The profit function p(x) of a tour operator is modeled by p(x) = −2x2 + 900x − 40000, where x is the average number of tours he arranges per day. What is the range of the average number of tours he must arrange per day to earn a monthly profit of at least $60,000?
between 200 and 250; exclusive
between 200 and 250; inclusive
less than 250
more than 200
Solving the quadratic function, it is found that the range is of:
between 200 and 250; inclusive
The profit for x tours is modeled by the following equation:
[tex]p(x) = -2x^2 + 900x - 40000[/tex]
It is concave down, so the monthly profit will be of at least $60,000 between the two roots when [tex]p(x) = 60000[/tex]. Thus:
[tex]60000 = -2x^2 + 900x - 40000[/tex]
[tex]2x^2 - 900x + 10000 = 0[/tex]
Simplifying by 2:
[tex]x^2 - 450x + 50000 = 0[/tex]
Which has [tex]a = 1, b = -450, c = 50000[/tex]
Then:
[tex]\Delta = (-450)^2 - 4(1)(50000) = 2500[/tex]
[tex]x_{1} = \frac{-(-450) + \sqrt{2500}}{2} = 250[/tex]
[tex]x_{2} = \frac{-(-450) - \sqrt{2500}}{2} = 200[/tex]
At least $60,000 includes $60,000, thus the interval is inclusive, and the correct option is:
between 200 and 250; inclusive
A similar problem is given at https://brainly.com/question/25181401
Multiply. 3 1/3 1 3/4 Express your answer in simplest form. 5 5/12 5 5/6 6 5/6 6 5/12
Answer:
[tex]5\frac{5}{6}[/tex]
Step-by-step explanation:
[tex]3\frac{1}{3}*1\frac{3}{4}[/tex]
[tex]\frac{10}{3} *\frac{7}{4} \\[/tex]
[tex]\frac{10*7}{3*4}[/tex]
[tex]\frac{70}{12}[/tex]
First you can divide both sides by 2
[tex]\frac{70}{12}=\frac{35}{6}[/tex]
Now make it as a mix number
[tex]\frac{35}{6} =5\frac{5}{6}[/tex]
Hope this helps you.
Let me know if you have any other questions :-)
Which algebraic expression represents
the phrase "half the value of x" ?
Answer:
½x - 40
Step-by-step explanation:
Eliot went to the store and bought 4 1/2 pounds of chicken for $12.00. What was the cost per pound of chicken? round you answer to the nearest cent is necessary.
I will give you brainly
Answer:
$2.67
Step-by-step explanation:
$12.00 divided by 4.5 (aka four and a half) = 2.6666 = amount per pound
Round to the nearest cent. 2.666, that last six makes the six in the hundredths place round up to 7.
Easy math problem.....
Answer:
A should be correct.
Step-by-step explanation:
Given, a = 1/2 and b = -1/3
First, let's solve the numerator. Then we have:
1/2 - 1/3
= 1/6
Since we found out our numerator, It is time to find out our denominator.
We have:
1/2 x -1/3
= -1/6
Since we now know the numerator and the denominator, we can now find out what is a+b/ab. We can find that by adding the numerator and denominator.
1/6 divided by -1/6 is equaled to -1.
Therefore, A should be correct.
Kind requests:
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Answer:
A. -1
Step-by-step explanation:
1/2 + -1/3
-------------
1/2 x -1/3
First, make 1/2 and -1/3 have the same denominator
1/2 x 3/3 = 3/6
-1/3 x 2/2 = -2/6
Add
3/6 + -2/6 = 1/6
Multiply
1/2 x -1/3
1 x -1
-------
2 x 3
= -1/6
This makes the big equation
1/6
-----
-1/6
Simplify
1/6 / 1/6
-----------
-1/6 / 1/6
1/-1
or -1
a. 2300ml=_____l b. 9400ml=_____l c. 9l=________ml d. .7l=_______ml e. 9.7l=_____ml
f. 670ml=_______l g.217ml=_______l h. 1200ml=______l
Answer:
a) 2300 ml = 2.3 l
b) 9400 ml = 9.4 l
c) 9 l = 9000 ml
d) 7 l = 7000 ml
e) 9.7 l = 9700 ml
f) 670 ml = 0.67 l
g) 217 ml = 0.217 l
h) 1200 ml = 1.2 l
Step-by-step explanation:
For converting milliliter to liter, divide the number (ml) by 1000. For converting liter to milliliter multiply the number (l) by 1000.
The values for three different sets of data are shown below.
Data
Data Set
Values
1
52, 55, 59, 53, 50
2
40, 49, 43, 42, 90, 38
3
24, 30, 26, 31, 40, 26
Without calculating any statistics, Jadyn knows that data set 1 would have the least mean absolute deviation among the three sets. Which statement explains how she knows?
Sets 2 and 3 have an even number of values.
Set 1 has the least number of values.
Sets 2 and 3 contain outliers.
Set 1 contains an outlier.
Answer:
data set 3 would have the least mean absolute deviation among the three sets since there is less spread of the data and the data values in set-3 lie close to the mean.
Step-by-step explanation:
The mean absolute deviation is a measure of spread of the data.
If the data values in the given data set are widely spread then we obtain a higher mean absolute deviation.
if the data values of a given data set are close to each other i.e there is a less spread of the data and hence the mean absolute deviation will be low as the data values will lie close to the mean.
We are given three data set as:
set- 1 42, 48, 50, 88, 49
set- 2 63, 29, 35, 28, 30
set- 3 2, 5, 3, 8
Hence, we could observe that the data values in set 1 and set 2 are widely spread.
In set-1 the data value 88 is much higher value as compared to other data values.
Similarly in set-2 the data value 63 is again a much higher value as compared to other data values.
Whereas in set-3 the data values are all closely related and there is not much spread in the data.
Answer:
It is c
Step-by-step explanation:
Choose the grid reference number for the mine shown.
A. 631226
B. 126362
Answer:
631226
Step-by-step explanation:
The grid reference number for the mine shown is (63.35, 12.7).
What is coordinate plane?A coordinate plane is a two-dimensional surface formed by two number lines. It is formed when a horizontal line (the X-axis) and a vertical line (the Y-axis) intersect at a point called the origin. The numbers on a coordinate grid are used to locate points.
From the given grid,
The reference point is (63.35, 12.7)
Therefore, the grid reference number for the mine shown is (63.35, 12.7).
Learn more about the coordinate plane here:
https://brainly.com/question/24134413.
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HELLLP IM GIVING BRAINLYEST TO THE RIGHT ANSWER
Answer:
Well, what's the question?
which ratios are equivalent to 7: 15.
Help ASAP!!! ILL GOVE BRAINLIEST IF YOU GET IT RIGHT!
Step-by-step explanation:
I am not sure but i think it is D or E (last 2 choices)
Sorry if wrong
A coffee shop sells lattes for $4 and cappuccinos for $3. Last Friday, they sold 78 drinks for a total of $252.
How many cappuccinos were sold?
Number of sold cappuccinos will be 60.
What is linear expression?
A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.
Given that;
A coffee shop sells lattes for $4 and cappuccinos for $3.
Last Friday, they sold 78 drinks for a total of $252.
Now,
Let number of lattes = x
Number of cappuccinos = y
Since, Last Friday, they sold 78 drinks.
So, we can formulate;
x + y = 78 ... (i)
And, Last Friday, they sold 78 drinks for a total of $252.
So, we can formulate;
4x + 3y = 252 ... (ii)
Solve equation (i) and (ii) we get;
x + y = 78
4x + 3y = 252
Multiply by 4 in equation (i) and subtract from (ii) we get;
4x + 3y - 4x - 4y = 252 - 312
- y = - 60
y = 60
And, x + y = 78
x + 60 = 78
x = 18
Thus, Number of sold cappuccinos will be 60.
Learn more about the linear expression visit:
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Can you help me solve pleas
f(x)=x3+8x2+5x−50 factored
Answer:
[tex](x+5)^{2} (x-2)[/tex]
Step-by-step explanation:
1) Factor [tex]x^3} +8x^{2} +5x-50[/tex] using polynomial division.
[tex](x^{2} +10x+25)(x-2)[/tex]
2) Rewrite [tex]x^{2} +10x+25[/tex] in the form [tex]a^{2} +2ab+b^{2}[/tex], where a = x and b = 5.
[tex](x^{2} +2(x)(5)+5^{2} )(x-2)[/tex]
3) Use Square of Sum: [tex](a+b)^{2} =a^{2} +2ab+b^{2}[/tex].
[tex](x+5)^{2} (x-2)[/tex]
The correct equation that goes through the point (3, 4) and is parallel to the line y=2x+1
Answer: y = 2x -2
Step-by-step explanation: parallel is same slope diff y intercept
y = 2x
4 = 2(3) + x
4 = 6 + x
x = -2
Find the measures of the following angles
Answer:
HGD: 117
FDG: 180
Step-by-step explanation:
Answer:
<HDG = 117 degrees
<FDG = 63 degrees
Step-by-step explanation:
Its a straight line
These are supplementary angles
If its a striaght line its 180 degrees.
We already know theres a 63 degrees so we jsut gotta subtract
180-63=117
So 117 degrees for HDG
The denominator of a fraction is 4 more than its numerator. If the fraction equals 1/3, what is the fraction?
Answer:
Hello,
Here is your answer:
2/6
Simplify
10-2
103
-100,000
*
1
10
1
10
100,000
RETRY
Answer:
100,000
Step-by-step explanation:
[tex] (\dfrac{10^{-2}}{10^3})^{-1} = [/tex]
When you divide powers with the same base, subtract the exponents.
[tex] = (10^{-2 - 3})^{-1} [/tex]
[tex] = (10^{-5})^{-1} [/tex]
To raise a power to a power, multiply the exponents.
[tex] = 10^{-5 \times (-1)} [/tex]
[tex] = 10^5 [/tex]
[tex] = 100,000 [/tex]
english 2 hhhhhhhheeeelllpppp
The correct answer is C.
Hope this helps !! :)
x-2y=-8 slope intercept form
need it asap plz
Answer:
y = 1/2x + 4
Step-by-step explanation:
hope this helps
WILL MARK BRAINLIEST!
Identify if the polynomial is a monomial, binomial, trinomial or multinomial.
Answer:
multinomial
Step-by-step explanation:
polynomial are equal to multinomial
Are the shapes simliar?
a
No
b
Yes
c
There is no way to determine this.
Answer:
yes
Step-by-step explanation:
could I get brainliest please
what is b divided by b% of b? PLS HELP
Answer:
b / (b/100×b)
= b / (b/50
= 50b/b
= 50
Step-by-step explanation:
brainliest plz
Answer:
b²/0.0b
Step-by-step explanation:
You're asking what is
[tex] \frac{b}{b\%} \times b[/tex]
Know that b% translates to b/100=0.0b
b×b=b²
Therefore it becomes
[tex] \frac{ {b}^{2} }{0.0b} [/tex]
solve an equation to find the value of x
Answer:
(7+x)°=180-130
x=50-7
x=43
A video game store was getting rid of old games, selling them 5 for $102.05. If they sold 3 games, how much money would they have made?
First determine how much one game would be and then calculate how much they would make selling 3 games. You must answer BOTH.
one game costs $________
3 games would make them $_______
Answer:
20.41
Step-by-step explanation:
I got the answer by doing 102.05 divided by 5 the took that number and multiplied it by 3 to get the answer 61.23
A secretary can type 960 words in 6minutes how many words can she type in 1 hour
Answer:
9600 words in an hour.
Step-by-step explanation:
There are sixty minutes in an hour.
60/6=10
multiply 960 by 10
960*10=9600
The secretary can type 9600 words in 1 hour.
Lamar made $110 for 5 hours of work.
At the same rate, how much would he make for 12 hours of work?
Answer:
264
Step-by-step explanation:
to find one hour
110÷5=22 per hour
12×22=264
Answer: Lamar would make $264 in 12 hours of work.
First we would try to find how much he would make in an hour, so technically the unit rate.
TO find the unit rate we have to do 110/5 which is equal to $22
Then we know that Lamar is working for 12 hours and that he makes $22 per hour. SO, 12 times 22 is 264.
Step-by-step explanation:
I hope this helps, if you are having a tough time with math you can use:
khan academy
math nation
and many more free sites!
PLS HELP DUE IN 1 HOUR
write the expression using positive exponents
1/3^-5
Explanation:
The rule used is [tex]\left(\frac{a}{b}\right)^{-c} = \left(\frac{b}{a}\right)^{c}[/tex]
That rule says to go from a negative exponent to a positive exponent, we apply the reciprocal of the fraction.
So,
[tex]\left(\frac{1}{3}\right)^{-5} = \left(\frac{3}{1}\right)^{5} = 3^5[/tex]
can someone help me please
Answer:
53 degrees
Step-by-step explanation:
m<J = m<Q
what is dividing fractions
Answer:
The simplest way I can describe dividing fractions is like multiplying fractions but upside down.
Example:
1/2 ÷ 1/3
To do this, the easiest way is to "flip" the second fraction.
It then becomes:
1/2 × 3/1
Then you just multiply across and you get a product of 3/2 or 1 1/2