The bicycles which the shop should build to minimize the average cost per bicycle is 25 bicycles
How to find number of bicycles that will minimize average cost?Average cost function:
C(x) = 0.2x² - 0.1x + 3.799This is a quadratic function, So
a = 0.2b = -0.1c = 3.799Average cost is minimum when
x = - b / 2a
= -(-0.1) / 2(0.2)
= 0.1 / 0.4
x = 1/4
Number of bicycles which should to minimize average cost per bicycle = minimum average cost × total cost
= 1/4 × 100
= 25 bicycles
Therefore, the number of bicycles which will minimize the average cost function is ,25 bicycles.
Complete question:
Aki's bicycle designs has determined that when x hundred bicycles are built, the average cost per bicycle is given by C(x)=0.2x^2-0.1x+3.799, where C(x) is in hundreds of dollars. How many bicycles should the shop build to minimize the average cost per bicycle?
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Given the inequality 4(n − 5) < 3(n + 11), determine which integer makes the inequality false.
S:{4}
S:{11}
S:{53}
S:{−8}
Answer:
C
Step-by-step explanation:
4(n-5)<3(n+11)
4n-20<3n+33
4n-3n<33+20
n<53
n is not 53 but less than 53.
A nursing administrator went through a sample of hospital records and found that, out of 500 randomly selected records, 217 of the patients had been admitted for heart issues. What is the sample statistic?
The sample statistic when the nursing administrator went through a sample of hospital records is 217.
What is statistic?A statistic is a metric used to describe a sample. Estimation or hypothesis testing can be used to determine how likely it is that a sample statistic differs from the population parameter.
A sample is an analytic subset of a larger population in statistics. The use of samples enables researchers to conduct studies with more manageable data and more quickly. Randomly drawn samples have little bias if they are large enough, but obtaining such a sample can be costly and time-consuming.
A sample statistic is a piece of statistical data derived from a small number of items. A sample is merely a subset of a population. Therefore, the 217 of the patients had been admitted for heart issues is the sample.
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Consider the function f(x) = √ x+2 and g(x) = ax+b. Find a and b, if fog (1) = 2 and g (-1)=2.
The value of a and b in the function f(x) = √ x+2 and g(x) = ax + b , is a = 0 and b = 2 .
In the question ,
it is given that ,
the function f(x) = √(x+2) and the function g(x) = ax + b
also given that
fog(1) = 2
f(g(1)) = 2
f(a + b) = 2 .... because g(1) = a + b
√(a + b +2) = 2
Squaring both the sides
a + b + 2 = 4
a + b = 2 .......(1)
also given that
g(-1) = 2
a(-1) + b = 2
-a + b = 2 .....(2)
Adding equation (1) and (2) , we get
2b = 4
b = 2
Substituting b = 2 in the a + b = 2 , we get
a + 2 = 2
a = 2 - 2
a = 0
Therefore , The value of a and b in the function f(x) = √ x+2 and g(x) = ax + b , is a = 0 and b = 2 .
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can someone pls help me i don’t ll get this
Answer: 6
Step-by-step explanation:
Angles opposite congruent sides in a triangle are congruent, so both angles are equal to [tex](13x-6)^{\circ}[/tex].
Since angles in a triangle add to [tex]180^{\circ}[/tex], so:
[tex]36+2(13x-6)=180\\\\2(13x-6)=144\\\\13x-6=72\\\\13x=78\\\\x=6[/tex]
What is the image point of (-6, -4) after the transformation T4.-1 ° ry=-x?
(16, 36) is the image point .
What is image point?
The provided point P is "reflected" in the mirror, appearing on the other side of the line at a distance equal to that from it. To see this, move the point P. Conventionally known as P' (pronounced "P prime"), the point P's reflection over the line is also referred to as the point P's "image."Reflecting (-6, -4) in the line y= - x yields the point (4, 6).
Dilating (4, 6) by a factor of 4 gives the point (16, 36).
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A firm makes circular drink mats , of radius 4.5cm , that are 3mm thick . They want to produce a rectangular box to hold a pile of 12 mats. What are the minimum dimensions of the box.
Please answer with working out
Thank you
Answer:
13.5
Step-by-step explanation: that's the minimum of dimensions for the box
What is the solution to the system of equations
The solution of the given system of equations is (-1, -2).
Explain the method of substitution?Three steps make up the substitution technique: For each of the variables, solve one equation. Put this expression (or plug it in) into the other equation, then solve it. To identify the corresponding variable, rewrite the value's original equation.We are aware that a linear system of equations can be solved using a substitution method.
The intersection of the two lines represents the system's solution.
The given equations are-
y = 3x+1 ...eq 1
y = -2x-4 ...eq 2
Put the value of eq 1 in eq2 .
3x+1 = -2x-4
3x + 2x = -4 - 1
5x = -5
x = -5/5
x = -1
Put the x in eq 1.
y = 3(-1)+1
y = -2
Thus, the solution of the given system of equations is (-1, -2).
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The complete question is-
What is the solution to the system of equations-
y=3x+1 ;
y=-2x-4
In how many ways can the digits in the number 7,550,000 be arranged
The number of ways the digits of the given number can be arranged would be = 5,040
What is factorials?Factorials are mathematical expressions that are used to show the number of ways a variable can be arranged in a data set.
The number of digits found in the number 7,550,000 = 7
The number of ways the digits can be arranged would be the factorials of 7 (7!) ;
= 7×6×5×4×3×2×1
= 5,040
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Suppose you earned a $710,000 bonus this year and invested it at 8.25% per year. how much could you withdraw at the end of each of the next 20 years? select the correct answer.
Withdraw at the end of each of the next 20 years is [tex]710000(1.0825)^{20}[/tex]
What do you mean by simple interest and compound interest?
Simple interest can be defined as the amount that is paid back using borrowed money over a period of time.
simple interest:
Simple interest can be defined as the principal of a loan or deposit that an individual puts into a bank account.
Compound interest:
Compound interest is interest that accrues on the principal and accrues interest.
Given:
Principal, P = $710000
Rate of interest, r = 8.25%
Time period, t = 20 years
withdrawal at the end of 20 years , A = [tex]P(1+r)^{t}[/tex]
A = [tex]710000(1+8.25/100)^{20}[/tex] = [tex]710000(1+0.0825)^{20}=710000(1.0825)^{20}[/tex]
Therefore, withdraw at the end of each of the next 20 years is [tex]710000(1.0825)^{20}[/tex]
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Help on number 1 please!! Thanks.
Answer:
I believe the answer is c
The graphs of f(x) and g(x) are shown below. On a coordinate plane, a straight line with negative a slope represents f (x) = negative x. The line goes through points (0, 0), (negative 6, 6) and (6, negative 6). On a coordinate plane, a straight line with a positive slope represents g (x) = 2 x. The line goes through points (negative 3, negative 6), (0, 0) and (3, 6). Which of the following is the graph of (g – f)(x)? On a coordinate plane, a straight line with a negative slope goes through points (negative 2, 6), (0, 0), and (2, negative 6) On a coordinate plane, a straight line with a negative slope goes through points (negative 6, 6), (0, 0), and (6, negative 6). On a coordinate plane, a straight line with a positive slope goes through points (negative 2, negative 6), (0, 0), and (2, 6).
The option that is the graph of (g – f)(x) is; On a coordinate plane, a straight line with a positive slope goes through points (negative 2, negative 6), (0, 0), and (2, 6).
How to Interpret Inequality Graphs?We are given the function as;
f(x) = -x
Now, the line passes through the points (0,0),(-6,6) and (6,-6) is;
The function given as; g(x) = 2x
This line passes through the points (-3,-6),(0,0) and (3,6).
Before we graph (g - f)(x), we have to first simplify it to get;
The graph of of (g - f)(x)
(g - f)(x) = g(x) - f(x)
= 2x - (-x)
= 3x
At x = 0, we have;
(g - f)(0) = 3(0) = 0
At x = 2, we have;
(g - f)(2) = 3(2) = 6
At x = -2, we have;
(g - f)(-2) = 3(-2) = -6
At x = -6, we have;
(g - f)(-6) = 3(-6) = -18
Looking at the options, option C is true
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The function f(x) is graphed below. How many points on the graph
represent a relative extreme value?
From the given graph of the function, the number of points on the graph representing relative extreme value are two (b and d).
As given in the question,
For the given graph of a function,
Number of points represented on the graph are 5
Points are a, b, c, d, e
Point a, c, e are on the x-axis.
Relative extreme value representing the maximum and minimum value of the graphed function.
For the given graph,
Maximum value represented by point d.
Minimum value represented by point b.
Number of points representing relative extreme values are 2 ( b and d).
Therefore, from the given graph of the function, the number of points on the graph representing relative extreme value are two (b and d).
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A line intersects the points
(8, -4) and (-6, 10).
m = -1
Write an equation in point-slope form
using the point (8, -4).
-
y + 4 = [?] (x −
Enter
Answer:
y + 4 = -(x - 8)
Step-by-step explanation:
The point-slope form equation is y - y1 = m(x - x1)
Since we're given m and since they use the 4 from (8, -4) as y - (-4) = y+4, we simply need to plug in 8 into the RHS of the equation and you can check the math.
If you substitute 8 and -4 for y and x, you have:
-4 + 4 = -1(8 - 8)
0 = -1 * 0
0 = 0
You'd get -2 on both sides if you used -6 and 10, but having an equal equation means our math is true/accurate.
17 Solve the inequality. Graph the solution. 4.2y ≤ -12.6 The solution is and then where it goes on thr number line
The solution to this inequality in interval notation is {-∞, -3} and it goes to the left on the number line.
What is an inequality?In Mathematics, an inequality can be defined as a mathematical relation that is typically used for comparing two (2) or more numerical data such as integers, and variables in an equation based on any of the following inequality symbols:
Greater than (>).Less than (<).Greater than or equal to (≥).Less than or equal to (≤).From the information provided, we have the following inequality:
4.2y ≤ -12.6
Dividing both sides of the inequality by 4.2, we have the following:
y ≤ -12.6/4.2
y ≤ -3
In conclusion, a solution to this inequality is equal to {-∞, -3} as shown in the number line (graph) attached below.
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Solve the following expression when
t = 6 and d = 8
t + d/8-6
Answer:
1
Step-by-step explanation:
Replace the variable letter with the number.
t + d / 8 - 6
6 + 8 / 8 - 6
6 + 1 - 6
7 - 6
1
PLEASE HURYYY RIGHT NOW
Answer:
Only Julia's Question.
Step-by-step explanation:
Julia: 8÷[tex]\frac{1}{4}[/tex]
Tanveer: 8*1/4
What is the slope of the
function below?
(4,4)
(3, 3)
Slope = [?]
Answer:
slope is m=1
Step-by-step explanation:
Answer: 1
Step-by-step explanation: use the slope formula to find the slope m
−18 < 9x
how to solve and answer
Answer:
x> 2
Step-by-step explanation:
18< 9x Divide both sides by 9
2<x or x > 2 All the numbers greater than 2 is a solution.
Atudent mark tardy 5 different times in 40 days what percentage was he tardy
The percentage is the indicating hundredth is 12.5%.
What is the percentage?A specific number in every hundred is what is meant by the percentage. It is a fraction with 100 as the denominator, and one percent is used to symbolize it.
Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
A student was marked tardy five different times in a 40-day period.
Percentage of 5 among 40
= (5/40) x 100
= 12.5%
Hence, The percentage of times the students marked will be 12.5%".
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someone help pls due soon
Answer:
snap to solve
Step-by-step explanation:
u can use snap to solve to get ur answers
Answer:
Step-by-step explanation:
cost price = $640
sell price = $940
percentage = ?
Rate * Base = Amount
Percent * Sell Price = Cost Price
P * 940 = 640
P940 = 640
P940/940 = 640/ 940
P = 0.66666667
Percent = (0.66666667 × 100)/100 = 66.666667
Correct Answer is 66 2/3%
change to exponential form
(4√ x5)
Ling tried to solve an equation.
12=p+6.2
12 + 6.2 = p + 6.2- 6.2 Setting up
18.2 = P Calculating
Answer:
p = 5.8
Step-by-step explanation:
12 = p + 6.2 Subtract 6.2 from both sides. Ling subtracted 6.2 from the right, but added it to the left side.
5.8 = p
It takes 3.5 ounces of cocoa to make a cup of hot chocolate how much cocoa is needed to make 7 cups of hot chocolate
Answer: 24.5
Step-by-step explanation: 3.5 x 7 = 24.5
Answer: 24.5 ounces
Step-by-step explanation:
3.5 times 7 = 24.5 ounces
If you have trouble try
3.5 + 3.5 + 3.5 + 3.5 + 3.5 + 3.5 + 3.5
PLEASE HELP ASAP! WILL GIVE BRAINLIEST AND FIVE STAR RATING FOR ACTUAL HELP! Describe the function‘s end behavior. f(x)=−10+6x^5+4x^3
as x→ ∞, f(x)→
as x→ −∞, f(x)→
Possible answers for both are:
-∞
∞
0
an asymptote
Answer: As x approaches infinity, f(x) approaches infinity.
As x approaches -infinity, f(x) also approaches - infinity.
Step-by-step explanation:
You can either graph this function on an online graphing (such as desmos. com) calculator to see the end behavior, or you can try inputting some numbers in. You could put in the number 1,2,3 and see that the graph will keep on increasing to positive infinity, and input the numbers -1,-2,-3 to see that the numbers will decrease to negative infinity.
Solve for a : a+4/5= 1/ 1/2
[tex]a=\frac{6}{5}[/tex].
Step-by-step explanation:1. Write the expression.[tex]a+\frac{4}{5} =\frac{1}{\frac{1}{2} }[/tex]
2. Convert the right hand side of the equation (check attached image 1).[tex]a+\frac{4}{5} =1*\frac{2}{1} \\ \\a+\frac{4}{5} =2[/tex]
3. Subtract 4/5 from both sides of the equation.[tex]a+\frac{4}{5}-\frac{4}{5} =2-\frac{4}{5}\\ \\a=\frac{2}{1}-\frac{4}{5}\\\\a=\frac{2*5}{1*5}-\frac{4}{5}\\ \\a=\frac{10}{5}-\frac{4}{5}\\ \\a=\frac{10-4}{5} \\ \\a=\frac{6}{5}[/tex]
4. Verify your answer.[tex](\frac{6}{5} )+\frac{4}{5} =\frac{1}{\frac{1}{2} }\\ \\\frac{10}{5} =2\\ \\2=2[/tex]
5. Conclude.[tex]a=\frac{6}{5}[/tex].
The graph shows the cost of grapes at a grocery store. What is the slope of the line?
The slope of the line shown in the graph is 4.5 .
In the question ,
it is given that ,
the amount of grapes is represented on x axis . and
the cost for that grape in the grocery store is represented on y axis .
to find the slope we need two points on the line ,
from the graph we can take two points as (1 , 4.5) and (2 , 9) ,
the slope can be calculated using the formula
slope = (change in y coordinate)/(change in x coordinate)
slope = (9 - 4.5)/(2 - 1)
slope = 4.5/1
slope = 4.5 .
Therefore , The slope of the line shown in the graph is 4.5 .
The given question is incomplete , the complete question is
The graph below shows the cost of grapes at a grocery store. What is the slope of the line?
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Jesse and Amir were assigned the same book to read. Jesse started reading on Saturday, and he is reading 30 pages a day. Amir didn't start until Sunday, but he is reading 35 pages a day.
How many days will it take Amir to catch up to Jesse, and how many pages will they each have read?
Answer the questions to solve this problem using a system of equations.
1. Write an equation to represent the number of pages Amir has read. Use x to represent the number of days Amir has been reading and y to represent the number of pages he has read. (1 point)
2. Write an equation to represent the number of pages Jesse has read.
Using x, the number of days Amir has been reading, write an expression to represent the number of days Jesse has been reading. Remember that Jesse started reading one day before Amir. Use this expression to write an equation for the number of pages Jesse has read. Let y represent the number of pages read. (1 point)
3. Write the system of equations using your answers from questions 1 and 2.
(2 points)
5. Solve the system of equations. Show your work. (2 points)
6. Interpret your solution. How many days does it take Amir to catch Jesse? At that time, how many pages have they read? (2 points)
1. An equation representing the number of days Amir has been reading and the number of pages he has read is y = 35x.
2. An equation representing the number of days Jesse has been reading and the number of pages she has read is y = 30 + 30x.
3. The system of equations from 1 and 2 is y = 35x and y = 30 + 30x.
4. At the end of Friday, after solving the equations, both Jesse and Amir read 210 pages each, with Jesse spending 7 days and Amir 6 days.
5. For Jesse and Amir, the equation solutions are y is 210 pages and x is 6 days.
6. After solving the equations, it will take Amir 6 days to catch up with Jesse and each person must have read 210 pages or a total of 420 pages.
What is a system of equations?A system of equations involves using more than one equation solved simultaneously.
Jesse's reading rate per day = 30 pages
Amir's reading rate per day = 35 pages
The number of pages read by Jesse, y = 30 + 30x
The number of pages read by Amir, y = 35x
Where x = the number of days they have been reading
Solving the equations:y = 30 + 30x and y = 35x
35x = 30 + 30x
35x - 30x = 30
5x = 30
x = 6 (30/5)
Jesse:y = 30 + 30x
y = 30 + 30(6)
y = 210
Amir:y = 35x
y = 35(6)
y = 210
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Word problem involving the Pythagorean Theorem
A kite is flying 8 ft off the ground. Its line is pulled taut and casts a 6-ft shadow. Find the length of the line. If necessary, round your answer to the nearest
tenth.
6
0f
x 5
The length of the line is 10ft
Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse in familiar algebraic notation, a2 + b2 = c2
Given that A kite is flying 8 ft off the ground. Its line is pulled taut and casts a 6-ft shadow
We have to find a third side
By using Pythagoras' theorem. a^2+b^2=c^2
8^2+6^2=c^2
64 +36 = c^2
c^2= 100
c^2= 10
Therefore the length of the line is 10ft
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Write the sentence as an equation.
191 is the same as 266 added to the product of 109 and
Answer:
191=266+109x
Step-by-step explanation:
It says 191 is the same as 266 added to the product of 109 and _____. i am guessing you meant to say a variable.
given that M > N, determine whether the inequality M/N > N/M is always sometimes or never true
Answer:
An equation is a proposition of two expressions that are equal.
Step-by-step explanation: