The height in terms of x is 4/x², the cost function is C(x) = 7x² + 16/x, and the dimensions for minimum cost are 2/∛7 and ∛14.
a)
It is given that we need to consider the length of the square side to be x ft and the height to be h ft.
The volume of any cuboid
= Length X breadth X height
Here,
length = breadth = x ft
height is h ft.
Volume id 4 ft³
Hence,
x²h = 4
or, h = 4/x²
b)
Since this is a box for the kitten to sleep in, it cannot have any lid.
Hence it will have one square side of area x² and 4 rectangular sides each of area xh
h = 4/x²
Hence,
xh = 4/x
The square bottom costs $7 per ft and the sides cost $4 per sq. ft
Hence cost to make the box
= 7x² + 4 X 4/x
= 7x² + 16/x
Hence, C(x) = 7x² + 16/x
c)
Here,
C(x) = 7x² + 16/x
Hence, to minimize the cost we will equate its first-order derivative with 0 to get
C'(x)= 0
or, 14x - 16/x² = 0
or, 14x³ - 16 = 0
or, 14x³ = 16
or, x³ = 16/14
or, x = 2/∛7
Hence h = 4∛14/4
= ∛14
Therefore, the dimensions are 2/∛7 and ∛14
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Complete Question
You are constructing a box for your cat to sleep in. The plush material for the square bottom of the box costs 7 dollars per square foot and the material for the sides costs 4 dollars per square foot. You need a box with a volume of 4 ft³. Use x to represent the length of the square base, and use h to represent the height of the box.
(a) Determine a formula for the height h in terms of x.
(b) Determine a formula for the total cost C(x) of the materials for the box.
(c) Find the dimensions (in ft) of the box that minimize cost. (length of base and height)
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Laurie works for the Mathville High School. Her weekly paycheck reads "You
worked 4s + 3 hours this week, at a rate of 2s + 4 dollars per hour. You earned
a gross amount of $700." How many hours did Laurie work this week?
The total number of hours that Laurie worked for the week is; 35 hours
How to solve Algebra Word Problems?The parameters given are;
Total number of hours worked for the week = 4s + 3 hours
Rate of earning = 2s + 4 dollars per hour
Gross Amount earned = $700
Thus;
(4s + 3)(2s + 4) = 700
8s² + 6s + 16s + 12 = 700
8s² + 22s + 12 = 700
8s² + 22s - 688 = 0
Solving this with an online quadratic calculator gives;
s = 8
Thus;
Total hours worked = 4(8) + 3 = 35 hours
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Find the least common denominator of 1/6 and 11/9
Answer:
LCD is 18
Step-by-step explanation:
1/6 = 3/18
11/9 = 22/18
(t-k=12
3t+2k = 141
The values of the variables t and k are 33 and 21, respectively.
We are given a system of two equations. The equations are linear in nature. Each equation represents a straight line. We need to find the solution to the system of linear equations. The coordinates of the intersection point of the straight lines are the solution. The equations are given below.
t - k = 12
3t + 2k = 141
We will substitute the value of t from the first equation into the second equation.
t = 12 + k
3t + 2k = 141
3(12 + k) + 2k = 141
36 + 3k + 2k = 141
5k = 105
k = 21
We will substitute the value of k into the first equation to find the value of t.
t = 12 + k
t = 12 + 21
t = 33
Hence, the values of t and k are 33 and 21, respectively.
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sandeep visited green glen apple orchard yesterday. he picked a basket of fresh apples in the field. he also got 3 pounds of pre-picked apples at the farm stand because they were overripe and perfect for making applesauce. the farm charges $4 a pound for apples, regardless of whether they're fresh or pre-picked. sandeep paid $30 in all. which equation can you use to find f, the number of pounds of fresh apples sandeep picked? how many pounds of fresh apples did sandeep pick? write your answer as a whole number or a decimal.
Sandeep picked up 4.5 pounds of fresh apples from the field
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the standard form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant.
Pounds of pre-picked apples picked up by Sandeep = 3 pounds
Charges per pound = $4
The total amount paid by Sandeep = $30
Let x be the pounds of fresh apples picked up by Sandeep
In the formulation of the equation we get the following:
Pounds of pre-picked apples*Charges per pound + Pounds of fresh apple picked*Charges per pound = Total amount paid by Sandeep
= 3*4 + x*4 = 30
12 +4x = 30
4x = 18
x = 4.5
So, fresh apples = 4.5 pounds
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the sum of the digits of a three-digit number is 26. the number is multiplied by 7 , then by 11 , and finally by 13. how many times will the digit 9 occur in the final product?
1001 many times will the digit 9 occur in the final product.
First of all,
13×7 × 11 =1001
The result is 4 digit number and hence when multiplied by 3 digit number, it is resulting in the number repetition.
123× 1001 = 123123
445 × 1001 = 445445
Based on this logic we can assume that,
Any 02 digit number multiplied by 101 will result. For Example:99 × 101 = 9999
85× 101 = 8585
20 × 101 = 2020.
2. Any 3 digit number multiplied with 1001 will result in same pattern. for example:
123 × 1001 = 123123
997 × 1001 = 997997
500× 1001 = 500500
Ans so on.
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The rate of petrol was RS 120 in January. After three months,rate of petrol was RS 150 Find the percentage increase in its rate
The percentage of increase in rate is 25%
Calculating the Percentage:The percentage is a value that is expressed as a fraction of 100. In simple words, the percentage means, a part per hundred. To calculate the percent of a number, divide the number by the whole and multiply by 100. It is denoted by the symbol “%”.
Here we have
The rate of petrol was Rs. 120
After three months the rate of petrol was Rs.150
The increased rate = Rs.150 - Rs. 120 = 30
The percentage of increase = ( Increased rate/ initial rate) × 100
= [tex]\frac{30}{120} \times 100[/tex] = 25%
Therefore,
The percentage of increase in rate is 25%
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03:Pretest
CR Algebra 1 A (GP) 22-23/3:Identifying and Using Properties
2. You roll a blue number cube and a green number cube. Find P a number less than 2 on the blue cube and an odd number on the green cube.
The probability P (a number less than 2 on the blue cube and odd number on the green cube) is 1/12.
What is probability?
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.
For the probability,
The sample space of a die is, S = {1,2,3,4,5,6}
The probability of getting a number less than 2 is P(x < 2) = 1/6
The probability of getting an odd number is P(Odd) = 3/6
The required probability is calculated as:
P = 1/6 * 3/6
P = 1/12
Hence, the value of P (a number less than 2 on the blue cube and odd number on the green cube) is 1/12.
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Calculate the quotient below and give your answer in scientific notation.
180
9 × 10^-5
=?
It take the speed of 299 m to travel 30 cm .
What is speed?
Speed is what it means. the speed at which an object's position changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed only has a direction and no magnitude, it is a scalar quantity.
Let us convert cm to m for distances
C = 2.998× 10^8 ms
The relationship between distance, speed, and time is
T =1 ×10^6/8
Because in this case you are being asked how long or time it takes, make it the subject.
Rounding the quotient produces.
Adjust it again to fit the scientific notation.
The result is -
d= c×t
d=2.998×10^8 m/s 10^6 m/s
d=2.998
As a mathematical expression, the time taken for light is 2.998
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gianna has $760 to spend at a bicycle store for some new gear and biking outfits.assume all prices listed include tax
she buys a new bicycle for $356.46
she buys 2 bicycle reflectors for $10.01 each and a pair of bike gloves for $20.72
she plans to spend some of all of the money she has left to buy new biking outfits for $45.35 each
The number of outfits that Gianna can buy given her budget is 8.
How many outfits can she buy?The first step is to determine the total cost of the items bought so far
Total cost = price of the bicycle + cost of the bicycle reflectors + cost of the bike gloves
Cost of the bicycle reflectors = cost of one reflector x 2
Cost of the bicycle reflectors = $10.01 x 2 = $20.02
Total cost = $20.02 + $356.46 + $20.72 = $397.20
Amount that is left to buy the outfits = amount Gianna has - total cost
$760 - $397.20 = $362.80
Number of outfits she can buy = amount left / cost of one outfit
Number of outfits she can buy = $362.80 / $45.35
Number of outfits she can buy = 8
Here is the complete question:
Gianna has $760 to spend at a bicycle store for some new gear and biking outfits. assume all prices listed include tax. she buys a new bicycle for $356.46. she buys 2 bicycle reflectors for $10.01 each and a pair of bike gloves for $20.72. she plans to spend some of all of the money she has left to buy new biking outfits for $45.35 each. How many outfits can she buy ?
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A supervisor records the repair cost for 17 randomly selected TVs. A sample mean of $94.57 and standard deviation of $20.65 are subsequently computed.
Determine the 80 % confidence interval for the mean repair cost for the TVs. Assume the population is approximately normal.
Step 1 of 2: Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
The 80 % confidence interval for the mean repair cost for the TVs will be [87.873,101.266] and the critical value that should be used in constructing the confidence interval is ±1.337 for 80% interval.
What is confidence interval?An area created using fixed-size samples of data from a population (sample space) that follows a particular probability distribution is known as a confidence interval. A selected population statistic is built into the interval with a specified probability.
Here,
df = 17-1=16
critical value = ±1.337 for 80% interval
lower end value,
-1.337=(x-94.57)/[20.65/√17]
x = 87.87
higher end value,
1.337=(x-94.57)/[20.65/√17]
x = 101.27
hence, 80% interval:[87.87 101.27]
The range of values within which the mean repair cost for TVs falls within an 80% confidence interval is [87.873,101.266], and a critical value of ±1.337 should be used to construct the confidence interval.
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Which expressions are equivalent? Choose ALL that apply.
9 to the fourth power
36
9•9.9•9
4 to the ninth power
94
For the given expressions , the equivalent expressions are as follow:
9 to the fourth power9•9.9•99⁴As given in the question,
Given expressions are given below:
9 to the fourth power369•9.9•94 to the ninth power9⁴Simplify and find the equivalent expression from the following given expressions:
9 to the fourth power=9⁴
= 9 × 9 × 9 × 9
= 6561
3636 = 6²
≠ 6561
9•9.9•9=9⁴
= 9 × 9 × 9 × 9
= 6561
4 to the ninth power= 4⁹
= 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4
=262144
≠6561
9⁴= 9⁴
= 9 × 9 × 9 × 9
= 6561
Therefore, for the given expressions , the equivalent expressions are as follow:
9 to the fourth power9•9.9•99⁴The complete question is :
Which expressions are equivalent? Choose ALL that apply.
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Riley has $200 she spends 60 on a video game what percent of her money does Riley spend?
Answer:
30%
Step-by-step explanation:
60/200 = 3/10 = 30%
What does PEMDAS mean??????
Answer:
My teacher uses:
Please Excuse My Dear Aunt Sally : PEMDAS
Parenthesis, exponents, multiplication, division, addition, subtraction
Step-by-step explanation:
Answer:
parenthesis, exponents, multiplication, division, addition, subtraction
Step-by-step explanation:
a production process manufactures items with weights that are normally distributed with mean 17 pounds and standard deviation 0.1 pound. an item is considered to be defective if its weight is less than 16.85 pounds or greater than 17.15 pounds. suppose that these items are currently produced in batches of 500 units. a) (10 points) find the probability that an inspected item is defective. b) (10 points) find the probability that at most 10% of the items in a given batch will be defective. hint: find the probability that an item is defective using normal probabilities. then, you can model number of defectives out of 500 as binomial
The probability that at most 10% of the items in a given batch will be defective = 0.31333
We are aware that the item is broken.
Rate it 17.15 if X is either less than 16.85 or is.
Therefore, we simply found the area of one tail and multiplied it by two as we have seen their identical distance from the Min.
Therefore, let's choose 16.85.
We'll calculate a Z score for that.
Therefore, let's go on to the X value less the mean more than the standard deviation
This may be 16.85 -70, which will be 0.15 divided by.1 negative.
You will have a result of -1.5.
As a result, the Z distribution's region to the left of negative 1.5 will have a value of 0.0668. Divide that amount by two.
Z-score=0.0668/2=0.31333
You will also receive 0.31333.
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PLS HELP ASAP!!!
Are the two lines in the picture parallel, perpendicular, skew, or neither? Be sure to explain your reasoning.
Answer:
The two lines are parallel!
Step-by-step explanation:
Perpendicular lines are those that intersect at a 90° angle.Skew lines are those that are neither parallel nor perpendicular.Parallel lines are those that travel in the same direction and angle, with the same amount of space between them.:)
You decide to buy a car that costs $19,000. You've heard that the car may
depreciate at a rate of 14% per year. At that rate, what will the car be worth
in six years?
Answer:
$7,686.77744
Step-by-step explanation:
19000-14%=16340
16340-14%=14052.4
14052.4-14%=12085.064
12085.064-14%=10393.155
10393.155-14%=8938.1133
8938.1133-14%=7686.77744
find the indefinite integral in two ways . explain any difference in the forms fo the answer tansec^2x
The Indefinite integral of the function [tex]\int \tan \left(x\right)\sec ^2\left(x\right)dx[/tex] = [tex]\frac{\tan ^2\left(x\right)}{2}[/tex]
Given;
To get the Indefinite integral of the function [tex]\int \tan \left(x\right)\sec ^2\left(x\right)dx[/tex] ;
Let;
⇒ [tex]\int \tan \left(x\right)\sec ^2\left(x\right)dx[/tex]
Assume tan(x) as 'u', then sec²(x)dx = du;
⇒ [tex]\int \:udu[/tex]
⇒ [tex]\frac{u^2}{2}[/tex]
⇒ [tex]\frac{\tan ^2\left(x\right)}{2}[/tex]
By adding a constant C;
⇒ [tex]\frac{\tan ^2\left(x\right)}{2}[/tex] + C
Hence, the Indefinite integral of the function [tex]\int \tan \left(x\right)\sec ^2\left(x\right)dx[/tex] = [tex]\frac{\tan ^2\left(x\right)}{2}[/tex]
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9a-b-2a-10b simplify this expression
A. -7a+11b
B. 11a+9b
C. -11a-9b
D. 7a-11b
please solve with explanation Q^Q
Answer:
9a-b-2a-10b=7a-11b
Step-by-step explanation:
collect the like terms, meaning add or subtract the numbers from the ones with the same variable(in this case a and b are the different variables)
9a-2a=7a
-b-10b=-11b
therefore, the correct answer is D
Step-by-step explanation:
Well , all you have to do is to collect the like terms bringing those with the same unknown together.
=9a-2a-b-10b
=7a-11b
Hey! i need help please!
The expression [tex]\sqrt[5]{36\cdot t^6\cdot w^{17}}[/tex] in simplified radical form obtained by using the laws of indices is presented as follows;
[tex]2\cdot t \cdot w^3\times t^{\frac{1}{5} }\cdot w^\frac{2}{5} = 2\cdot t \cdot w^3 \cdot \sqrt[5]{t \cdot w^2}[/tex]
What are the laws of indices?The laws of indices are a set of rules that can be used to simplify expressions of variables and numbers that consists of powers that have the same base.
The expression is; [tex]\sqrt[5]{36\cdot t^6\cdot w^{17}}[/tex]
The laws of indices which can be used to evaluate the expression includes;
xᵃ × xᵇ = xᵃ⁺ⁿxᵃ ÷ xᵇ = xᵃ⁻ᵇ(xᵃ)ⁿ = [tex]x^{a\times b}[/tex]x⁻ⁿ = 1/xⁿx⁰ = 1[tex]x^\frac{n}{m} =\sqrt[m]{x^n}[/tex]Expressing the index in terms of 5, we get;
[tex]\sqrt[5]{32\cdot t^6\cdot w^{17}} = \sqrt[5]{2^5\cdot t^5 \times t\cdot w^{15} \times w^2}[/tex]
[tex]\sqrt[5]{2^5\cdot t^5 \times t\cdot w^{15} \times w^2} = 2\cdot t\cdot w^3 \cdot \sqrt[5]{t \cdot w^2}[/tex]
The expression, [tex]\sqrt[5]{36\cdot t^6\cdot w^{17}}[/tex] in the simplified form is [tex]2\cdot t\cdot w^3 \cdot \sqrt[5]{t \cdot w^2}[/tex]
A second method evaluating the expression is presented as follows;
[tex]\sqrt[5]{32\cdot t^6\cdot w^{17}} = \sqrt[5]{2^5\cdot t^5 \times t\cdot w^{15} \times w^2}[/tex]
[tex]\sqrt[5]{2^5\cdot t^5 \times t\cdot w^{15} \times w^2} = 2^\frac{5}{5} \cdot t^\frac{5}{5} \times t\cdot w^{\frac{15}{3} } \times w^\frac{2}{5}[/tex]
[tex]2^\frac{5}{5} \cdot t^\frac{5}{5} \times t^{\frac{1}{5} }\cdot w^{\frac{15}{3} } \times w^\frac{2}{5} = 2\cdot t \cdot w^3\times t^{\frac{1}{5} }\cdot w^\frac{2}{5}[/tex]
[tex]2\cdot t \cdot w^3\times t^{\frac{1}{5} }\cdot w^\frac{2}{5} = 2\cdot t \cdot w^3 \cdot \sqrt[5]{t \cdot w^2}[/tex]
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6th grade math, please solve, 20 points.
-32 - (-5)=___
A. 37
B. 27
C. -27
D. -35
Answer:
-27
Step-by-step explanation:
Answer:
-27
Step-by-step explanation:
Since the problem says that you are subtracting -5 you have to turn everything that is on the right to a positive number like so:
-32 - (-5) ---> -32 + 5
So now all you have to do is add 5 to -32
Therefore equaling -27
So your final answer is C. -27
a1=−12an=an−1+5
What is the sixth term of this sequence?
The sixth term is a₆ = 13.
What is an arithmetic sequence?A sequence in which the difference between any two consecutive terms is the same is known as an arithmetic sequence.
Given that, a₁= -12 and aₙ = aₙ₋₁ + 5.
aₙ = aₙ₋₁ + 5
Substitute n = 2 into the above equation,
a₂ = a₂₋₁ + 5
a₂ = a₁ + 5
Substitute a₁ = -12 into the above equation,
a₂ = -12 + 5
a₂ = -7
Repeating the same process, a₃ = -2, a₄ = 3, a₅ = 8, and a₆ = 13.
Hence, the sixth term is a₆ = 13.
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Albert spends 2 hours a day on his homework and an hour playing video games. What percent of the day is it?
the area of a pond covered by algae is [tex]\frac{1}{4}[/tex] of a square meter on day 1 and it doubles each day. complete the table
Estimate 210 ÷ 5.2 . 9 3/4 +(-205). Is reasonable answer? Explain your answer
Using PEDMAS, the expression is 188.75
PEDMASBODMAS is an acronym and it stands for parentheses, exponents, division, multiplication, addition, subtraction. In certain regions, PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction) is used, which is the synonym of BODMAS.
To solve this problem, we just need to apply PEDMAS rule here and evaluate the expression.
210 ÷ 5.2 * 9 3/4 - 205 = 755 / 4 = 188.75
The expression has a value of 188.75
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The table shows the weights of bunches of
bananas and the price of each bunch. Identify
the constant of proportional
ity. Write an
equation to relate weight, w, to the price, p.
The constant of proportionality is: k = 0.45
The equation is: p = 0.45w.
How to Write the Equation of a Proportional Relationship?The equation that models the proportional relationship between two variables, x and y, can be expressed in slope-intercept form as y = kx, here, the value of k is the constant of proportionality between the two variables x and y.
Thus, constant of proportionality, k = y/x.
In the table given, we can use the coordinates of one point, (3, 1.35), to find the constant of proportionality, k:
Constant of proportionality, k = 1.35/3
Constant of proportionality, k = 0.45
To write the equation of the relationship between weight (w) and price (p), substitute k = 0.45 into p = kw.
p = 0.45w
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im so confused right now
Answer:
The solution is A. 183
Step-by-step explanation:
112-38×14÷14+109
= 74×1+109
= 74+109
= 183
Suppose you flip a penny and a dime. Use the following table to display all possible outcomes. Penny dime head ? head ? tail ? tail ? if each single outcome is equally likely, you can use the table to help calculate probabilities. What is the probability of getting two heads? a. P(2 heads) = one-half b. P(2 heads) = three-fourths c. P(2 heads) = startfraction 4 over 4 endfraction d. P(2 heads) = one-fourth.
In this position, if you flip a penny and a dime to get both heads option D). p(2 heads) = one-fourth is correct answer .
What is Probability ?It is simply the favorable number of outcomes divided by total outcomes is called probability.
favorable outcomes :-
Two Heads
condition 1 : coin-1 => head, coin-2 => headcondition 2: coin-1 => head, coin-2 => Tailcondition 3: coin-1 => Tail, coin-2 => headcondition 4: coin-1 => Tail, coin-2 => Tailonly one condition ( condition 1: coin-1 => head, coin-2 => head ) is favorable outcome of four conditions.
probability = one-fourth or [tex]\frac{1}{4}[/tex].
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The numbers 1-25 are written
on slips of paper and placed in a
bag. A number is chosen, it is not
replaced, then another is chosen.
What is the probability of getting
two numbers greater than 10?
please help asap
i already know that -7 is wrong
Answer:
Step-by-step explanation:
I thinkin it -43
Answer:
15
Step-by-step explanation:
because when the y value stays the same, the slope is 0
Ms. Michaels surveyed her class on whether they preferred free time at the beginning of class or at the end of class. If the ratio of students who prefer free time at the beginning of class to students who prefer free time at the end of class is 12 over 19, what does the ratio 12 over 19 represent?
A19 students prefer free time at the beginning of class, and 12 students prefer free time at the end of class.
B 19 students prefer free time at the beginning of class, and 31 students prefer free time at the end of class.
C 12 students prefer free time at the beginning of class, and 19 students prefer free time at the end of class.
D 31 students prefer free time at the beginning of class, and 12 students prefer free time at the end of class.
The ratio 12/19 means 12 students prefer free time at the beginning of the class and 19 students prefer free time at the end of the class. (option C)
What is ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
The general form of representing a ratio of between two quantities say 'a' and 'b' is a: b, which is read as 'a is to b'.
For example if the ratio of boys to girls in a school is 5:4, this means in the school 5boys to 4 girls , and 10boys to 8girls. It can also be expressed as 5/4
Therefore if 12/1,9 is the ratio of students that prefer free time at the beginning to students that prefer free time at the end of a class, then , 12 students prefer free time at the beginning and 19 prefer at the end of the class.
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Answer:
c
Step-by-step explanation:
pls