either team B or team C. Nancy can join either team A or team C. Who is most likely to win?AnnaNancyElenaAll have an equal probability to win.
Answers
Solution
We are given that
[tex]\begin{gathered} p(A)=0.2 \\ p(B)=0.45 \\ p(C)=0.35 \end{gathered}[/tex]Note 1: Probability Formula To use
[tex]p(A\cup B)=p(A)+p(B)-p(A\cap B)[/tex]Note 2: Team A, B and C are Mutually Exclusive
[tex]\begin{gathered} p(A)+p(B)+p(C)=0.2+0.45+0.35=1 \\ Th\text{ey are mutually exclusive} \\ A\cap B=B\cap C=A\cap C=\varnothing \\ p(A\cap B)=p(B\cap C)=p(A\cap C)=0 \end{gathered}[/tex]Therefore, the formula to use now is
[tex]p(A\cup B)=p(A)+p(B)[/tex]For Anna
Anna can join either team A or team B.
We calculate the probability
[tex]\begin{gathered} p(A\cup B)=p(A)+p(B) \\ p(A\cup B)=0.2+0.45 \\ p(A\cup B)=0.65 \end{gathered}[/tex]For Elina
Elina can join either team B or team C.
We calculate the probability
[tex]\begin{gathered} p(B\cup C)=p(B)+p(C) \\ p(B\cup C)=0.45+0.35 \\ p(B\cup C)=0.8 \end{gathered}[/tex]For Nancy
Nancy can join either team A or team C.
We calculate the probability
[tex]\begin{gathered} p(A\cup C)=p(A)+p(C) \\ p(A\cup C)=0.2+0.35 \\ p(A\cup C)=0.55 \end{gathered}[/tex]The one with the highest probability is most likely to win and that is
ELINA
Correct answer is Elina
Allen is choosing a 2 letter password from the letters ABCD. the password cannot be the same letter repeated in it .how many such passwords are possible?
Answers
Since we can choose 2 letters and they can not be the same, we have the following possibilities:
[tex]{}\lbrace AB,AC,AD,BC,BD,BA,CB,CA,CD,DA,DB,DC\rbrace[/tex]As we can note, there are 12 possible combinations of 2 different letters. So, How many such passwords are possible? The answer is 12 passwrods
Hello am I correct, if not can you help me understand?
Answers
total kilometer of journey = 353miles
she stopped at mile 36
nQuestion 6Mutiple Choice Worth 1 points)(06.04 MC)The length of a rectangle is represented by the function L(x)= 2x. The width of that same rectangle is represented by the function W(x)=8x²-4x+1. Which of the following shows the area of the rectangle interms of x?(L+ W)(x)=8x²-2x+1(L + W)(x)=8x² - 6x +1(L• W)(x)=16x-4x+1(L • W)(x)=16x³-8x²+2x
Answers
Answer:
[tex]D\text{ :}(L\text{ }\circ\text{ W\rparen\lparen x\rparen= 16x}^3-8x^2+2x[/tex]Explanation:
Here, we want to select the option that best represents the area of the rectangle in terms of x
Mathematically, the area can be calculated by:
[tex]A(x)\text{ = L\lparen x\rparen }\times\text{ W\lparen x\rparen}[/tex]We have that as:
[tex]\begin{gathered} 2x\text{ }\times\text{ 8x}^2-4x+1 \\ =\text{ 2x\lparen8x}^2-4x+1) \\ =\text{ 16x}^3-8x^2+2x \end{gathered}[/tex]A survey of a random sample of voters showsthat 56% plan to vote Yes to the newproposition and 44% plan to vote No. Thesurvey has a margin of error of +4%. What isthe range for the percentage of voters whoplan to vote Yes?
Answers
Answer:
G 52% to 60%
Explanation:
The percentage of voters that plan to vote Yes = 56%
The survey's margin of error = +/-4%
Therefore, the range for the percentage of voters who plan to vote Yes is:
[tex]\begin{gathered} 56\%\pm4\% \\ =56\%-4\%\text{ to }56\%+4\% \\ =52\%\text{ to }60\% \end{gathered}[/tex]The correct choice is G.
Don’t know how to solve with the -1 before the x
Answers
ANSWER and EXPLANATION
We are given a function and its inverse function:
[tex]\begin{gathered} f(x)=\frac{1}{2}x \\ f^{-1}(x)=2x \end{gathered}[/tex]To solve the problems, we have to substitute the values of x in the brackets into the appropriate function (or inverse function).
Therefore, we have that the value of the function for x = 2:
[tex]\begin{gathered} f(2)=\frac{1}{2}\cdot2 \\ f(2)=1 \end{gathered}[/tex]For x = 1, we have that the value of the inverse function is:
[tex]\begin{gathered} f^{-1}(1)=2(1) \\ f^{-1}(1)=2 \end{gathered}[/tex]For x = -2, we have that the value of the inverse function is:
[tex]\begin{gathered} f^{-1}(-2)=2\cdot-2 \\ f^{-1}(-2)=-4 \end{gathered}[/tex]For x = -4, we have that the value of the function is:
[tex]\begin{gathered} f(-4)=\frac{1}{2}\cdot-4 \\ f(-4)=-2 \end{gathered}[/tex]For the fifth option, substitute the value of the function at x = 2 into the inverse function.
That is:
[tex]\begin{gathered} f^{-1}(f(2))=f^{-1}(1)=2\cdot1 \\ f^{-1}(f(2))=2 \end{gathered}[/tex]For the sixth option, substitute the value of the inverse function at x = -2 into the function.
That is:
[tex]\begin{gathered} f(f^{-1}(-2))=f(-4)=\frac{1}{2}\cdot-4 \\ f(f^{-1}(-2))=-2 \end{gathered}[/tex]To find the general form of the function:
[tex]f^{-1}(f(x))=f(f^{-1}(x))[/tex]either substitute the function for x in the inverse function or substitute the inverse function for x in the function.
Therefore:
[tex]\begin{gathered} f^{-1}(f(x))=2(\frac{1}{2}x)) \\ f^{-1}(f(x))=x \end{gathered}[/tex]That is the answer.
I need help with this questionthe question to this question is below is a graph of a logarithmic function, identify it key characteristics. match accordingly
Answers
The answers to the problem :
[tex]\begin{gathered} 1.\text{ Domain : x >-6} \\ 2\text{ Range : -}\infty\text{ to +}\infty \\ 3.\text{ Aymptote : x = -6} \\ 4\text{. Transformation : left 6, down 1} \\ 5.\text{ End behaviour : As x approaches }\infty,\text{ f(x) approaches }\infty.\text{ As x approaches -6, f(x) approaches -}\infty \\ 6.\text{ x-intercept : (-4,0)} \end{gathered}[/tex]If you receive 360 promotional emails per month and only 2.5% percent of those emails are of interest to you, what is the expected number of promotional emails that will be of interest to you each month?
Answers
Total email 360
percentage email of interest 2.5%
Solution[tex]\begin{gathered} \frac{2.5}{100}\times360=9 \\ \end{gathered}[/tex]The final answer9 promotional emails that will be of interest to you each month210000The first five multiples for the numbers 4 and 6 are shown below.Multiples of 4: 4, 8, 12, 16, 20, ...Multiples of 6: 6, 12, 18, 24, 30,...What is the least common multiple of 4 and 6?222122423 24 25Mark this and returnSave and ExitNext
Answers
Answer: 12
Explanation
The least common multiple can be calculated by getting the factor of each number. As we are told, the multiples of 4 are 4, 8, 12, 16, 20, ..., and the multiples of 6 are 6, 12, 18, 24, 30, ....
Thus, the lowest factor that they share is 12.
Which of the following equations is equivalent to log(y)= 3.994
Answers
ANSWER:
[tex]y=10^{3.994}[/tex]STEP-BY-STEP EXPLANATION:
We have the following expression:
[tex]log\mleft(y\mright)=3.994[/tex]Applying property of logarithms we have:
[tex]\begin{gathered} \log _a(b)=c\rightarrow b=a^c \\ \text{ in this case:} \\ log(y)=3.994\rightarrow y=10^{3.994} \end{gathered}[/tex]lebron walked 4 1/2 miles to library in 2 1/4 hours. he walked the return trip at the same average rate , but a different route, taking my 2 1/2 hours. How many miles did lebron walk on the return trip?
Answers
Answer:
5 miles
Explanation:
First, we need to transform the mixed number into decimal numbers using as follows:
[tex]\begin{gathered} 4\frac{1}{2}=4+\frac{1}{2}=4+0.5=4.5\text{ miles} \\ 2\frac{1}{4}=2+\frac{1}{4}=2+0.25=2.25\text{ hours} \\ 2\frac{1}{2}=2+\frac{1}{2}=2+0.5=2.5\text{ hours} \end{gathered}[/tex]Now, the average rate was the same, so the ratio of the miles to the hours is always the same. Therefore, we can write the following equation:
[tex]\frac{\text{Miles}}{\text{Hours}}=\frac{4.5\text{ Miles}}{2.25\text{ Hours}}=\frac{x}{2.5\text{ Hours}}[/tex]Where x is the number of miles that Lebron walked on the return trip. So, solving for x, we get:
[tex]\begin{gathered} \frac{4.5}{2.25}=\frac{x}{2.5} \\ \frac{4.5}{2.25}\times2.5=\frac{x}{2.5}\times2.5 \\ 5=x \end{gathered}[/tex]Therefore, Lebron walked 5 miles on the return trip.
Customers can pick their own blueberries at Blueberry Hill. They pay $5 toenter the patch and $4 per pound for the blueberries they pick. Write anequation to model the total cost, y, for x pounds of blueberries.
Answers
SOLUTION
Step1; Write out the parameters
[tex]\begin{gathered} \text{entry fe}e=\text{ \$5} \\ \cos t\text{ of blueberries per pound=\$4} \end{gathered}[/tex]Step2: Write out the variables
[tex]\text{let y=total cost and x=number of bluerries}[/tex]Step3: write out the model
[tex]\begin{gathered} \text{The total cost=number of blueberries}\times\text{\$}4+\text{ the entry fe}e \\ y=4x+5 \end{gathered}[/tex]There
what is the shape of a cross section that is parallel to the bases
Answers
The cross-section that is parallel to the base will have a
RECTANGULAR Shape
It's just like cutting through the shape horizontally
how do you do this why does it make me put so many words
Answers
Part 5
we have the points
(0,4) and (4,8)
Find the slope
m=(8-4)/(4-0)
m=4/4
m=1
Find the equation in slope intercept form
y=mx+b
we have
m=1
b=4
so
y=x+4Part 6
we have the points
(0,8) and (2,4)
m=(4-8)/(2-0)
m=-4/2
m=-2
y=mx+b
we have
m=-2
b=8
so
y=-2x+8graph the quadrilateral with the given vertices in a coordinate plane. then show the quadrilateral in a a parallelogram
Answers
First, let's graph the polygon:
Now, let's prove it's a parallelogram by showing that the segments NP and RQ are parallel, and NR and PQ are parallel as well.
Let's prove that the angular coefficient is the same for NR and PQ
[tex]\begin{gathered} m_{NR}=\frac{0-(-4)}{-5-(-3)}=-\frac{4}{3} \\ \\ m_{PQ}=\frac{5-0}{0-3}=-\frac{4}{3} \end{gathered}[/tex]Then they're parallel, just to confirm, let's do the same for NP and RQ
[tex]\begin{gathered} m_{NP}=\frac{4-0}{0-(-5)}=\frac{4}{5} \\ \\ m_{RQ}=\frac{-4-0}{-2-(3)}=\frac{4}{5} \end{gathered}[/tex]Then it's parallel as well.
A seven digit telephone number is of theform ABC-DEFG. In one particular state,the digit ‘A’ is restricted to any numberbetween 1 and 9. The digits B and Carerestricted to any number between 2 and9. The digits D,E,F, and G have norestriction. How many seven digit phonenumbers are possible with theserestrictions?
Answers
9 x 8 x 8 x 10 x 10 x 10 x 10 = 5760000 possible phone numbers
if I need 1/2 cup of oil but I only have 1/3 cup of oil how much oil do I need
Answers
We need 1/2 cup of oil and we are told that we already have 1/3 cup of oil, to find out how much we need we subtract this and the result will be the amount of oil we need.
[tex]\frac{1}{2}-\frac{1}{3}=\frac{3-2}{6}=\frac{1}{6}[/tex]In conclusion, the answer is 1/3 cup of oil
Given the definitions of f(x) and g(x) below, find the value of g(f(-2)). f(x) = 5x + 4 g(x) = x^2 - 6x - 13
Answers
f(-2) = 5(-2) + 4
= -10 + 4
= -6
g(f(-2))
= -6^2 -6*-6 -13
= 36 + 36 - 13
= 59
Use the quadratic formula to solve for X. 3x^2 = -3x +7
Answers
The solutions are:
x = -2.11 or 1.11
Explanation:Given the equation:
[tex]3x^2=-3x+7[/tex]This can be written as:
[tex]3x^2+3x-7=0[/tex]Comparing this with the general equation;
[tex]ax^2+bx+c=0[/tex]We see that;
[tex]\begin{gathered} a=3 \\ b=3 \\ c=-7 \end{gathered}[/tex]The quadratic formula is:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Substitute the values of a, b, and c
[tex]\begin{gathered} x=\frac{-3\pm\sqrt[]{3^2-4\times3\times(-7)}_{}}{2\times3} \\ \\ =\frac{-3\pm\sqrt[]{9+84}}{6} \\ \\ =\frac{-3\pm\sqrt[]{93}}{6} \\ \\ =\frac{-3\pm9.64}{6} \\ \\ x=\frac{-3+9.64}{6}=1.11 \\ \\ OR \\ x=\frac{-3-9.64}{6}=-2.11 \end{gathered}[/tex]Which of the following equations is equivalent to the given equation?
Answers
Answer:
[tex]\begin{equation*} 5(7a+5)-80=4(3a+15) \end{equation*}[/tex]Explanation:
Given the equation:
[tex]\frac{7a+5}{8}-2=\frac{3a+15}{10}[/tex]First, find the lowest common multiple of the denominators 8 and 10.
• The LCM of 8 and 10 = 40
Then, multiply all through by 40:
[tex]\begin{gathered} \frac{40(7a+5)}{8}-2(40)=\frac{40(3a+15)}{10} \\ \implies5(7a+5)-80=4(3a+15) \end{gathered}[/tex]The third option is equivalent.
Answer:
5(7a + 5) - 80 = 4(3a + 15)
Step-by-step explanation:
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]10 Students share 1 hour to give their science reports
Answers
Answer:
1/10
Explanation:
If 10 students share 1 hour, we need to divide 1 hour into 10 students. So, the fraction is
[tex]\frac{1\text{ hour}}{10\text{ students}}=\frac{1}{10}[/tex]It means that each student has 1/10 hour to give the science report.