Answer: To find the number of cars that should be produced to incur minimum cost, we need to find the minimum value of the cost function C(x). Since C(x) is a quadratic function, it will have a minimum value, which is either a relative minimum or an absolute minimum. To find the number of cars that should be produced to incur the minimum cost, we will find the derivative of C(x) and set it equal to zero.
To find the derivative of C(x), we can use the power rule, which states that the derivative of x^n is n*x^(n-1).
The derivative of C(x) = 21000 - 90x + 0.1x^2 is
C'(x) = -90 + 0.2x
To find the minimum cost, we set C'(x) equal to zero and solve for x:
-90 + 0.2x = 0
0.2x = 90
x = 450
So, producing 450 cars will incur the minimum cost.
To verify that this is indeed a minimum, we can find the second derivative of C(x) which is 0.2, since the second derivative is positive, we can confirm that x = 450 is a relative minimum.
Alternatively, we can substitute x = 450 into the cost function and find the minimum value, which is C(450) = 21000 - 90(450) + 0.1(450)^2, which is less than any other value of C(x) for x≠450.
Therefore, to incur the minimum cost, 450 cars should be produced.
Step-by-step explanation:
suppose you own a swimming pool with dimensions 4.93 m x 9.69 m x 1.75 m. what is the volume of your pool in gallons?
22084.78 gallons is the volume of your pool.
Any rectangular solid's volume, V, is equal to the sum of its dimensions, height, width, and depth. In terms of the area of the base, we might alternatively express the formula for a rectangular solid's volume. The base's surface area, B, is equal to its length x width.
Dimensions of the pool = 4.93 m x 9.69 m x 1.75 m
Volume = 4.93 x 9.69 x 1.75
= 83.6 cubic meter
1 cubic meter = 264.172 gallons
83.6 cubic meter = 83.6 x 264.172
= 22084.78 gallons
Hence, 22084.78 gallons is the volume of your pool.
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a local ice cream store is analyzing the day's sales. each serving came in either a cup or a cone, but not both, and the ratio of servings to cups was 7:47:47, colon, 4. what was the ratio of servings to cones?
The ratio of servings to cones is 47:4.
In mathematics, a ratio is a way of comparing two or more values. It is usually represented as a fraction, with the values being separated by a colon (:). For example, if you have 7 apples and 4 oranges, the ratio of apples to oranges would be 7:4. This can also be written as 7/4 or 1.75. Ratios can also be written as a decimal or a percentage. Ratios can be used to compare quantities, sizes, or measurements in different units.
If the ratio of servings to cups is 7:47:47:4, that means for every 7 servings, there are 47 cups.
Since the servings came in either a cup or a cone, but not both, the ratio of servings to cones is the remaining portion of servings that are not accounted for in the ratio of servings to cups.
So, it's 7 servings + 47 cups = 47 servings + 4 cups.
Therefore, the ratio of servings to cones is 47:4.
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Find the equation of line that passes through the points (2,0) and (5,12). Write the equation in slope-intercept form.
Answer:
y=4x+2
Step-by-step explanation:
slope (12-0)/(5-2)=4
y=4x+b
plug in (2,0)
b=2
y=4x+2
I need help with this!
Use your formula 1/2(a+b)h, to determine the height of a trapezoid with an area of 24 cubic centimeters and base lengths of 9 cm and 7 cm.
Answer:
H (Height) = 3
Step-by-step explanation:
We have the formula A = 1/2(a+b)h
Let's identify all variables
A = 24
a = 9
b = 7
h = ?
Lets plug all that in:
24 = 1/2(9+7)h
9+7 = 16
24 = 1/2(16)h
Half of 16 is 8 so to simplify the rest...
24 = 8h
To get h alone we will divide both sides of the equation by 8
24/8 = h
24/8 = 3
Making H = 3
Jorge’s family has visited 38 of the 50 states in America. What fraction of the states
have they visited?
To find the fraction of the states that Jorge's family has visited, we can use the formula:
visited states / total states
In this case, Jorge's family has visited 38 states out of a total of 50 states, so the fraction of states they have visited is:
38 / 50
You can simplify this fraction by dividing both the numerator and denominator by the greatest common divisor of 38 and 50 which is 2, so the fraction is
19/25
So, Jorge's family has visited 19/25 of the states in America.
Jorge's family has visited 19/25 of the states in America.
What are fractions?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
In this case, Jorge's family has visited 38 states out of a total of 50 states, so the fraction of states they have visited is:
38 / 50
You can simplify this fraction by dividing both the numerator and denominator by the greatest common divisor of 38 and 50 which is 2, so the fraction is
19/25
19 out of the 25 American states have been visited by the Jorge family.
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what language used orthogonality as a primary design criterion and more orthogonal than other languages?
ALGOL 68 is a language that prioritized orthogonality as a key design requirement. ALGOL 68's primary objectives and design tenets are as follows:
1. a thorough and clear design;
2. an orthogonal design
3. Safety
4. Efficiency: Mode-independent parsing, independent compilation, loop optimization, representations in small and big character sets, static mode verification, etc.
As a programming language, Algol 68 offers certain unique and practical concepts that were ground-breaking at the time and have appeared, in varying degrees, in various languages afterwards.
Orthogonal design, which means that core concepts stated in the language can be used anyplace that usage can be said to "make sense." Completeness and clarity of explanation (as facilitated by the adoption of two-level grammar, which sparked many critical reactions).
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a passenger jet took 3 hours to fly 1800 miles in the direction of the jet stream. The return trip against the jet stream took 4 hours. What was the jets speed in still air and the jet streams speed?
The speed of the jet in still air is 525miles per hour and the speed of the jet stream is 75miles per hour
What is speed ?speed is defined as the rate of change of distance with time. It is measured in meter per second and it is a scalar quantity. It has other units like miles per hour, kilometers per hour e.t.c
The speed of the jet with jet stream = displacement /time = 1800/3 = 600 miles/hour
The speed of the jet against = distance /time = 1800 / 4 = 450 miles per hour
The speed of the jet in still air will be the average speed of the jet to and fro. = (600+450)/2
= 1050/2
= 525 miles per hour
Therefore the speed of the jet in still air = 525 miles per hour
Also, the the jet stream speed = 525- 450 = 75 miles per hour.
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what is 5g=20 step by step
Answer:
4
Step-by-step explanation:
It says 5g is 20. To figure out the value of g, you need to divide 5g by 5, and 20 by 5, which gives the answer of g=4
-2(x + 5)² = 20
solve by square root!
27×9^3x can be written as 3^k
[tex]27\cdot 9^{3x}\implies 3^3\cdot (3^2)^{3x}\implies 3^3\cdot 3^{6x}\implies {\Large \begin{array}{llll} 3^{3+6x} \end{array}}[/tex]
using only quarters, nickels, and pennies, what is the minimum number of coins needed to make $0.88?
Elle wants to spend at most Php80 on dairy products. Each liter of goat milk costs
Php130 and each liter of cow's milk costs Php65. Find the possible number of each dairy product
Elle can buy maximum 0.6 liters of goat milk and 1.2 liters of cow's milk.
What System of linear inequalities?
A system of linear inequalities is similar to a system of linear equations, except that it is made up of inequalities rather than equations. To represent scenarios with various restrictions, systems of linear inequalities are utilized.
Let x be the number of liters of goat milk and y be the number of liters of cow's milk that Elle wants to buy. We know that:
x + y ≤ 80 (because Elle wants to spend at most Php80)
130x + 65y ≤ 80 (because each liter of goat milk costs Php130 and each liter of cow's milk costs Php65)
This is a system of linear inequalities, and the solution set is the set of all possible combinations of x and y that satisfy both inequalities.
The inequality 130x + 65y ≤ 80 represents a line in the plane, and the inequality x + y ≤ 80 represents a region that is "bounded" by this line.
The solution set for the inequalities are x <= 0.6 and y <= 1.2.
So, Elle can buy maximum 0.6 liters of goat milk and 1.2 liters of cow's milk.
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Determine whether the pairs of triangles are congruent.
~Circle yes, no, or not enough information. Explain your choice.
Answer:
No
Step-by-step explanation:
I got the postulates mixed up. These triangles have the same angle measurements but the lengths of the sides are different so the answer is no. These triangles do not follow the AAS, SSS, SAS, or ASA postulates.
Answer:
Step-by-step explanation:
Yes, it is congruent because SSA.
Louise sold 168 soft pretzels. If she sold them in groups of 12 soft pretzels, how many groups did she sell?
The value your tikto channel is depreciating at a rate of 13% per year. In 2002, it was worth $288. Find the value of your declining channel in 2016.
Round your answer to the cent place
The value of your declining channel in 2016, given the depreciation rate, would be $ 40. 99
How to find the value of the channel ?The value of the channel can be found by the formula :
= Original value of the channel x ( 1 - rate of depreciation ) ^ number of years
Rate of depreciation = 13 %
Number of years :
= 2016 - 2002
= 14 years
The value of the channel is therefore:
= 288 x ( 1 - 13 %) ¹⁴
= $ 40. 99
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4.
What is the constant of proportionality? What does it represent?
Answer:
In Explanation
Step-by-step explanation:
The constant of proportionality is a value that relates two variables that have a proportionate relationship. It is often represented by the letter "k".
For example, if two variables x and y are directly proportional, their relationship can be represented by an equation of the form y = kx, where k is the constant of proportionality. In this equation, the value of k represents the ratio of y to x and it is constant, meaning that it does not change as the values of x or y change.
In physics, the constant of proportionality also appears in many mathematical models of natural phenomena, such as Hooke's law (F = km) which relates the force applied on an object (F) to its displacement (x) with a spring constant (k), and Ohm's law (V = IR) which relates the voltage (V) across a resistor to the current (I) flowing through it with a resistance constant (R).
The constant of proportionality can have different units of measure depending on the context and is used to make quantitative predictions about the relationship between the variables. In some cases, it can be used to determine the behaviour of a system or physical process.
(Please give brainlist)
The balance in Jamie's checking account in the month of June was thrice the amount of what it was in the month of May he swiped his card for $69 in the restaurant which caused this account to be overdrawn by nine
The balance of Jamie's checking account in the month of May is given as follows:
$20.
How to obtain the balance?The balance in the month of May is obtained applying the proportions in the context of this problem.
He swiped his card for $69 in the restaurant which caused this account to be overdrawn by nine, hence the June balance is of:
-9 + 69 = $60.
The balance in Jamie's checking account in the month of June was thrice the amount of what it was in the month of May, hence the May's balance is given as follows:
3x = 60
x = $20.
Missing InformationThe problem asks for the balance of the checking account in the month of May.
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4 If you have 5 pounds of trail mix, how many bags can you make so that each bag
contains 1 pounds?
Answer:
5 bags
Step-by-step explanation:
if there are 5 pounds of trail mix and each bag needs to contain 1 pound, that can be equally divided into 5 bags where each bag contains 1 pound each
for a random sample of 100 people, what is the probability that the sample mean will be within 5 points of the population mean
The probability that the sample mean will be within 5 points of the population mean is 0.95 or 95%
Central Limit TheoremThe Central Limit Theorem (CLT), a foundational idea in statistics, holds that, regardless of the underlying population distribution, the distribution of the sample means will be about normal given a big enough sample size. The CLT is crucial because it enables us to draw conclusions about a population based on a sample, even when the population is not normal.
According to the CLT, as the sample size grows, sample means will approach population means and their standard deviations will fall. The standard error, also known as the standard deviation of the sample means, is calculated by dividing the standard deviation of the population by the square root of the sample size.
According to the Question
The sample mean for a random sample of 100 individuals is most likely to be within 5 points of the population mean. The distribution and standard deviation of the population, however, would determine the precise likelihood. The standard error may be used to determine a confidence interval for the population mean if the population standard deviation is known. A 95% confidence interval is frequently used, which is equivalent to 1.96 standard deviations from the mean. In this instance, especially with a large sample size, there is a good likelihood that the sample mean will be within 5 points of the population mean.
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Which triangles are similar to ΔDEF?
Answer:
A) ΔDFG
and
C) ΔFEG
Answer: FEG
Step-by-step explanation:
It can't be the others, so process of elimination.
Ken’s seventh grade class plans to collect empty aluminum pop cans as a fund raiser to buy two new books for the school library. The books will cost a total of $50.
a. If $0. 25 per pound is the current price for aluminum at the recycling center, how many pounds of empty cans will the class have to collect? (3 points) Work: Answer __________________
b. Six empty cans weigh about 3. 5 ounces. How many empty cans will the class have to collect to meet their quota of pounds? Round your answer to the nearest whole number. (3 points) Work: Answer __________________
a.) The number of pounds of empty cans needed by the class is 200 pounds.
b.) The number of empty cans needed by the class to collect are 5486 cans.
The books will cost a total amount of $ 50.
If $ 0.25 per pound is the current price for aluminium at the recycling centre, the number of pounds the class will have to collect is found by dividing the total amount needed by cost per pound is,
⇒ 50/0.25 = 200
b.) Six empty cans weigh 3.5 ounces.
1 pound = 16 ounces
200 pounds = 200 × 16 = 3200 number of ounces
3200/3.5 = 914.29
914.29 × 6 = 5485.7 cans ≈ 5486 cans
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The resistances of then randomly selected 100-ohm resistors have been recorded: 79. 9, 85. 9, 87. 0, 96. 7, 107. 4, 100. 8, 115. 4, 117. 9, 98, and 102. 6 ohms. The individual resistances are known to follow a normal distribution with a mean of 100 ohms and a standard deviation of 10 ohms. (a) Calculate the sample mean resistance associated with the ten resistors. (b) For a sample size of ten, find the probability of obtaining a sample mean as large as or larger than the one calculated in part (a). (c) For a sample size of ten, find the probability of obtaining a sample mean with a resistance between 95 and 105 ohms
If the individual resistances are known to follow a normal distribution with a mean of 100 ohms and a standard deviation of 10 ohms , then the sample mean resistance associated with the ten resistors is 99.16 ohms .
The resistors of randomly selected 100 ohms resistors are recorded as :
⇒ 79.9, 85.9, 87.0, 96.7, 107.4, 100.8, 115.4, 117.9, 98, and 102.6 ;
we have to fins the sample mean resistance associated with the 10 resistors .
the number of resistors(n) = 10 ;
the sum of 10 resistors is ⇒ 79.9 + 85.9 + 87.0 + 96.7 + 107.4 + 100.8 + 115.4 + 117.9 + 98 + 102.6
⇒ 991.6/10 = 99.16 .
Therefore , the sample mean resistance is 99.16 ohms .
The given question is incomplete , the complete question is
The resistances of then randomly selected 100-ohm resistors have been recorded: 79.9, 85.9, 87.0, 96.7, 107.4, 100.8, 115.4, 117.9, 98, and 102.6 ohms. The individual resistances are known to follow a normal distribution with a mean of 100 ohms and a standard deviation of 10 ohms.
Calculate the sample mean resistance associated with the ten resistors .
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What is the perimeter of the given composite figure? I believe it’s 140 but would like a check from someone smarter than I lol.
The perimeter of the given composite figure is given as follows:
105 ft.
How to obtain the perimeter of a polygon?The perimeter of a polygon is obtained as the sum of all the outer side lengths of the polygon.
The side lengths for the polygon in this problem are given as follows:
45 ft.40 ft.15 ft.5 ft.Hence the perimeter for the polygon is calculated as follows:
45 + 40 + 15 + 5 = 105 ft.
(sum of all the outer side lengths).
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3) Make the following number 100 times
greater.
6.4
Answer: 640
Step-by-step explanation:
6.4 * 100 = 640
15 foot ladder leaning agaisnt a building touches the wall 12 feet above the ground how far from the building is the bottom of the ladder
The bottom of the ladder is 9 feet from the wall.
Using the Pythagorean Theorem, we can calculate the distance from the wall. The Pythagorean Theorem states that for a right triangle, the sum of the squares of the sides is equal to the square of the hypotenuse. In this case, the hypotenuse is 15 feet and the side adjacent to the wall is 12 feet.
The formula for the Pythagorean Theorem is a^2 + b^2 = c^2.
We can solve for the distance from the wall (a). a^2 = c^2 - b^2, so a^2 = 15^2 - 12^2, which equals a^2 = 225 - 144, so a^2 = 81. Taking the square root of both sides, a = 9 feet.
Therefore, the bottom of the ladder is 9 feet from the wall.
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LMNO is a parallelogram. If NM = x + 12 and OL = 2x + 8, find the value of x and then find NM and OL.
The value of the sides, NM and OL are 16 and 8 respectively
How to determine the value
To determine the value of x, we have the note the properties of a parallelogram.
The properties of a parallelogram includes;
Opposite sides of a parallelogram are parallelOpposite sides of a parallelogram are congruentOpposite angles of a parallelogram are congruentInterior angles are supplementaryEach diagonal of a parallelogram divides it into two congruent trianglesThe diagonals of a parallelogram bisect each other at right angleThen, we have;
NM = OL
substitute the values
x + 12 = 2x + 8
Now, collect like terms
x = 4
NM = 4 + 12 = 16
OL = 16
Hence, the value are 4 and 16
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May I have help on this please?
Answer:
yeah you can
Step-by-step explanation:
what do you need help with lol
A bakery offers 10 kinds of cookies, 5 of which are frosted. The baker wants to put 3 different cookies in bags to sell.
From the 10 types of cookies, what is the probability that the baker places 3 frosted cookies into a bag?
A: 4/5
B: 5/126
C: 1/12
D: 3/20
Answer:
I think 3/20 of a chance of putting 3 frosted cookies in bags to sell.
Step-by-step explanation:
Hope it helps! =D
what are the dimensions of a rectangular tract of land when it’s perimeter is 44 kilometers and it’s area is 120 square kilometers
Answer:
The dimensions of the rectangular tract of land with a perimeter of 44 kilometers and an area of 120 square kilometers are:
Length = 10 kilometers
Width = 12 kilometers
Explanation: To find the dimensions of a rectangular tract of land when its perimeter and area are known, you can use the formulas:
Perimeter = 2(length + width)
Area = length * width
We know that:
Perimeter = 44 kilometers
Area = 120 square kilometers
So, we can use these values to set up the following equation:
44 = 2(length + width)
And we can solve for length and width.
44 = 2(length + width)
22 = length + width
And now we know that the sum of the length and width of the rectangular tract is 22 kilometers.
Now we have to use the area formula:
Area = length * width
120 = length * width
We can use the value we have for the sum of the length and width to find either the length or the width of the rectangular tract.
For example, we can use the equation:
length = 22 - width
And substitute it into the area equation:
120 = (22 - width) * width
And then we can solve for width:
120 = 22 * width - width^2
width^2 - 22 * width + 120 = 0
We can use the quadratic formula to solve for width.
width = (22 +/- sqrt(22^2 - 4 * 1 * 120))/ 2
So,
width = (22 +/- sqrt(484 - 480))/ 2
width = (22 +/- sqrt(4))/ 2
width = (22 +/- 2)/ 2
width = (24)/ 2
width = 12
So, the width of the rectangular tract is 12 kilometers.
And we can use the equation:
length = 22 - width
to find the length
length = 22 - 12 = 10
So, the dimensions of the rectangular tract of land with a perimeter of 44 kilometers and an area of 120 square kilometers are:
Length = 10 kilometers
Width = 12 kilometers
coach mac finds a new practice court for the basketball team. if the width of the rectangular lot is 16 feet less than the length, and the perimeter is 160 feet, what are the dimensions of the new practice court?
perimeter of rectangle = 2W + 2L
first complete these equations: 160 = ?W + ? L ; W = L - ?
The dimensions of the new practice court is 45.5 feet by 29.5 feet.
The equations should be completed as 160 = 2W + 2L; W = L - 16
How to calculate the perimeter of a rectangle?Mathematically, the perimeter of a rectangle can be calculated by using this mathematical expression;
P = 2(L + W) or P = 2L + 2W
Where:
P represents the perimeter of a rectangle.L represents the length of a rectangle.W represents the width of a rectangle.Since the width of the rectangular lot is 16 feet less than the length, we have:
W = L - 16
Substituting the given parameters into the perimeter formula, we have;
160 = 2L + 2W
160 = 2(L - 16) + 2L
160 = 2L - 32 + 2L
160 = 4L - 32
4L = 182
L = 45.5 feet.
For the width, we have:
W = L - 16
W = 45.5 - 16
W = 29.5 feet.
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