Answer:
1. Cost per customer: 10 + x
Average number of customers: 16 - 2x
[tex]\textsf{2.} \quad -2x^2-4x+160\geq 130[/tex]
3. $10, $11, $12 and $13
Step-by-step explanation:
Given information:
$10 = cost of buffet per customer16 customers choose the buffet per hourEvery $1 increase in the cost of the buffet = loss of 2 customers per hour$130 = minimum revenue needed per hourLet x = the number of $1 increases in the cost of the buffet
Part 1
Cost per customer: 10 + x
Average number of customers: 16 - 2x
Part 2
The cost per customer multiplied by the number of customers needs to be at least $130. Therefore, we can use the expressions found in part 1 to write the inequality:
[tex](10 + x)(16 - 2x)\geq 130[/tex]
[tex]\implies 160-20x+16x-2x^2\geq 130[/tex]
[tex]\implies -2x^2-4x+160\geq 130[/tex]
Part 3
To determine the possible buffet prices that Noah could charge and still maintain the restaurant owner's revenue requirements, solve the inequality:
[tex]\implies -2x^2-4x+160\geq 130[/tex]
[tex]\implies -2x^2-4x+30\geq 0[/tex]
[tex]\implies -2(x^2+2x-15)\geq 0[/tex]
[tex]\implies x^2+2x-15\leq 0[/tex]
[tex]\implies (x-3)(x+5)\leq 0[/tex]
Find the roots by equating to zero:
[tex]\implies (x-3)(x+5)=0[/tex]
[tex]x-3=0 \implies x=3[/tex]
[tex]x+5=0 \implies x=-5[/tex]
Therefore, the roots are x = 3 and x = -5.
Test the roots by choosing a value between the roots and substituting it into the original inequality:
[tex]\textsf{At }x=2: \quad -2(2)^2-4(2)+160=144[/tex]
As 144 ≥ 130, the solution to the inequality is between the roots:
-5 ≤ x ≤ 3
To find the range of possible buffet prices Noah could charge and still maintain a minimum revenue of $130, substitute x = 0 and x = 3 into the expression for "cost per customer.
[Please note that we cannot use the negative values of the possible values of x since the question only tells us information about the change in average customers per hour considering an increase in cost. It does not confirm that if the cost is reduced (less than $10) the number of customers increases per hour.]
Cost per customer:
[tex]x =0 \implies 10 + 0=\$10[/tex]
[tex]x=3 \implies 10+3=\$13[/tex]
Therefore, the possible buffet prices Noah could charge are:
$10, $11, $12 and $13.
Solve: 4 x 11 + 5 x 28 + 4
Answer:
188
Step-by-step explanation:
1 - Multiply the numbers
4 * 11 * 5 * 28 + 4
44 + 5 * 28 + 4
2 - Multiply the numbers
44 + 5 * 28 + 4
44 + 140 + 4
3 - Add the numbers
44 + 140 + 4
188
ANSWER: >> 188
If sin theta = 3/4 and is in the first quadrant, then cos theta
Answer:
[tex]\frac{\sqrt{7} }{4}[/tex]
Step-by-step explanation:
since sin theta = 3/4, opposite length = 3 units and hypotenuse length = 4 units
by pythagoras' theorem, adjacent length = [tex]\sqrt{7}[/tex]
thus cos theta = adjacent/hypotenuse = [tex]\frac{\sqrt{7} }{4}[/tex]
Which expression can be used to determine the volume of water in a rain barrel after days if there were 179.2 gallons of water in the barrel and 10.6 gallons are used each day?
The required expression is given by 179.2 - 10.6d.
There were 179.2 gallons of water in the barrel and 10.6 gallons are used each day
Volume, is defined as the ratio of the mass of object to its density.
the volume of water in a rain barrel after "d"days
When there were 179.2 gallons of water in the barrel and 10.6 gallons are used each day.
since the amount of water is getting consumed day by day
therefore, the expression can be given as
= 179.2 - 10.6d
Thus, the required expression is 179.2 - 10.6d.
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Given the following rectangle and circle, what appropriate value of x are the two areas equal? A: x= 3.4 B: x=5.8 C: x= 10.2 D: the curves do not intersect, so there is no solution
The correct option is D:
the curves do not intersect, so there is no solution
For what values of x are the two areas equal?
The area of the rectangle is given by:
f(x) = (x + 7)*(5x - 3)
f(x) = 5x² -3x + 35x - 21
f(x) = 5x² + 32x - 21
For the circle, the area is:
g(x) = 2*pi*(x + 6)^2
g(x) = 2pi*x^2 + 12pi*x + 72pi
The solution is given g(x) = f(x).
By graphing both functions (the green curve is the area of the rectangle, the orange one is the area of the circle). The two curves never do intercept, so the correct option is D.
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A uniform rod of length 8 m has 20kg. What is the mass per meter.?
Answer:2.5 kg per meter
Step-by-step explanation:since the rod is uniform i simply divided the weight of the rod(20kg), by the length of the rod(8m). 20kg/8m = 2.5kg/m
Which expression is not a polynomial?
A. 4-3x+ 5x6
B. x²-x-12
X+3
C. 5x2 + 4x+1
D. 8x¹0+2x+5
Option b) [tex]x^{2} -x-\sqrt{x} +3[/tex] is not a polynomial
Polynomial equation is equation of dependent variables which is related to the independent variable.
since, the equation ,[tex]x^{2} -x-\sqrt{x} +3[/tex] contains the square root of variable that's why its not a polynomial.
Thus, Option b) [tex]x^{2} -x-\sqrt{x} +3[/tex] is not a polynomial
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Find the probability. If 81% of scheduled flights actually take place and cancellations are independent events, what is the probability that 3 separate flights will all take place
The probability that 3 separate flights will all take place is 0.531441
let A = event of scheduled flight actually take place
According to the question, P(A)=0.81
Given that 3 separate flights will all take place is an independent event.
Hence, we can use the multiplicative rule which says If the probability that one given flight takes place is 0.81 then the probability of 3 flights taking place is:
P(A∩B∩C) = P(A)*P(B)*P(C)
= 0.81*0.81*0.81
= 0.531441
so, the Probability that 3 separate flights will take place is 0.531441
The formula used for independent events:
P(A∩B∩C) = P(A)*P(B)*P(C)
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please help with this problem asap?!
Answer:
x=7/9
Step-by-step explanation:
- Rewrite as x = 0.77777
- Setup another equation:
10x = 7.7777
x = 0.7777
- Substract and get to :
9x = 7
- Finally, solve for X
x = 7/9
Can someone help me out on matching these angles? ASAP, gotta have answers fast pls
Answer:
8. a , c
9. b
10. c
Jenny’s family is traveling on a long road trip. The first day they traveled 11,405.59 yards. On the second day they traveled 12,048.82 yards. On the third day they traveled 9,014 yards. How many yards did they travel during the 3 day road trip?
Answer:
32468.41 yards
Step-by-step explanation:
11,405.59 + 12,048.82 + 9,014 = 32468.41
32468.41 yards
1.) Find the distance between F( 5, - 2 ) and A( -1, 4)
Answer:
8.49 units
Step-by-step explanation:
1. The distance formula is: [tex]\sqrt{(x2-x1)^{2} +(y2-y1)^{2} }[/tex]
2. Let's plug in the numbers: [tex]\sqrt{(-1-5)^{2} +(4--2)^{2} }[/tex]
3. [tex]\sqrt{(-6)^{2} +(6)^{2} }[/tex]
4. [tex]\sqrt{36 + 36}[/tex]
5. [tex]\sqrt{72}[/tex] ≈ 8.485
Find the measure of x.
X
56.76°
56.76
x = [?]
Round to the nearest hundredth.
HELP
Given S(0, -5), T(-6,0), U(-3,1),
and V (-9, y). Find y such that
ST lI UV.
Answer: 6
Step-by-step explanation:
The slope of ST is
[tex]\frac{-5-0}{0-(-6)}=-\frac{5}{6}[/tex]
The slope of UV is
[tex]\frac{y-1}{-9-(-3)}=\frac{y-1}{-6}[/tex]
Since parallel segments have the same slope,
[tex]-\frac{5}{6}=-\frac{y-1}{6}\\\\5=y-1\\\\y=6[/tex]
The vehicle preference of police officers and firefighters is given in the table. Based on the information in the table, which or the following is an example of independent events
Answer:
Step-by-step explanation:
I had this exact question and I figured it out.
the answer is: P(police officer and chooses car)
In order to get this answer I did the P(police officer) X P(choosing car)
It ended up being 36/45 X 15/45. Which is equal to around .2666667.
Now you take the Intersection of police officer and chooses car and you divide it by 45. That value on the chart is 12.
lucky enough, the product of 36/45 and 15/45 is equal to 12/45.
So 0.8 X 0.33 = .26
.26 = .26
Answer:
answer is P(police officer and chooses car)
Step-by-step explanation:
the probability of P(policer officer) and P(choose a car) are independent probabilities ( they are not overlapping probabilities)
Who is the Father of Algebra ?
Answer:
Al- khwarizmiStep-by-step explanation:
that is my
Answer:
Muhammad ibn Musa al-Khwarizmi
محمد بن موسی خوارزمی
Which phrase best describes the translation from the graph y = (x + 2)2 to the graph of y = x2 + 3?
The parent. function shifted down by 2 units to produce x² and to the right by 3 units to produce y = x^2 + 3
What is translation?This is a way of changing the position of an object on an xy-plane.
Given the parent function expressed as y = (x + 2^)2
From the resulting image after translation, we can see that the parent. function shifted down by 2 units to produce x² and to the right by 3 units to produce y = x^2 + 3
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Triangle L M Q is cut by perpendicular bisector L N. Angle N L Q is 32 degrees and angle L M N is 58 degrees.
Is TriangleMNL ≅ TriangleQNL? Why or why not?
Yes, they are congruent by either ASA or AAS.
Yes, they are both right triangles.
No, AngleM is not congruent to AngleNLQ.
No, there are no congruent sides.
Both triangles are congruent by either ASA or AAS Congruence Theorem. hence, the right answer is A: Yes, they are congruent by either ASA or AAS.
What is ASA Congruence Theorem?The ASA Congruence Theorem states that the two triangles are congruent if they have two pairs of congruent angles and a pair of congruent included sides.
The AAS Congruence Theorem states that the two triangles are congruent if they have two pairs of congruent angles and a pair of congruent non-included sides.
Triangle LMQ is shown in the figure attached below.
Thus, Proving
Triangle MNL ≅ triangle QNL (ASA)
Triangle MNL and triangle QNL have two pairs of congruent angles:
<LNM ≅ LNQ and <MLN and <QLN
Also, they have a common side: side LN (included side).
Therefore, Triangle MNL and triangle QNL are congruent by ASA.
Triangle MNL ≅ triangle QNL ( by AAS)
Triangle MNL and triangle QNL have two pairs of congruent angles:
<LNM ≅ LNQ and <NML and <NQL
Also, they have a common side: side LN (non-included side).
Thus, Triangle MNL and triangle QNL are congruent by ASA.
Hence, the right answer is: A: Yes, they are congruent by either ASA or AAS.
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Answer: option A
Step-by-step explanation:
Alyssa's favorite tennis team has 8 players on them. She has taken a picture with every single athlete individually and wants to post some of the pictures on her wall. But she only wants to post 3 pictures on her wall. How many different sets of pictures can she post on her wall
56 sets of pictures she can post on her wall
It is given that alyssa's favorite tennis team has 8 players on them. She has taken a picture with every single athlete individually and wants to post some of the pictures on her wall. But she only wants to post 3 pictures on her wall.
For this we hve to use factorials. In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. The factorial of n also equals the product of n with the next smaller factorial: For example, The value of 0! is 1, according to the convention for an empty product.
So it will be - [tex]\frac{8!}{3!(8-3)!}[/tex] as this is the formula for combination
This will be 56.
Thus, 56 sets of pictures she can post on her wall
Which of the following represents a function?
Please help
Answer:
(2,3),(4,3),(-2,-3),(-4,-3)
Step-by-step explanation:
A function is defined as a relation in which each domain element (x-value) is paired with exactly one range element (y-value).
This means that each value we input for x must have only one possible output. If the same x-value yields more than one y-value, it is not a function.
The correct answer, as shown above, meets the criteria of a function, as each x-value is shown to produce exactly one y-value. In this set of ordered pairs, if x = 2, then y = 3, and if x = -2, then x = -3.
A set of ordered pairs is not a function if there are ordered pairs with the same x-values but different y-values.
In the other sets of ordered pairs, one x-value has more than one possible y-value. Let's use the last set as an example:
(5,1),(5,2),(5,3),(5,4)
Inputting 5 as x produces four different y values; there is no one y value for the x-value. y could equal 1, 2, 3, or 4.
Solve the inequality.
-2x + 8 < 14
and -3x - 9 ≥ -12
x>?
and
x≤
Answer:
x > -3 and x ≤ 1
Step-by-step explanation:
[First inequality]
Given:
-2x + 8 < 14
Subtract 8 from both sides:
-2x < -6
Divide both sides by -2, since it's negative we also flip the sign:
x > 3
[Second inequality]
Given:
-3x - 9 ≥ -12
Add 9 to both sides:
-3x ≥ -3
Divide both sides by -3, since it's a negative we also flip the sign:
x ≤ 1
If 1600 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
The largest possible volume of the box is 6158.394 cm^3.
Define the dimensions of the box to be L, W, and H.
Square base, L = W
Area: A = L^2 * H
Surface Area (Base + Area of 4 sides):
1600 = L^2 + 4 (L*H) ⇒ H = (1600 - L^2) / (4L)
Area: A = 400L - (1/4)L^3
Maximum (Derivative) A' = 400 - (3/4)L^2
Solving for 0
0 = 400 - (3/4)L^2
L^2 ⇒ (40 * SQRT(3)) / 3 = 23.094 (Maximum)
Solving for dimensions, known L=23.094
L = 23.094 cm
W = 23.094 cm
H ⇒ (1600 - L^2) / (4L) = (20 * SQRT(3) / 3) = 11.547 cm
Volume ⇒ L*W*H = 6158.394 cm^3
To locate the most viable extent, add the greatest viable mistakes to every dimension, then multiply. To find the minimum viable volume, subtract the greatest feasible mistakes from each measurement, then multiply.
Volume is a scalar amount expressing the amount of 3-dimensional area enclosed by a closed surface. For example, the gap that a substance or 3-D shape occupies or consists of.
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To conduct a survey on current social work majors, a researcher gets a list of all students who have declared a social work major from the registrar from which a sample will be drawn. This list is known as a (n):
The list is known as the sampling frame.
To conduct a survey on current social work majors, a researcher gets a list of all students who have declared a social work major from the registrar from which a sample will be drawn.
This list is known as a sampling frame.
The sampling frame is the list from which units are drawn for the sample.
Hence, the list is known as the sampling frame.
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27.
Make an orthographic drawing with top, left, front, and right side view of the model below.
front right
The orthographic projection based on the information given is illustrated below.
What is orthographic projection?It should be noted that orthographic projection is a common method that's used for representing three-dimensional objects where each of the object is viewed along parallel lines that are perpendicular to the plane of the drawing.
In this case, it is a form of parallel projection, where all the projection lines are orthogonal to the projection plane which then results in every plane of the scene appearing in affine transformation on the viewing surface.
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Suppose it is known that the individual lost more than 12 pounds in a month. Find the probability that he lost less than 19 pounds in the month.
The probability that he lost less than 19 pounds is 7 / 9.
According to statement
The weight loss by individual is 12 Pounds
So, by uniform distribution probability
P(c ≤ x ≤ d) = (d - c) / (b - a)
Substitute the values in it then
P(12 ≤ x ≤ 19) = (19 - 12) / (20 - 11)
P(12 ≤ x ≤ 19) = 7 / 9
So, the probability that he lost less than 19 pounds is 7 / 9.
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At a certain zoo, the average mass of one blue whale is measured to be 1.9 × 105
kilograms. Use scientific notation to express the mass of 140 blue whales.
Answer:
2.7930 × [tex]10^{4}[/tex]
Step-by-step explanation:
1.9 × 105 × 140 = 27,930
Scientific notation: 2.7930 × [tex]10^{4}[/tex]
What contribution to geometry is attributed to the work of René Descartes?
René Descartes provided the first systematic link between Euclidean geometry and algebra.
What is Geometry?This branch of mathematics involves the study of object shape, their spatial relationship and that of their surrounding space.
René Descartes is referred to as the father of analytic geometry due to him establishing the relationship between Euclidean geometry and algebra.
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2 people can paint a fence in one hour. how long would it take 10 people. give your answer in minuets
Step-by-step explanation:
no of people=2
time taken=1/60mins
no of people=10
time taken=1/x
2=1/60
10=1/x
x=12mins
A rectangular prism has a square base with a width of 6 and a volume of 360 cm3. If a square pyramid has a base with the same width and height, what is the volume of the pyramid?
2c+2b in standard from
Answer:
2c+2b
Step-by-step explanation:
this is because standard form only applies to no. from 10 and above , furthermore, they are unlike terms
URGENT CAN SOMEBODY PLEASE ANSWER THESE 2 QUESTIONS
Answer:
A: y=2x+4
B. 34° Celsius
Step-by-step explanation:
A:
Since the temperature goes up at a steady rate of 2 degres per minute, we can assume that 2 is our slope. Since the graph shows us that 4 is the y-intercept, we can substitute both the slope and y-intercept into the equation of a line, or y=mx+b. (m is our slope and b is our y-intercept.)
Doing so gives you:
[tex]y = 2x + 4[/tex]
B.
Using the above formula (y=2x+4), we can substitute x with 15 (since x is the minutes that pass).
Doing so gives you y=30+4, the sum of which is 34.
Therefore, the answer should be 34° Celsius.