Answer: (1) The least number of meals is 26 (2) She loses 150 if she caters no meal in one week. (3) Her profit would be 2,650 if she caters for 50 meals in one week
Step-by-step explanation: The weekly profit is given as a quadratic equation which is;
P = 2x² -44x - 150
We begin by solving for the value of x.
When 2x² -44x - 150 = 0
Divide all through by 2
x² - 22x - 150 = 0
By factorization,
(x - 25) (x + 3) = 0
(x -25) = 0 OR (x + 3) = 0
When x - 25 = 0
x = 25
When x + 3 = 0
x = -3
What this implies is that when Amelia caters for 25 meals in a week, her profit is calculated as follows
P = 2x² - 44x -150
P = 2(25)² - 44(25) - 150
P = 2(625) - 1100 - 150
P = 1250 - 1100 - 150
P = 0
(1) Therefore she must cater for at least 26 meals before she can begin to make any profit.
(2) She loses 150 if she caters no meal in one week.
This can be calculated as follows;
When x = 0,
P = 2x² - 44x - 150
P = 2(0)² - 44(0) - 150
P = 0 - 0 -150
P = -150
(3) When she caters 50 meals her profit becomes 2,650
P = 2x² - 44x - 150
P = 2(50)² - 44(50) - 150
P = 2(2500) - 2200 - 150
P = 5000 - 2200 - 150
P = 2650
1) The least number of meals Amelia needs to cater in order to begin making a profit is 25.
2) Amelia loses $150 if she caters no meals in a week.
3) For catering 50 meals, Amelia's profit is $2650.
Explanation:1) To find the least number of meals Amelia needs to cater in order to begin making a profit, we need to determine when her profit, P, becomes positive. In other words, we need to solve the quadratic equation 2x^2 - 44x - 150 = 0 for x. This equation can be factored as (2x + 6)(x - 25) = 0. Therefore, x = -3 or x = 25. Since the number of meals cannot be negative, the least number of meals Amelia needs to cater in order to begin making a profit is 25.
2) If Amelia caters no meals one week, the profit, P, is given by P = 2(0)^2 - 44(0) - 150. Simplifying this equation, we get P = -150. Therefore, Amelia loses $150 if she caters no meals in a week.
3) To find Amelia's profit for catering 50 meals, we substitute x = 50 into the profit equation P = 2x^2 - 44x - 150. Plugging in x = 50, we get P = 2(50)^2 - 44(50) - 150 = 5000 - 2200 - 150 = $2650.
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plz help me plz hurry What is the solution to the system of equations?
7 x minus 2 y = negative 24. 5 x + 5 y = 15.
Answer:
x=-2 y=5
Step-by-step explanation:
7x-2y=-24
5x+5y=15
35x-10y=-120
10x+10y=30
45x=-90
x=-2
-10+5y=15
5y=25
y=5
The solution of the equations is, x=-2 and y=5.
What is an equation?An equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
The given expressions are solved as below:-
7x-2y=-24
5x+5y=15
35x-10y=-120
10x+10y=30
45x=-90
x=-2
The second equation is solved as below:-
-10+5y=15
5y=25
y=5
Hence, the solutions are x=-2 and y=5.
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Product of 3 and 25 plus the product of 5 and 30?
It has to be an expression
Answer:
3(25)+5(30)
Step-by-step explanation:
Product means multiplying 2 things together and expression means you do not solve the equation you just leave it be
juan needs to measure 6 cups of flour for a recipe.he only has a 1/4 cup measuring cup.how many times must he fill the measuring cup to get 6 cups of flour
Answer:
24
Step-by-step explanation:
1 time=1/4 cups
xtimes=6 cups
Cross multiply
6×1=x×1/4
6=x/4
Make x the subject of formula by cross multiplying
x=4×6
x=24
So the final answer is 24
Write the order pair that represents YZ. Then find the magnitude of YZ. Y(5,4), Z (0,-3)
Answer:
Ordered pair of YZ is (-5,-7) and magnitude of YZ is 8.602
Step-by-step explanation:
Given data:
Two pairs Y (5,4) and Z (0, -3)
To find: ordered pair of YZ
YZ = Z - Y = (0-5, -3-4)
= (-5, -7)
Hence ordered pair of YZ is (-5,-7)
To find: magnitude of YZ.
Here Y and Z are initial and final points of vector. Magnitude of YZ is distance between points Y and Z. Distance formula is
Distance = [tex]\sqrt{(x2-x1)^{2} + (y2-y1)^{2} }[/tex]
magnitude of YZ = [tex]\sqrt{(0-5)^{2} + (-3-4)^{2} }[/tex]
= [tex]\sqrt{74}[/tex]
= 8.602
Another method:
magnitude of YZ = |YZ|
|YZ| = [tex]\sqrt{(-5)^{2} + (-7)^{2} }[/tex] ...............(since |xy| = [tex]\sqrt{(x)^{2} + (y)^{2} }[/tex]
= [tex]\sqrt{74}[/tex]
= 8.602
magnitude of YZ = 8.602
Answer:
D
Step-by-step explanation:
(-5,-7);√74 units
Which equation can be used to find the volume of the cylinder?
s = 6 cm
h = 8 cm
OV= *(6) (8)
O V= x(12)?(8)
O V = $(8) (6)
V = x(8)?(8)
Answer:
Option 1: [tex]V=\pi (6)^{2} (8) \\[/tex]
Step-by-step explanation:
This is because when we plug in the value given in the picture.
Formula [tex]V=\pi r^{2} h[/tex]
The way we write this is by using our "r" which is 6. We plug in the 6 for "r" so the equation will look something like this: [tex]V=\pi (6)^{2} (h)[/tex]
Then we will plug in our height "h", which is 8. So the equation will look something like this: [tex]V=\pi (6)^{2} (8)[/tex]
So that's it. Very simple. Just remeber to keep the formula in mind and you will get the hang of it.
I hope this help! :D
The equation to find the volume of the cylinder is V = π ( 6 )² ( 8 )
What is a Cylinder?A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The volume of a cylinder is
Volume of Cylinder = πr²h
Surface area of cylinder = 2πr ( r + h )
where r is the radius of the cylinder
h is the height of the cylinder
Given data ,
Let the volume of the cylinder be V
Let the radius of the cylinder be r = 6 cm
Let the height of the cylinder be h = 8 cm
Now , Volume of Cylinder = πr²h
On simplifying , we get
V = π ( 6 )² ( 8 )
V = 288π cm³
Hence , the equation is V = π (6 )² ( 8 )
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Which of the following is(are) the solution(s) to | X+10 | = 3x-2?
Answer:
x = 6
Step-by-step explanation:
Solve for x by simplifying both sides of the equation, then isolating the variable.
Answer:
x = { 3, -2 }
Step-by-step explanation:
Let's actually find the solutions to | X+10 | = 3x - 2. Because of the absolute value operator this breaks down into two simpler problems:
1) x + 10 = 3x - 2, or 12 = 4x. Then x = 3
2) -(x + 10) = 3x - 2, or -x - 10 = 3x - 2, or -8 = 4x. Then x = -2
All of the following proportions are equivalent except
b/a=d/c
a/b=cid
a/c=b/d
a/d=c/b
What is a common binomial factor
Select the correct answer. What is the range of the function f(x) = 12 − 3x for the domain {-4, -2, 0, 2, 4}? A. {24, 18, 12, 6, 20} B. {6, 12, 18, 24, 30} C. {-12, -6, 0, 6, 12} D. {0, 6, 12, 18, 24}
so the right answer is of option D...
What is the domain of y = csc(x)?
The domain of y = cosec(x) includes all real numbers except for the integer multiples of [tex]\pi[/tex], where the sine function equals zero and the cosecant function is undefined.
The domain of a function is the set of all possible input values (usually x values) for which the function is defined. In the case of y = cosec(x), the cosecant function is the reciprocal of the sine function, meaning cosec(x) = 1/sin(x). Since the sine of an angle can be zero and division by zero is undefined, the domain of y = cosec(x) must exclude any x values where sin(x) = 0.
The sine function is zero at integer multiples of [tex]\pi[/tex], so the domain of cosec(x) is all real numbers except for integer multiples of [tex]\pi[/tex]
What is a difference between a rectangular prism and a cube?
Which is not equal to 400
Answer:
399
Step-by-step explanation:
The only expression that does not equal 400 is c. 500 - 200.
How to determine the expression that is not equal to 400From the question, we have the following parameters that can be used in our computation:
a. 2 * 200
b. 800/2
c. 500 - 200
d. 300 + 100
Evaluating each of the options, we have the following
a. 2 * 200 = 400
b. 800/2 = 400
c. 500 - 200 = 300
d. 300 + 100 = 400
Hence, the only option that does not equal 400 is c. 500 - 200.
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Question
Which is not equal to 400
a. 2 * 200
b. 800/2
c. 500 - 200
d. 300 + 100
What’s the definition of the number i?
Answer:
B. i = √(−1)Step-by-step explanation:
When (i) is multiplied to itself it = -1
The number (i)is used for imaginary numbers.
What is the other dimension of the rectangular cross section that is perpendicular to the base (the face that is shaded) and
passes through the midpoints of the 10 cm edges?
centimeters by 18 centimeters
2
8
10
18
Answer:
8
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
Convert 0.85 to a percent.
Answer:
85%
Step-by-step explanation:
Multiply both numerator and denominator by 100. We do this to find an equivalent fraction having 100 as the denominator. 0.85 × 100100.
= (0.85 × 100) × 1100 = 85100.
Write in percentage notation: 85%
Answer:
85%
Step-by-step explanation:
To convert a number to a percent, you need to multiply it by 100 and add a percent symbol to the end. 0.85*100=85%. Hope this helps!
The polynomial p(w) = 3w^3 - 20w^2 + 37w - 20 has a known factor of (w-4). Rewrite p(w) as a product of linear factors.
Answer:
(w - 4)(w - 1)(3w - 5)
Step-by-step explanation:
Using Synthetic division to find the quotient on dividing p(w) by (w - 4)
4 | 3 - 20 37 - 20
12 - 32 20
-----------------------------
3 - 8 5 0 ← remainder = 0
quotient = 3w² - 8w + 5 = (3w - 5)(w - 1)
p(w) = (w - 4)(w - 1)(3w - 5)
Help plzz ASSAP
The function f(x) = 30x + 150 represents the total cost of a gym membership at Jon's Gym for x months plus a signup fee. Bella's Gym has a signup fee of $50 and charges $45 dollars per month. Which statement is true.
Select one
The signup fee at Jon's Gym is $100 more than the signup fee at Bella's Gym
Jon's Gym charges $15 more per month Bella's Gym
The signup fee at Jon's Gym is $15 more than the signup fee at Bella's Gym
Jon's Gym charges $100 more per month than Bella's Gym.
Answer: The signup fee at Jon's Gym is $100 more than the signup fee at Bella's Gym
Step-by-step explanation:
Hi, to answer this question we have to write an equation for the cost of Bella's Gym
Jon's Gym: f(x) = 30x + 150
Bella's Gym has a signup fee of $50 and charges $45 dollars per month.
So, we have to multiply the number of months (x) by the cost per month, and add the signup fee cost (50).
Bella's Gym: f(x) = 45x+ 50
Since Jon's signup fee is 150 and Bella's signup fee is 50 , the difference of both costs is 100 (150-50=100), and since Jon's gym has the more expensive fee:
The signup fee at Jon's Gym is $100 more than the signup fee at Bella's Gym
Final answer:
The statement that the signup fee at Jon's Gym is $100 more than the signup fee at Bella's Gym is true.
Jon's Gym charges $30 per month while Bella's Gym charges $45 per month; thus, Jon's Gym charges $15 less, not more.
Explanation:
Comparing the costs of gym memberships at Jon's Gym and Bella's Gym requires analysis of the initial signup fees and the monthly rates. The function for Jon's Gym, f(x) = 30x + 150, indicates a signup fee of $150 and a monthly rate of $30. Bella's Gym has a signup fee of $50 and a monthly rate of $45. To determine the true statement, we compare these numbers directly:
The signup fee at Jon's Gym is $100 more than the signup fee at Bella's Gym ($150 - $50 = $100).The other statements provided in the question can be dismissed as false:
Jon's Gym does not charge $15 more per month than Bella's Gym; it charges $15 less per month.The signup fee at Jon's Gym is not $15 more than the signup fee at Bella's Gym; it is $100 more.Jon's Gym does not charge $100 more per month than Bella's Gym.Therefore, the correct statement is that The signup fee at Jon's Gym is $100 more than the signup fee at Bella's Gym.
Madi is 5 times as old as Brecken. In 12 years, she will be twice as old as he will be then. How old are they now?
Madi is 4 and Bracken is 20.
In 12 years Madi will be 16 and bracken will be 32 which is twice the age of Madi.
What is the value of x to the nearest whole number?
Answer:
65
Step-by-step explanation:
Use the formula: a²+b²=c²
63²=3969
16²=256
Add them = 4225 = c²
[tex]\sqrt{4225} = \sqrt{c^2}[/tex]
65 = c (or x in this case)
Answer:
17.96
Step-by-step explanation:
To find the hypotenuse we are will have to use Sine, since we are only given the degree and opposite leg. [tex]sin(degree)=\frac{Opposite}{Hypotenuse}[/tex]
[tex]sin(63)=\frac{16}{x}[/tex]
Let's cancel the x on the right side by multiplying both sides by x
sin(63)x = 16
Divide both sides by sin(63) [Or 0.866, depending on the type of calculator you have]
sin(63)x ÷ sin(63) = 16 ÷ sin(63)
x = 17.9572198
I really need help please dont put a crazy answer for points I NEED HELP! WILL MARK BRAINLIEST!!! If Pam works more than 40 hours per week, her hourly wage for every hour over 40 is 1.5 times her normal hourly wage of $7. Write a piecewise-defined function that gives Pam's weekly pay P(h) in terms of the number of hours h that she works.
Answer:
Sorry I made a mistake here is a picture of the answer. I hope this helps.
Pam's weekly pay can be modeled using a piecewise function. If Pam works 40 hours or less, her pay is her hourly rate times her hours worked. However, if she works more than 40 hours, her pay is her standard pay for 40 hours plus 1.5 times her hourly rate for each hour beyond 40.
Explanation:Pam's weekly pay, P(h), can be defined piecewise, meaning we split up h (the total hours she works) into different 'pieces' based on the terms of her pay structure. In this case, the 40 hour standard work week serves as the dividing line between these pieces. The piecewise function could be represented as follows:
P(h) = { $7h, if h <= 40
$7*40 + $7*1.5*(h-40), if h > 40 }
In this function, when Pam works 40 hours or fewer (h <= 40), her pay is simply her hourly wage ($7) times the number of hours worked. However, if she works more than 40 hours (h > 40), her pay is her standard weekly pay for the first 40 hours ($7 times 40) plus 1.5 times her hourly wage for each hour beyond 40 hours.
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40x + 13 - 45x
The standard form is
Will give 20 points
Given the matrices:
What is the size of the product C = AB?
that is the answer for the first part what are the answers for the second part
Find the product of C = AB.
c11 =
c12 =
c21 =
c22 =
Answer:
Next frame (6) is C
Frame 7 is D then A
Frame 8 is D
Frame 9 is scalar, neither, matrix, matrix
Step-by-step explanation:
Doing the assignment rn :)
Answer:
C =AB
2 x 2
second part
c11=-1 c12=3 c21=3 c22=-3
third part
d11=0 d12=6 d21=1 d22=-4
Step-by-step explanation:
Correct on edge 2023
What is the solution to the inequality -4(5/2+3/2x)>8?
A. x > -1/2
B. x < 1/3
C. x < -3
D. x > 3
Answer:
C
Step-by-step explanation:
Given
- 4([tex]\frac{5}{2}[/tex] + [tex]\frac{3}{2}[/tex] x) > 8 ← distribute parenthesis on left side
- 10 - 6x > 8 ( add 10 to both sides )
- 6x > 18
Divide both sides by - 6, reversing the symbol as a result of dividing by a negative quantity
x < - 3 → C
A taxi charges a $3 initial fee,plus $1.50 per mile traveled.
What is the total cost of a 4.5- mile taxi trip?
A $9.00
B $9.50
C $9.75
D $10.00
Answer:
C
Step-by-step explanation:
$1.50 multiplied by 4.5 = 6.75
$6.75 plus $3 = $9.75
Answer:
$9.75
Step-by-step explanation:
1.50 per mile traveled
1.50 x 4.5 = 6.75
plus the additional fee of three dollars
6.75 + 3.00 = 9.75
The diameter of a circle is 7 feet. Find the radius
Answer:
3.5 feet
Step-by-step explanation:
Diameter = 7 feet
Radius = Diameter × [tex]\frac{1}{2}[/tex]
Radius = [tex]\frac{7}{2}[/tex] = 3.5 feet
Which expression is equivalent to sine StartFraction 7 pi Over 6 EndFraction?
Answer:
The answer is D: sin 11pi/6
<3
Step-by-step explanation:
The expression that is equivalent to the given expression is Sin(11π/6).
The given trigonometric expression is: [tex]Sin \frac{7\pi }{6}[/tex]
[tex]Sin\frac{7\pi }{6}[/tex] can be written as [tex]Sin(\pi +\frac{\pi }{6} )[/tex]
What is the value of Sin(π+θ)?The value of [tex]Sin(\pi +\theta)[/tex] is [tex]-Sin\theta[/tex].
So, [tex]Sin(\pi +\frac{\pi }{6} )=-Sin\frac{\pi }{6}[/tex]
We know that
[tex]Sin(2\pi -\theta)=-Sin\theta[/tex]
Or, [tex]-Sin\theta=Sin(2\pi -\theta)[/tex]
So, [tex]-Sin\frac{\pi }{6} =Sin(2\pi -\frac{\pi }{6} )[/tex]
[tex]-Sin\frac{\pi }{6} =Sin\frac{11\pi }{6}[/tex]
So, the required expression is [tex]Sin\frac{11\pi }{6}[/tex].
Therefore, the expression that is equivalent to the given expression is Sin(11π/6).
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Which equation can be used to find the length of side x?
The equation that can be used to find the length of side x is:
cos(25°) = x / 32.
The equation that can be used to find the length of side x is:
cos(25°) = x / 32
This equation is based on the trigonometric ratio tan, which is defined as
the opposite side over the adjacent side.
In this case, the opposite side is x and the adjacent side is 32.
We know the angle between these two sides is 25°, so we can use the
tan function to solve for x.
x = cos(25°) * 32
x = 14.65 cm
Therefore, the equation that can be used to find the length of side x is:
cos(25°) = x / 32
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Find the area of the shaded region
A. 1256
B. 425
C. 201
D. 531
E. 603
F. 249
(12m / 8m)
Answer:
A. 1256
Step-by-step explanation:
You have to find the radius of the shaded circle
So you can add 12 + 8 = 20
Or you can find the diameter of the two circles. The diameter of the first circle is 12 + 12 = 24 and the second circle is 8 + 8 = 16 + 20 + 40 is the diameter of the shaded circle. Since radius is half of diameter 40 ÷ 2 = 20
So now since you know the radius of the shaded circle you can find the area
A = πr²
A = 3.14 x 20²
A = 3.14 x 400
A = 1256
2. Below is a list of grades on
a math test. What is the
range of the scores?
Answer:
31
Step-by-step explanation:
The range can be found by subtracting the lowest number in the set from the highest, so one can conclude how large the gap in between the two is.
the lowest number her is 68 and the highest is 99
99-68=31
Answer:
31 is the range
Step-by-step explanation:
the range is the number between the highest data and the lowest data. You take your largest number in the data and subtract it from the highest.
Largest 99
smallest 68
99 - 68 = 31
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Please help me...
What is the function that matches the description.
A sine function whose amplitude is 5 and Period is 12.
Answer:
Last one
Step-by-step explanation:
f(x) = Asin(Bx) + C
C = 0
A = 5
B = 2pi/12 = pi/6
f(x) = 5 sin[(pi/6)x]