Answer:
The right answer is:
(A) [tex]40x-300.25[/tex]
(B) [tex]15[/tex]
(C) [tex]383[/tex]
Step-by-step explanation:
Given:
Producing x items,
= [tex]55x+300[/tex]
Revenue x items,
= [tex]95x-0.5^2[/tex]
= [tex]95 x-0.25[/tex]
Part A:
= [tex]R(x)-C(x)[/tex]
By putting the values, we get
= [tex](95x-0.25)-(55x-0.25)[/tex]
= [tex]40x-300.25[/tex]
Part B:
We know,
P(x) = $300
⇒ [tex]300=40x-300.25[/tex]
[tex]40x=600.25[/tex]
[tex]x=\frac{600.25}{40}[/tex]
[tex]=15.00625[/tex]
or,
[tex]=15[/tex]
Part C:
We know,
P(x) = $15,000
⇒ [tex]40x-300.25=15000[/tex]
[tex]40x=15300.25[/tex]
[tex]x=\frac{15300.25}{40}[/tex]
[tex]=382.50625[/tex]
or,
[tex]=383[/tex]
The values of x that create a profit of $300 is 60 or 20 items.
What is profit?Profit is the difference between revenue and cost, it is given by:
Profit = revenue - cost
a) From the situation:
Profit (P) = 95x−0.5x² - (55x + 300)
P = -0.5x² + 40x - 300
B) For a profit of $300:
-0.5x² + 40x - 300 = 300
-0.5x² + 40x - 600 = 0
x = 60 and x = 20
c) For a profit of $15000:
-0.5x² + 40x - 300 = 15000
-0.5x² + 40x - 15300 = 0
The equation cannot be solved
The values of x that create a profit of $300 is 60 or 20 items.
Find out more on profit at: https://brainly.com/question/1078746
A car travels 1/8 mile in 2/13 minutes. What is the speed in terms of miles per minute?
Answer:
13/16 miles per minute
Step-by-step explanation:
Take the miles and divide by the minutes
1/8 ÷ 2/13
Copy dot flip
1/8 * 13/2
13/16 miles per minute
can someone please solve 3x^2+4x-7<13
Answer:
[tex]-\frac{10}{3}<x<2\:[/tex]
Step-by-step explanation:
Rewrite in standard form: [tex]3x^2+4x-20<0[/tex]
Factor: [tex]\left(x-2\right)\left(3x+10\right)<0[/tex]
Solve individually for x:
[tex]x-2<0\\x<2[/tex]
[tex]3x+10<0\\3x<-10\\x<\frac{-10}{3}[/tex]
Combine:
[tex]-\frac{10}{3}<x<2\:[/tex]
-4 is a whole number
Answer:
false
Step-by-step explanation:
a whole number is a number that doesnt contain a fraction or negative value
Can someone please help
Answer:
he didnt build the field
Step-by-step explanation:
f
Can someone explain how to solve this step by step? Thank you
Answer:
x=10
Step-by-step explanation:
Using the Rational Roots Test, we can say that the potential rational roots are
± (1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90).
Unfortunately, there doesn't really seem to be an easy way to figure out which numbers are actually roots outside of guess and check. Therefore, to solve this, we'll have to go through numbers until we hit something.
To make the process faster, I wrote a Python script as follows:
numbers = [1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90]
negative_numbers = [i * (-1) for i in numbers]
numbers = numbers + negative_numbers
for i in numbers:
if (i**3 - 10*(i**2) + 9*i-90) == 0:
print(i)
The result comes out as 10, meaning that 10 is our only rational root. Using the Factor Theorem, we can say that because 10 is a root, (x-10) is a factor of the polynomial. Using synthetic division, we can divide (x-10) from the polynomial to get
10 | 1 -10 9 -90
| 10 0 90
_________________
1 0 9 0
Therefore, we can say that
(x³-10x²+9x-90)/(x-10) = (x²+0x+9), so
x³-10x²+9x-90 = (x-10)(x²+9)
As the only solution to x²+9=0 contains imaginary numbers, x=10 is the only solution to x³-10x²+9x-90 = (x-10)(x²+9) = 0
When using a regression equation, the difference between the formulas used to calculate the confidence interval estimate and prediction interval estimate is ______.
Answer:
the addition of "1" to the quantity under the radical sign.
Step-by-step explanation:
Using a regression equation :
The confidence interval is obtained using the relation :
yhat ± t(α/2) * s√(1/n + (Xp - xbar)²/SSx)
yhat = Predicted value
s = estimated standard deviation of yhat
x = Xp
The prediction interval is obtained using the relation :
yhat ± t(α/2) * s√(1 + 1/n + (Xp - xbar)²/SSx)
Hence, from the formula stated abibeb, we can see that, the only difference is the 1 added to the prediction interval formula.
What is the value of Z? Z =2^3
the value of Zis 8.
Z =2^3=8
Now we have to,
find the required value of Z.
→ Z = 2^3
→ [Z = 8]
Therefore, value of Z is 8.
The product of two consecutive odd integers is 143. If x is the smallest of the integers, write an equation in terms of x that describes the situation, and then find all such pairs of integers.
The equation that describes the situation is _________________
The positive set of integers is _______________________
The negative set of integers is _______________________
Answer:
Step-by-step explanation:
x(x+2) = 143
:::::
x² + 2x - 143 = 0
x = [-2 ±√(2²-4(1)(-143))]/[2(1)] = 11, -13
:::::
11 and 13
:::::
-13, -11
twelve people enter a contest. prizes will be given for first second and third place. how many ways can the prizes be given
Answer:
1320 ways
Step-by-step explanation:
Number of contestants = 12
Positions that are n be awarded = First, Second, Third
Number of contestants who could be first = 12 (all 12 contestants)
Number of contestants who could be second = 11 (all 12 contestants - first)
Number of contestants who could be third = 10 (all 12 contestants - first and second )
The number of ways prices can be given :
(1st * 2nd * 3rd) = 12 * 11 * 10 = 1320 ways
Find all two - digit numbers with the following property: the difference of the number and the number with the same digits in reverse order is 54.
Answer:
17
26
35
44
53
62
71
80
Step-by-step explanation:
Let's solve the problem step by step.
Let's assume the two-digit number is represented as "AB," where A represents the tens digit and B represents the units digit. According to the problem, the difference between the number "AB" and the number "BA" is 54.
So, we have the equation:
(10A + B) - (10B + A) = 54
Simplifying the equation, we get:
9A - 9B = 54
Dividing both sides of the equation by 9, we have:
A - B = 6
Now, we need to find two-digit numbers where the difference between the tens digit and the units digit is 6. The possible combinations are:
(1, 7)
(2, 8)
(3, 9)
(4, 10) - But 10 is not a valid unit digit since it exceeds the range of a two-digit number.
So, the valid two-digit numbers that satisfy the given condition are:
17
26
35
44
53
62
71
80
Therefore, there are 8 two-digit numbers that have a difference of 54 when subtracted from the number formed by reversing their digits.
Billy's heart rate is 13 beats every 10 seconds. What is his heart rate in beats per MINUTE (bpm)?
Reminder: 1 Minute=60 Seconds
(A)23 bpm
(B)63 bpm
(C)78 bpm
(D)130 bpm
Find the area of the shaded region.
A. 112.5 in²
B. 73.5 in²
C. 122.5 in²
D. 147 in²
9514 1404 393
Answer:
B. 73.5 in²
Step-by-step explanation:
The triangle area is half the rectangle area, so the shaded area is also half the rectangle area:
A = 1/2LW = 1/2(21 in)(7 in) = 73.5 in²
Answer:
B.) 73.5 in2
Step-by-step explanation:
I got it correct on founders edtell
is absolute value of -998
Answer:
998.
Step-by-step explanation:
Just get rid of the negative sign
Answer:
This should 998 I guess
Step-by-step explanation:
Minus the negative signs
An office manager booked 55 airline tickets. He booked 6 more tickets on Airline A than Airline B. On Airline C, he booked 5 more than twice as many tickets as on Airline B. How many tickets did he book on each Airline?
9514 1404 393
Answer:
A: 17B: 11C: 27Step-by-step explanation:
If we let a, b, c represent tickets booked on airlines A, B, C, respectively, then we have ...
a + b + c = 55
a - b = 6
-2b + c = 5
Using the last two equations to write expressions for a and c, we have ...
a = b +6
c = 5 +2b
These can be substituted into the first equation to give ...
(b +6) +b +(5 +2b) = 55
4b +11 = 55
4b = 44
b = 11
a = b+6 = 17
c = 5 +2b = 27
He booked 17 tickets on Airline A, 11 tickets on Airline B, and 27 tickets on Airline C.
6.) What are the coordinates of D, E and F after a reflection over the y-axis?
D'(-3,-3) E (5,0) F (2,2)
D'(3,3) E'(-5,0) F'(-2,-2)
D'(3,-3) E (0,5) F'(-2,2)
Can you add 5 xy + 4 yx
Answer: Yes, we can add them as they are like terms
The answer we get after adding is 9xy
Step-by-step explanation:
Even though 'xy' and 'yx' seem to be different, we must remember that multiplication is commutative and hence 'xy' and 'yx' are the same
The answer we get after adding is 9xy
Answer:
Yes, and you get 9xy
Step-by-step explanation:
4yx = 4xy
Yes, you can add them.
5xy + 4xy = 9xy
the distance between the point 0,0 and 5, 12
Answer:
13
Step-by-step explanation:
the formula for distance is √(X2-X1)^2 + (y2-y1)^2
=√(5-0)^2 + (12-0)^2
=√5^2 + 12^2
=√25+144
=√169
=13
^please answer, thanks in advance ^
Answer:
There is not enough information to determine the mean, the median is 28.
There is not enough information to determine the mean absolute deviation, the interquartile range is 18
Step-by-step explanation:
The box plot given has a skewed distribution, this means that both the mean and median values are not the same. From a box plot, the median value Can be obtained as the point in between the box.
From the box plot given, the marked point in between the box is 28 cm
Hence, Median = 28 cm
The mean cannot be inferred from the skewed box plot.
There is also not enough information to determine the mean absolute deviation ;
The interquartile range:
(Q3 - Q1)
Q3 = upper quartile, the endpoint of the box = 40
Q1 = the starting point of the box = 22
IQR = Q3 - Q1
IQR = 40 - 22 = 18
During a Team scavenger hunt event, the average number of steps taken was 1800. Calculate the distance traveled using 10,000 steps = 5 miles. Using a time of 27 minutes to complete the event, calculate your average speed.
Answer:
The average speed was of 2 miles per hour.
Step-by-step explanation:
Average speed:
Average speed is distance divided by time.
Distance:
Solved by proportions, using rule of three.
1800 steps - x miles
10,000 steps - 5 miles
[tex]10000x = 5(1800)[/tex]
[tex]x = \frac{9000}{10000}[/tex]
[tex]x = 0.9[/tex]
Distance of 0.9 miles.
Using a time of 27 minutes to complete the event, calculate your average speed.
Distance of 0.9 miles in 27/60 of an hour. So
[tex]d = \frac{0.9}{\frac{27}{60}} = \frac{60(0.9)}{27} = 2[/tex]
The average speed was of 2 miles per hour.
Which choice is equivalent to the fraction below? (Hint: Rationalize the
denominator and simplify.)
2-√2
2 + 2
A. 2.
B. 2-3
o
C. 3-2.12
D. 6 - 42
6)Factor: x^2+1/3x+1/36
Answer:
2
Step-by-step explanation:
I need someone to do this question
Answer:
$1487.50
Step-by-step explanation:
9514 1404 393
Answer:
$1487.50
Step-by-step explanation:
The amount of interest due is ...
I = Prt
where P is the loan amount, r is the annual rate, and t is the number of years. Here, t = 6 months = 1/2 year, so the interest due is ...
I = $1400×0.125×1/2 = $87.50
The total amount due is the sum of the loan amount and the interest:
due = $1400 +87.50 = $1487.50
The total amount due after 60 months is $1487.50.
7 x 5/6 simplified!!
Answer:
5 5/6
Step-by-step explanation:
7 x 5 = 35
35/6 = 5 5/6
Answer:
5 5/6
Step-by-step explanation:
7 * 5/6
7/1 * 5/6
Multiply the numerators
7*5 = 35
Multiply the denominators
1*6 = 6
Numerator over denominator
35/6
Change to a mixed number
6 goes into 35 5 times with 5 left over
5 5/6
Use the figure to find x
Answer:
The value of x is [tex]\frac{7\sqrt{6}}{2}[/tex]
Solution given:
AB=7
BD=x
<BAC=60°
<DBC=45°
In right angled triangle ABC
Tan 60°=opposite/adjacent
Tan 60°=BC/AB
Substitute value
[tex]\sqrt{3}[/tex]=[tex]\frac{BC}{7}[/tex]
BC=[tex]7\sqrt{3}[/tex]
again
In right angled triangle BCD
Using Cos angle
Cos 45=adjacent/hypotenuse
Cos45°=BD/BC
Substituting value
[tex]\frac{\sqrt{2}}{2}=\frac{x}{7\sqrt{3}}[/tex]
Doing criss cross multiplication
[tex]\frac{\sqrt{2}}{2}*7\sqrt{3}=x[/tex]
x=[tex]\frac{7\sqrt{6}}{2}[/tex]
A box of tangerines that weighs 5 pounds costs $4.25.
What is the cost per pound?
Answer:
$0.85
Step-by-step explanation:
$4.25 divided by 5 pounds equals $0.85 per pound.
Answer:
$0.85
Step-by-step explanation:
Find the unit rate.
4.25/5=x/1
Solve for x. X= 4.25/5=0.85
So 1 lb of tangerines costs $0.85.
Boat A leaves a dock headed due east at 2:00PM traveling at a speed of 9 mi/hr. At the same time, Boat B leaves the same dock traveling due south at a speed of 15 mi/hr. Find an equation that represents the distance d in miles between the boats and any time t in hours.
Answer: [tex]17.5t[/tex]
Step-by-step explanation:
Given
Speed of boat A is [tex]v_a=9\ mi/hr[/tex]
Speed of boat B is [tex]v_b=15\ mi/hr[/tex]
Both are moving perpendicular to each other
Distance traveled by Boat A [tex]x_a=9t[/tex]
Distance traveled by Boat B [tex]x_b=15t[/tex]
Distance between them is given by Pythagoras theorem
[tex]\Rightarrow d^2=(x_a)^2+(x_b)^2\\\\\Rightarrow d^2=(9t)^2+(15t)^2\\\\\Rightarrow d=\sqrt{(9t)^2+(15t)^2}\\\\\Rightarrow d=\sqrt{81t^2+225t^2}\\\\\Rightarrow d=\sqrt{306t^2}\\\\\Rightarrow d=17.49t\approx 17.5t\ \text{miles}[/tex]
Distance between them is [tex]17.5t[/tex]
write an expression to represent the sum of 3 and the quotient of a number divided by 6
Solve the following system of equations
x^2+2y^2=59
2x^2+y^2=43
Answer: x = (-3,3), y = (-5,5)
Step-by-step explanation:
Add both of the equations together, for [tex]3x^{2}+3y^{2} = 102[/tex]. Now we can divide both sides by 3, getting[tex]x^2+y^2=34[/tex]. we subtract the first equation from our equation we just got, getting [tex]y^2=25[/tex] y= (5,-5). once we plug that in, we get [tex]50+x^2 = 59[/tex], [tex]x^2 = 9[/tex] x = (-3,3)
Juan borrowed $ 3, 500 from a credit union for 6 years and was charged simple interest at a rate of 4.97 %. What is the amount of interest he paid at the end of the loan?
Answer:
$4543.70
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Simple Interest Rate Formula: [tex]\displaystyle A = P(1 + rt)[/tex]
P is principle amountr is ratet is timeStep-by-step explanation:
Step 1: Define
Identify
P = 3500
t = 6
r = 4.97% = 0.0497
Step 2: Find Interest
Substitute in variables [Simple Interest Rate Formula]: [tex]\displaystyle A = 3500(1 + 0.0497 \cdot 6)[/tex](Parenthesis) Multiply: [tex]\displaystyle A = 3500(1 + 0.2982)[/tex](Parenthesis) Add: [tex]\displaystyle A = 3500(1.2982)[/tex]Multiply: [tex]\displaystyle A = 4543.7[/tex]Work out m and c for the line: y + 3 x = 1
Answer:
look at diagram above. Use y=mx+c
