Using the vertex of a quadratic function, she should harvest her honey after 64 days to maximize profit.
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex][tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]Considering the coefficient a, we have that:
If a < 0, the vertex is a maximum point.If a > 0, the vertex is a minimum point.The profit function is given as follows:
P(t) = -16t² + 2050t + 150.
The coefficients are a = -16 < 0, b = 2050, c = 150, hence the t-value of the vertex is:
[tex]t_v = -\frac{b}{2a} = -\frac{2050}{-32} = 64[/tex]
Hence she should harvest her honey after 64 days to maximize profit.
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In survey of 100 students in the institute of Language Studies at Addis Ababa University,
the numbers of students studying various languages were found to be English 28,
Amharic 30, Afan Oromo 42, English and Afan Oromo 10, English and Amharic 8,
Amharic and Afan Oromo 5, and all the three languages 3. How many students
a. were studying none of the languages?
b. had Afan Oromo as their only language?
c. studied Amharic if they studied Afan Oromo?
Answer:
a. 17
b. 30
c. 5
Step-by-step explanation:
English (E) = 28 - 15 (10+8-3) = 13
Amharic (A) = 30 - 10 (8+5-3) = 20
Afan Oromo (AO) = 42 - 12(10+5-3) = 30
E+AO = 10
E + A = 8
A + AO = 5
A + AO + E = 3
a. 13 people spoke just English+ 20 people who just spoke Amharic + 30 people who just spoke Afan Oromo+ The multilingual people (10+8+5-3=20) which is 83, so that means that 17 learned no language.
b. 42 People learned Afan Oromo, but only 30 of them learned that language separately. 10 People learned it along with English, and 5 learned it with Amharic. However, 3 of those people were the same, so 12 people of those 42 spoke multiple languages. Therefore, only 30 people spoke just Afan Oromo.
c. This one is kinda just a trick question, they want you to overthink it because of the 3 who learned all, but it's just 5 like it says in the question.
The mean of a set of numbers is 500. a. If 10 is added to each of the numbers in the set, then what will be the mean of the new set? The mean of a set of numbers is 500 . a . If 10 is added to each of the numbers in the set , then what will be the mean of the new set ?
Answer:
510
Step-by-step explanation:
Assume 2 numbers 500,500.. with a mean of 500
so if we add 10 to each of the two numbers, mean will be:
[tex]\frac{510+510}{2}=510[/tex]
Of course you can vary the set and the numbers and still get the same mean
If you want to study which science course students liked the most during high school, you should survey... science teacher's, because they know what students like. science majors, because they love science. O the lunch room, because they will consist of all genders and ages and be unbiased about science. graduating seniors, because they have taken a wider variety of science courses. If you want to study which science course students liked the most during high school , you should survey ... science teachers , because they know what students like . science majors , because they love science . O the lunch room , because they will consist of all genders and ages and be unbiased about science . graduating seniors , because they have taken a wider variety of science courses .
Answer:
the last option
Step-by-step explanation:
please put brainliest
How many 4-character passwords can you generate if the first character can be any letter of the English alphabet, the next two characters can be any two digits from 0 to 9, and the last one can be any of the characters %,*, or #? (Repetition is allowed!)
There are 7,800 different passwords.
How many different passwords can be generated?
Here we need to count the number of options for each of the digits of the password.
The first character has 26 options (26 letters in the alphabet).
The second character has 10 options (ditis from 0 to 9), and also does the third character
The fourth character has 3 options (%,*, or #)
The total number of different passwords that can be generated is given by the product between the numbers of options, so we have:
C = 26*10*10*3 = 7,800
There are 7,800 different passwords.
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What is the measure of arc ECF in circle G? pls show work, I don't get edge teachers
The measure of arc ECF in circle G is 98°. The correct option is the second option 98°
Circle GeometryFrom the question, we are to determine the measure of arc ECF
By using the one of the circle theorems
The angle subtended by an arc of a circle is twice the angle it subtends anywhere on the circle's circumference
In the given diagram,
∠F = 1/2 ×104°
∠F = 52°
∠D + ∠E + ∠F = 180° (Sum of angles in a triangle)
∠D + 79° + 52° = 180°
∠D = 180° - 79° - 52°
∠D = 49°
m arc ECF = 2 × m ∠D
m arc ECF = 2 × 49°
m arc ECF = 98°
Hence, the measure of arc ECF in circle G is 98°. The correct option is the second option 98°
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Simplify:
(12+14) x 8+ (8² +4²) =
Answer:
288
Step-by-step explanation:
[tex]26 * 8+(2^{6} +2^{4} )\\\\208+(64+16)\\208+80[/tex]
Answer:
288
Step-by-step explanation:
PEMDAS
Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
Parentheses and Exponents:
(26) x 8+(64+16) (28) x 8+(80)
Multiplication:
26 x 8 + 80 208+80
Addition:
208+80= 288
Write an equation of the line passing through the point (6,4) that is perpendicular to the line y=- 1/2x +4
Hello,
"perpendicular to the line y= - 1/2x +4 "
so y = -1/2x + p
-1/2 × 6 + p = 4 ⇔ -3 + p = 4 ⇔ p = 4 + 3 = 7
y = -1/2x + 7
Given segment AC and point B that lies on AC,
find CB if AC = 17, AB = 32 + 3x, and CB=57+6x
CB=
I give brainliest
The total length of the segment AC is the sum of AB and CB, which gives, CB = 9
How can the length of CB be found?The given parameters are;
AC = 17AB = 32 + 3•xCB = 57 + 6•xRequired: CB
Solution:
AC = AB + CB by segment addition property
Therefore;
AC = 17 = 32 + 3•x + 57 + 6•x = 89 + 9•x
17 = 89 + 9•x
[tex]x = \frac{17 - 89}{9} = - 8[/tex]
CB = 57 + 6•x = 57 + 6 × (-8) = 9
Therefore;
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PLS ANSWER PLS!
Two functions are represented below.
FUNCTION A FUNCTION B
y=35x (looked at linked image)
What is the difference in the rate of change between Function A and Function B? Be sure to include the rate of change of each function in your answer
The difference in the rate of change of both functions is: 15.
What is the Rate of Change of a Function?Rate of change of a linear function = change in y / change in x.
Function A is given as: y = 35x. The rate of change for function A is 35.
From the graph of function B, using two points, (1, 50) and (2, 100):
Rate of change = (100 - 50)/(2 - 1)
Rate of change = 50.
Therefore, the difference in the rate of change of both functions = 50 - 35 = 15.
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Which answer is correct?
The reason that would support that is ∠B ≅ ∠B , the reflective property of equality.
What are similar triangles?Similar triangles are triangles that have their corresponding angles equal and the ratio of their corresponding lengths also equal.
Analysis:
triangle BDE and BAC share the same angle B
which means ∠DBE = ∠ABC.
The reflective property of equality says a number is always equal to itself. Therefore, ∠B ≅ ∠B
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A particular sawdust pile has a base diameter of 25 feet when the height is 20 feet. Find the volume of this sawdust pile when it is 30 feet high.
The volume of the sawdust pile is 11,039.06 ft³.
What is the volume of the pile?The shape of the sawdust pile would be a cone. The diameter is always proportional to its height.
Diameter = k x height
where k is equivalent to the rate of increase of the diameter with respect to the increase in height.
25= k20
k = 25 / 20
k = 1.25
Diameter when height is 30 ft = 1.25x 30 = 35.50 feet
Volume of the sawdust = [tex]\frac{1}{3}[/tex]πr²h
Where:
π = 3.14 r = radius = diameter / 2 = 35.50 / 2 = 18.75h = 30[tex]\frac{1}{3}[/tex] x 3.14 x 18.75² x 30 = 11,039.06 ft³
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Given h(f)=-2(f+5)^2+4 find h(-8)
Answer:
h(-8)= -14
Step-by-step explanation:
[tex]h(-8)=-2(-8+5)^2+4 \\h(-8)=-18+4=-14[/tex]
[tex]\huge\boxed{-14}[/tex]
We have the following equation:
[tex]h(f)=-2(f+5)^2+4[/tex]
Substitute in [tex]-8[/tex] for [tex]f[/tex] and simplify.
[tex]\begin{aligned}h(-8)&=-2(-8+5)^2+4&\textsf{Substitute.}\\&=-2(-3)^2+4&\textsf{Add.}\\&=-2\cdot9+4&\textsf{Simplify the power.}\\&=-18+4&\textsf{Multiply.}\\&=\boxed{-14}&\textsf{Add.}\end{aligned}[/tex]
Write an expression that is equal to 20 usong only one 2 and two 4s and any number of math symbols
Answer:
4^2+4
Step-by-step explanation:
one 2 and two 4s
so 4^2+4=16+4=20
so 4^2+4
(calculation)
Volume (to the nearest tenth)
Answer:
913
Step-by-step explanation:
cylinder:
radius=5.6 height=7
first lets find the volume of the cylinder the formula for the volume of a cylinder is pi times radius squared times height. so after plugging in the height and radius you get 689.64242
cone:
radius=5.6 height=6.8
now the volume of the cone, the formula for the volume of a cone is pi times radius squared times height/3. so after plugging in the height and radius of the cone you get 223.31278
so 689.64242 + 223.31278= 912.9552 and that rounded to the nearest tenth is 913
If f(x) = x2 + x and g(x) = x − 3, find f(g(7)).
The value of f(g(7)) is 20
How to determine the composite functions?The functions are given as:
f(x) = x^2 + x
g(x) = x - 3
Start by calculating g(7)
g(7) = 7 - 3
Evaluate
g(7) = 4
So, we have:
f(g(7)) = f(4)
Substitute 4 for x in f(x) = x^2 + x
f(4) = 4^2 + 4
Evaluate
f(4) = 20
Hence, the value of f(g(7)) is 20
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(PLEASE HELP FAST!!!) Which expression gives the area of triangle QRS?
The expression which gives the area of triangle QRS is [tex]\frac{1}{2} (9)(15)sin(20^{o} )[/tex].
We need to find the area of triangle QRS.
How do I find the area of a triangle using trigonometry?The area of a triangle can be expressed using the lengths of two sides and the sine of the included angle. Area of Δ = ½ ab sin C.
Now, the area of the triangle QRS[tex]=\frac{1}{2} (9)(15)sin(20^{o} )[/tex]
Therefore, the expression which gives the area of triangle QRS is [tex]\frac{1}{2} (9)(15)sin(20^{o} )[/tex].
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What is the solution set for this inequality? 5x − 4 < 11 + 8x
Answer: x>-5
Step-by-step explanation:
add 4 to both sides
5x-4+4<11+8x+4
simplify
5x<8x+15
subtract 8x from both sides
5x-8x<8x+15
simplify
-3x<15
divide both sides by -3 and switch inequality sign
-3x/-3>-15/-3
x>-5
[tex]\large\displaystyle\text{$\begin{gathered}\sf 5x-4 < 11+8x \end{gathered}$}[/tex]
Simplify both sides of the inequality.
[tex]\large\displaystyle\text{$\begin{gathered}\sf 5x-4 < 8x+11 \end{gathered}$}[/tex]
Subtract 8x from both sides.
[tex]\large\displaystyle\text{$\begin{gathered}\sf 5x-4-8x < 8x+11-8x \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf -3x-4 < 11 \end{gathered}$}[/tex]
Add 4 to both sides.
[tex]\large\displaystyle\text{$\begin{gathered}\sf -3x-4+4 < 11+4 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf -3x < 15 \end{gathered}$}[/tex]
Divide both sides by -3.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{-3x}{-3} < \frac{15}{-3} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf x > -5 \ \ \iff \ \ \ Answer \end{gathered}$}[/tex]
{ Pisces04 }wo competing companies are having sales on projectors. Projector #MD375 has a retail price of $1,200. The Office Spot is advertising #MD375 for 20% off, while Office & Beyond has stated they will match any competitor’s advertised special and take an additional 15% off of the competitor’s advertised price. How much money is saved by purchasing the projector from Office & Beyond instead of the Office Spot?
The amount of money that is saved by purchasing the projector at Office and beyond is $144.
How much money is saved?The first step is to determine the price of the projector at The Office spot.
Discounted price : (1 - 0.20) x $1200
0.80 x $1200 = $960
The second step is to determine the price of the projector at the Office and Beyond.
Discounted price : (1 - 0.15) x $960 = $816
Difference in price : 960 - 816 = $144
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Problem 10-09 (Algorithmic) Cress Electronic Products manufactures components used in the automotive industry. Cress purchases parts for use in its manufacturing operation from a variety of different suppliers. One particular supplier provides a part where the assumptions of the EOQ model are realistic. The annual demand is 5,300 units, the ordering cost is $70 per order, and the annual holding cost rate is 25%.
The economic order quantity is 385 and reorder point is 254.
Economic order quantity (EOQ)a. Economic order quantity (EOQ)
EOQ=√2×D×C÷H
Where:
D =Annual Demand
S = Cost of Ordering
H=Holding cost
Hence:
EOQ=√2×5300×70÷.25×20
EOQ=√742,000÷5
EOQ=√148,400
EOQ=385
b. Reorder point
Reorder point=5300/250×12 days
Reorder point=254
c. Reorder point
Reorder point=5300/250×35 days
Reorder point=742
d. Reorder point
Reorder point=742-385
Reorder point=357
Therefore the economic order quantity is 385 and Reorder point is 254.
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The complete question is:
a. If the cost of the part is $20 per unit, what is the economic order quantity?
b. Assume 250 days of operation per year. If the lead time for an order is 12 days, what
is the reorder point?
c. If the lead time for the part is seven weeks (35 days), what is the reorder point?
d. What is the reorder point for part (c) if the reorder point is expressed in terms of the inventory on hand rather than the inventory position?
Use your calculator to find the approximate value of e. (Round to 4 decimal places)
Using a calculator to find the approximate value of e in
F(e)=e^{2e} we have F(e)=229.6516. This is further explained below.
What is maclurin polynomial?Generally, To approximate a function f (x) f (x) f (x) for values of x near to zero, one may use a power series known as a Maclaurin series.
In conclusion, Using your calculator to find the approximate value of e in
F(e)=e^{2e}
We have
F(e)=e^{2e}
F(e)=229.6516
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The product of 12, x and y. Translate the following phrase into an algebraic expression. Do Not simplify.
The product of 12, x, and y written in an algebraic expression is 12xy.
What are algebraic expressions?Algebraic expressions are mathematical expressions containing variables, coefficients, and their arithmetic operators such as addition, subtraction, multiplication, and division.
An algebraic expression can be used to interpret and solve mathematical word problems.
From the information given:
The algebraic expression can be translated as 12x × y = 12 xy.
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The algebraic expression that can be translated as product of 12, x and y is 12 xy.
What are algebraic expressions?Expressions are used to interpret mathematical problems
From the question given we are to translate the product of 12, x and y.
The product of 12 and x is 12x
The product of 12x and y is 12xy, hence the algebraic expression that can be translated as product of 12, x and y is 12 xy.
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which expressions are equivalent to 3x
x is powering both numbers so it can be outside the parenthesis.
We have given that 3^x.
What is the expression?An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
The first one isn't an answer because 3^x is exponential while x^3 is a cubic function.
If you draw them you will see that they are very different.
B is correct because we can divide both numerator and denominator by 6 and we get 3^x.
C is not correct because x is not powering 3 so we cannot divide both by 6D is correct because 3^(x-1) is the same as
and when multiplied by 3 we get 3^x
3^x*3^(-1) = 3^x/3
E is not correct.
will understand after the explanation in DF is correct.
x is powering both numbers so it can be outside the parenthesis.
The question is incomplete the complete question is,
Which expressions are equivalent to the one below? Check all that apply.
3^x
A. x^3
B.(18/6)^x
C.18^x/3
D.3(3^(x-1))
E.3(3^(x+1))
F.18^x/6^x
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Study: Factoring Polynomials Completely
What are the possible roots of the polynomial function below? (Check all
that apply.)
F(x) = 2x² + 5x -5
Answer:
x = 0.76556443 x = -3.26556443
Step-by-step explanation:
You can use the quadratic formula to find the roots.
A sample of size 400 has mean =6.0. Can it be regarded as a sample from a large population with mean 6.25 inches and standard deviation 2.25 inches ? using α=0.05
The value of Z at the 5% level is not significant if the sample of size 400 has mean is 6.0.
What is the standard deviation?It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.
[tex]\rm \sigma = \sqrt{\dfrac{ \sum (x_i-X)}{n}[/tex]
σ is the standard deviation
xi is each value from the data set
X is the mean of the data set
n is the number of observations in the data set.
The standard error of the estimated mean:
[tex]\rm = \dfrac{2.5}{\sqrt{400}}[/tex]
= 0.1125
x = 6.0–6.2 = 0.2
[tex]\rm Z = \dfrac{0.2}{0.1125}[/tex]
Z = 1.778
This is not significant at the 5% level.
This would have been significant at the 5% level if the same sample means had been found using a sample size of merely 500.
Thus, the value of Z at the 5% level is not significant if the sample of size 400 has mean is 6.0.
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A train travels 65 miles and then stops in a city. Then it travels at a speed of 95 miles per hour before reaching its last stop.
Enter a linear model which represents the total distance traveled, d, by the train, as a function of t, the number of hours
after leaving the city
Step-by-step explanation:
as speed is always
distance/time
we need to multiply speed by the time traveled to get the distance traveled.
so,
d = 95t + 65
after all, until it reached the city it traveled already 65 miles (we don't know the speed, but it does not matter for the question about the total distance traveled), which we need to add to get the total distance.
Find the exponential function that contains the points (3,24) and (4,48).
The required exponential function that contains the points (3,24) and (4,48) is y = 3(2)^x
Exponential functionsThe standard exponential function is expresses as y = ab^x
Given the coordinate points (3,24) and (4,48), the equivalent equations are:
24 = ab^3 ......... 1
48 = ab^4
Take the ratios
48/24 = b^4/b^3
2 = b
Substitute b = 2 into equation 1
24 = a(2)^3
8a = 24
a = 3
Hence the required exponential function that contains the points (3,24) and (4,48) is y = 3(2)^x
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There's 18 deer and 52 lions if 10 lions eat 17 deer how many deer are left
Answer:
1 deer
Step-by-step explanation:
18 deer minus 17 eaten leaves 1 deer
Suppose you have opened some Nutty Bars to check the company’s claim of an “average” of 8 peanuts per bar. Here is what you found after opening 10 bars: 5, 8, 8, 8, 11, 7, 8, 6, 6, and 6. Which average should the company use to support their claim?
The company should use the median to support their claims.
Which measure of average should the company use?Measures of average commonly used are mean and median.
Mean is the sum of the numbers divided by the total number
Mean : (5 + 6 + 6 + 6 + 7 + 8 + 8 + 8 + 8 + 11) / 10 = 7.3
Median is the number at the center of the dataset when it is arranged either in ascending or descending order.
Median = 8
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Solve the mathematical puzzle.
Determine the digits of Y
from these clues.
The digits of Y
add to 16.
The first digit is 4 times the third digit.
The second digit is 3 times the third digit.
Y is a three digit number.
Answer:
862
Step-by-step explanation:
4 x 2 = 8
3 x 2 = 6
8 + 6 + 2 = 16
When sending a letter, Bobby pays a fixed amount for letters weighing up to an ounce. He then pays a smaller, fixed amount for each additional ounce (or part of an ounce). The cost of sending the letter in cents is modeled by the function y = 30 + 20(x - 1), where x is the weight of the letter in ounces. What does the number 20 describe?
A function assigns the values. The number 20 describes the cost that Bobby needs to pay for each extra ounce of letters.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
In the given function y = 30 + 20(x - 1), the number 20 describes the cost that Bobby needs to pay for each extra ounce of letters.
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