To optimise the volume while maintaining the total dimensions at 7 inches, the camera's dimensions should be roughly 3.01 inches besides 3.311 inches besides 0.679 inches.
What 3 dimensions do we have?
The homes we reside in and the items we use on a daily basis all have three dimensions: length, weigth, and breadth.
Let's start by assigning variables to the dimensions. Let x be the height of the camera, then the length must be 1.1 times the height, which gives us a length of 1.1x.
The width is not explicitly given, but we can express it in terms of x and 1.1x. Since the sum of the dimensions is 7 inches, we have:
x + 1.1x + w = 7
where w is the width of the camera. Simplifying this equation, we get:
2.1x + w = 7
w = 7 - 2.1x
Now we can express the volume of the camera in terms of x:
V = x(1.1x)(7 - 2.1x)
Simplifying this expression, we get:
V = 8.235x³ - 15.365x² + 7x
To find the maximum volume, we need to find the value of x that maximizes V. We can do this by taking the derivative of V with respect to x, and setting it equal to zero:
dV/dx = 24.705x² - 30.73x + 7 = 0
Using the quadratic formula, we can answer this quadratic equation:
x = (-b ± √(b² - 4ac)) / 2a
where a = 24.705, b = -30.73, and c = 7. Plugging in these values, we get:
x = 0.735 inches or x = 3.01 inches
Since x represents the height of the camera, we discard the smaller root and take x = 3.01 inches.
Then the length is 1.1 times the height, which gives us a length of 3.311 inches.
The width can be found using the equation w = 7 - 2.1x, which gives us w = 0.679 inches.
Therefore, the dimensions of the camera should be approximately 3.01 inches by 3.311 inches by 0.679 inches to maximize the volume while keeping the sum of the dimensions at 7 inches.
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exponential and logarithmic functions
The half-life of Potassium-40 is 1.25 billion years. The decay equation for Potassium-40 can be expressed as N(t) = N0e-kt, where N(t) is the amount of Potassium-40 at time t, N0 is the initial amount of Potassium-40, and k is the decay constant.
What is decay constant?Decay constant is a measure of the rate at which a radioactive sample decays. It is usually expressed as the probability of a given radioactive nucleus decaying per unit time. It is related to the half-life of a radioactive sample, which is the time it takes for half of the sample to decay.
To answer part b, we need to solve N(t) = 15 mg. When rearranged, this equation becomes t = ln(15/N0)/(-k). Using the given initial amount of 36 mg and the calculated decay constant of 0.00056, we find that it will take 1.44 billion years for the specimen to decay to 15 mg.
For part c, we can use the same equation and solve for N(t). We get N(t) = N0e-kt, where N(t) is the amount of Potassium-40 at time t, N0 is the initial amount of Potassium-40, and k is the decay constant. Using the initial amount of 36 mg and the decay constant of 0.00056, we find that after 300 million years, there will be 27.72 mg of Potassium-40 left.
For part d, we can solve N(t) = N0/8. When rearranged, this equation becomes t = ln(N0/8)/(-k). With the initial amount of 36 mg and the decay constant of 0.00056, we find that it will take 2.68 billion years for Potassium-40 to decay to one-eighth of its original amount.
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Using trigonometry, work out the length y Give your answer in centimetres to 1 d.p. Y 6.1 cm 39° Not drawn accurately
The length of y is given as follows:
y = 7.8 cm.
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:
Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle.In the context of this problem, we have that y is the hypotenuse, while 6.1 cm is the side length adjacent to the angle of 39º, hence:
cos(39º) = 6.1/y
y = 6.1/cosine of 39 degrees
y = 7.8 cm.
Missing Information6.1 cm is adjacent to the angle of 39º, while y is the hypotenuse.
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The backyard of a new home is shaped like a trapezoid with a height of 46 ft and bases of 90 ft and 112ft. What is the cost of putting sod on the yard, if the landscaper charges $ 0.25 per square foot for sod?
The cost of putting sod on the yard is $1161.5
What exactly is a trapezoid?A trapezoid is a polygon that has just one pair of parallel sides. The two extra sides of a trapezoid, known as the legs, are not parallel.
The price is calculated by multiplying the area in square feet by the price per square foot.
The formula for a trapezoid's area is
A = (1/2)([tex]b_{1}[/tex] + [tex]b_{2}[/tex])h.
where h represents height and [tex]b_{1}[/tex] and [tex]b_{2}[/tex] represent base lengths.
The area is
A = (1/2)(90 ft + 112 ft)(46 ft)
= 4646 [tex]ft^{2}[/tex]
when the supplied information is filled in.
Given that each square foot costs $0.25,
the price for this many square feet (4646[tex]ft^{2}[/tex] ) is $0.25/[tex]ft^{2}[/tex] × $989.23.
The cost of sodding the backyard will be $1161.5 according to the landscaper.
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remove all the perfect sqaures from 15*3y
the expression 15*3y with all perfect squares removed is 9 * 5y, or simply 45y if you prefer not to factor it further.
What is factor?In mathematics, a factor is a number or expression that divides another number or expression exactly, leaving no remainder. For example, 2 and 3 are factors of 6, because 6 can be divided by 2 and by 3 without any remainder. Similarly, (x - 3) is a factor of the expression x^2 - 9, because if we divide [tex]x^{2}[/tex]- 9 by (x - 3), we get x + 3 with no remainder. Factoring is the process of breaking down a number or expression into its factors. Factoring is an important concept in many areas of mathematics, including algebra, number theory, and calculus.
by the question.
Remove all the perfect squares from 15*3y
The expression 15*3y can be simplified as follows:
15*3y = 45y
To remove all perfect squares from this expression, we need to find the perfect squares that divide into 45.
The prime factorization of 45 is:
45 = [tex]3^{2}[/tex] * 5
So, the perfect squares that divide into 45 are[tex]3^{2}[/tex] = 9.
To remove the perfect squares from 45y, we can factor out 9 from 45, and get:
45y = 9 * 5y
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Which is an example of a survey involving quantitative data?
The number of cavities each person has had is an example of a survey involving quantitative data.
Quantitative data is any data that can be expressed in numerical terms and can be measured or counted. It includes variables such as counts, amounts, measurements, or ratings. In the given options, the number of cavities each person has had is a numerical variable that can be counted and analyzed statistically, making it an example of quantitative data. Other options, such as favorite food or color of the walls, are qualitative data, which is non-numerical and cannot be measured in numerical terms.
Quantitative data is commonly used in surveys, experiments, and statistical analyses to study patterns and relationships between variables. It allows for precise measurements, comparisons, and statistical modeling. Examples of quantitative data include age, height, weight, temperature, test scores, sales figures, and population counts. By contrast, qualitative data is often used to explore attitudes, beliefs, perceptions, or opinions, and is typically recorded as text or verbal data. Examples of qualitative data include interviews, open-ended survey questions, observations, and focus group discussions.
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The complete question is:
Which survey uses quantitative data, as an example?
each person individual's preferred food.
how many cavities each individual has had.
the color of each person's bedroom's walls.
the type of car each individual person owns.
For each of the figures, write an absolute value equation to satisfy the given solution sets: -8 and -2
An absolute value equation to satisfy the given solution sets: -8 and -2 is |x+5|=3
Define equationIn mathematics, an equation is a statement that two expressions are equal. An equation consists of variables, constants, and mathematical operations (such as addition, subtraction, multiplication, division, exponentiation, etc.). The variables in an equation are often represented by letters, and the equation indicates that certain combinations of these variables and constants have the same value. Equations are commonly used in mathematics, physics, engineering, and many other fields to model and solve problems.
From the diagram you can see that the solutions of the equation are and
1. Determine the middle number between -8 and -2:
1/2(-8-2)=-5
2. Find the distance between points x=-5and x=-2:
d=-2+5=3
3. Writhe an absolute value equation :
|x+5|=3
Image is attached below.
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The equation 71. 40=(11. 9)6 shows how much it cost for a
company to buy 6 new uniforms. How much does it cost per
uniform?
Please please help me quiz.
If the cost for the 6 new uniforms is denoted by 71.40 = (11.9)6 , then the cost per uniform is $11.9 .
The equation which shows how much it cost for a company to buy 6 new uniforms is represented as : 71.40 = (11.9)6 ,
In order to find the cost per uniform, we need to divide both sides of the cost equation by 6:
On dividing both the sides of cost-equation by 6,
We get;
⇒ 71.40/6 = [(11.9)6]/6,
On simplifying ,
We get,
⇒ 71.40/6 = 11.9
Therefore, it cost the company 11.9 dollars each for the new uniform.
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2x+3y=4
2x=7y+24
can you help me solve this problem
Therefore , the solution of the given problem of equation comes out to be the system of equations has an answer of x = 5 and y = -2.
How are equations used?Mathematical formulas frequently use the same variable letter to try to enforce harmony among two assertions. Many academic numbers are shown to be equal using mathematical expression, also known as assertions. In this case, instead of splitting 12 into two parts, the normalise adds b + 6 using the example of y + 6. It is possible to determine the link number between each sign portion and the line length.
Here,
One of the solutions for a single variable should be solved in terms of the other.
We can find x from the first solution by solving in terms of y:
=> 2x + 3y = 4
=> 2x = 4 - 3y
=> x = (4 - 3y)/2
Solve for the other variable by substituting the formula for the variable from step 1 into the other equation.
Change x in the second expression to (4 - 3y)/2:
=> 2x = 7y + 24
=> 2((4 - 3y)/2) = 7y + 24
=> 4 - 3y = 7y + 24
=> -10y = 20
=> y = -2
Solve for the other variable by substituting the value of the variable from step 2 into one of the initial formulae.
When the first solution is used:
=> 2x + 3y = 4
=> 2x + 3(-2) = 4
=> 2x - 6 = 4
=> 2x = 10
=> x = 5
As a result, the system of equations has an answer of x = 5 and y = -2.
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What is the general form and explanation of Gaussian Function in Statistical Method?
Thank you
The Gaussian Function in statistical method is defined as follows:
f(x) = (1 / σ√(2π)) e^(-0.5((x-μ)/σ)²)
In which the parameters are listed as follows:
μ is the mean of the distributionσ is the standard deviation of the distributione is the mathematical constant approximately equal to 2.71828π is the mathematical constant approximately equal to 3.14159x is the variable of the function.What is the Gaussian Function?The Gaussian function is a widely used probability density function in statistics, also known as the normal distribution or bell curve, and has the equation defined at the beginning of the answer.
The curve is symmetrical around the mean (μ) of the distribution. The standard deviation (σ) of the distribution determines the width of the curve, with smaller standard deviations resulting in narrower curves and larger standard deviations resulting in wider curves.
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how much is x?
44=-7+x
Answer: x=51
Step-by-step explanation: Add 7 to both sides of the equation.
Please give brainliest !!
Answer:
x = 51
Step-by-step explanation:
44 = -7 + x
+7 +7
51 = x
x = 51
A hot-air balloon is floating over a river valley. At noon, the pilot increases the balloon's altitude to get a better view of the surroundings. This situation can be modeled as a linear relationship. What does the slope of the line tell you about the situation?
The slope of the line in this situation tells us the rate of change of the balloon's altitude with respect to time.
The slope of a line represents the ratio of the change in the vertical coordinate (altitude) to the change in the horizontal coordinate (time). In this scenario, as the pilot increases the balloon's altitude to get a better view of the surroundings, the altitude changes with respect to time.
Thus, the slope of the line represents the rate of change of the balloon's altitude with respect to time. A steep slope indicates a rapid change in altitude over time, while a gentle slope indicates a slower change. By analyzing the slope, the pilot can adjust the altitude of the balloon as needed to achieve the desired view.
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1.
An artist wants to sell prints of her paintings. She orders a set of prints for each of two of her paintings.
Each set contains regular prints and glossy prints, as shown in the table. Find the cost of one glossy
print.
The cost of one glossy print is $7.84.
What is quadratic equation?A quadratic equation is a polynomial equation of degree 2, where the largest exponent of the variable is 2.
An example of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable.
Let the cost of one regular print be "x" and the cost of one glossy print be "y".
From the first row, we can set up the equation:
45x + 30y = 465
From the second row, we can set up another equation:
15x + 10y = 155
We can solve for one variable in terms of the other in the second equation:
15x + 10y = 155
10y = 155 - 15x
y = (155 - 15x)/10
We can substitute this expression for y into the first equation:
45x + 30y = 465
45x + 30((155 - 15x)/10) = 465
Multiplying both sides by 10 to eliminate the fraction:
450x + 300(155 - 15x) = 4650
Simplifying:
450x + 46500 - 4500x = 4650
-4050x = -41850
x = 10.32 (rounded to the nearest hundredth)
Now we can substitute this value for x into the expression for y:
y = (155 - 15x)/10
y = (155 - 15(10.32))/10
y = 7.84 (rounded to the nearest hundredth)
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A scatter plot is shown:
What type of association does the graph show between x and y? (4 points)
Group of answer choices
Linear positive association
Nonlinear positive association
Linear negative association
Nonlinear negative association
Answer:
Linear positive association
Step-by-step explanation:
Linear positive associationNonlinear positive associationLinear negative associationNonlinear negative associationIf these are the 4 answer choices then it would be linear positive, because it is single line and moving up on the x-axis
4.02 Lesson check ! (2)
The given sequence -1, -2, -6, -24 is not arithmetic.
How to determine if the sequence is arithmetic?An arithmetic sequence is a sequence where the difference between any pair of consecutive terms is a constant knowed as the common difference, and if d is that common difference, we can write the recursive formula as:
f(n) = f(n - 1) + d
Here we have the sequence:
-1, -2, -6, -24
Taking the differences we will get:
-2 - (-1) = -1
-6 - (-2) = -4
-24 - (-6) = -18
The differences are different, thus, this is not an arithmetic sequence.
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[tex]4/7 + 3/4 + 1/8[/tex]
Fraction
Therefore , the solution of the given problem of fraction comes out to be 81/56 is the result of adding the three decimals.
A fraction is what?Any combination of like-sized pieces or portions can represent a whole. Standard English defines "quantity" as "a portion" of a particular measure. 8, 3/4. Wholes also include fractions. In mathematics, numerals are expressed by the ratio of quotient to ratio. Every one of these fractions of integers are simple fractions. The fraction contains a fraction, but the fraction's remainder is a challenging fraction. because the values, 4.91, and numerators of real fractions can vary.
Here,
We must identify a common denominator in order to combine these fractions. Finding the denominators' least common multiple (LCM), in this instance 56, is one way to accomplish this.
=> 4/7 + 3/4 + 1/8 = (4/7) * (8/8) + (3/4) * (14/14) + (1/8) * (7/7)
=> 32/56 + 42/56 + 7/56
=> (32 + 42 + 7)/56
=> 81/56
Therefore, 81/56 is the result of adding the three decimals. The ultimate solution is this fraction because it cannot be further condensed.
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Plsss I needdd this answer asp
Applying the power rules, it was found that the equivalent expressions are: [tex]6^{(x+7)}*(2)^{5x}[/tex] and [tex](2)^{5x+1}*6^{(x+6)}*3[/tex].
Power RulesThe main power rules are presented below.
Multiplication with the same base: you should repeat the base and add the exponents.Division with the same base: you should repeat the base and subtract the exponents.Power. For this rule, you should repeat the base and multiply the exponents.Exponent negative - For this rule, you should write the reciprocal number with the exponent positive.Zero Exponent. When you have an exponent equal to zero, the result must be 1.For solving this question, you should apply the power rules and check the options are equivalent to the given expression [tex]6*(36)^{\frac{x}{2}+3}*(2)^{5x}[/tex].
From the power rules, you can simplify the given expression, as shown below.
[tex]6*(36)^{\frac{x}{2}+3}*(2)^{5x}=6*(6^2)^{\frac{x}{2}+3}*(2)^{5x}\\ \\ 6*(36)^{\frac{x}{2}+3}*(2)^{5x}=6*(6)^{x+6}*(2)^{5x}\\ \\ 6*(36)^{\frac{x}{2}+3}*(2)^{5x}=6*6^x*6^6*(2)^{5x}\\ \\ 6*(36)^{\frac{x}{2}+3}*(2)^{5x}=6^{(x+7)}*(2)^{5x}[/tex]
Then, you should find an expression equivalent to [tex]6^{(x+7)}*(2)^{5x}[/tex].
Option 1 - [tex]6^{(x+7)}*(2)^{5x}[/tex]This expression is exactly the result of the simplification done in the expression given [tex]6*(36)^{\frac{x}{2}+3}*(2)^{5x}[/tex].
It is equivalent to [tex]6^{(x+7)}*(2)^{5x}[/tex].
Option 2- [tex]6^{(2x+6)}*(2)^{5x}[/tex]The expression [tex]6^{(2x+6)}*(2)^{5x}[/tex] is not equivalent to [tex]6*(36)^{\frac{x}{2}+3}*(2)^{5x}[/tex].
Option 3- [tex](2)^{5x+1}*6^{(x+6)}*3[/tex][tex](2)^{5x+1}*6^{(x+6)}*3= 2^{5x}*2^1*6^x*6^6*3\\ \\ (2)^{5x+1}*6^{(x+6)}*3= 2^{5x}*6^x*6^6*6\\ \\ (2)^{5x+1}*6^{(x+6)}*3= 2^{5x}*6^x*6^7\\ \\ (2)^{5x+1}*6^{(x+6)}*3= 2^{5x}*6^{x+7}[/tex]
The expression [tex](2)^{5x+1}*6^{(x+6)}*3[/tex] is equivalent to [tex]6*(36)^{\frac{x}{2}+3}*(2)^{5x}[/tex].
Option 4- [tex]32^x*(216)^{\frac{x}{2}+3}[/tex][tex]32^x*(216)^{\frac{x}{2}+3} =2^{5x}*(6^3)^{\frac{x}{2}+3}\\ \\ 32^x*(216)^{\frac{x}{2}+3} =2^{5x}*(6^\frac{3x}{2} )*6^9}\\ \\[/tex]
The expression [tex]32^x*(216)^{\frac{x}{2}+3}[/tex] is not equivalent to [tex]6*(36)^{\frac{x}{2}+3}*(2)^{5x}[/tex].
Option 5- [tex]32^x*(6)^{\frac{x}{2}+4}[/tex][tex]32^x*(6)^{\frac{x}{2}+4}=2^{5x}*6^{\frac{x}{2} }*6^4[/tex]
The expression [tex]32^x*(6)^{\frac{x}{2}+4}[/tex] is not equivalent to [tex]6*(36)^{\frac{x}{2}+3}*(2)^{5x}[/tex].
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Shefali goes to a farmers’ market every Saturday. Two Saturdays ago, Shefali purchased 3 apples and 4 oranges for a total of $3.47 . Last Saturday, she purchased 1 2 12 oranges, but no apples, and spent $6.36 . Today, she only has one $10 bill. Given that none of the prices have changed over the last 3 weeks, what is the maximum number of apples she can purchase today?
The maximum number οf apples she can purchase is 15.
Let's start by finding the cοst οf οne apple and οne οrange using the infοrmatiοn frοm twο Saturdays agο:
3a + 4ο = 3.47, where "a" is the cοst οf οne apple and "ο" is the cοst οf οne οrange.
We can simplify this equatiοn by dividing bοth sides by 3: a + 4/3 ο = 1.1567
Nοw, let's use the infοrmatiοn frοm last Saturday:
12ο = 6.36
ο = 0.53
We can substitute this value οf "ο" intο οur simplified equatiοn tο find the cοst οf οne apple:
a + 4/3(0.53) = 1.1567
a = 0.63
Sο, οne apple cοsts $0.63 and οne οrange cοsts $0.53.
If Shefali has οne $10 bill and she wants tο buy the maximum number οf apples, she can spend at mοst $10 οn apples. Let "n" be the number οf apples she can buy:
0.63n ≤ 10
n ≤ 15.87
Since Shefali can't buy a fractiοnal part οf an apple, the maximum number οf apples she can purchase is 15.
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The temperature in austria one morning was -5 degrees celcias at 08 oclock and increased by 2 degrees celcias every hour until 12 oclock ,what will be the temperature be at half past 11
the temperature in Austria will be 10 degrees Celsius at half past 11.
We can start by calculating how much the temperature will increase from 8 am to 12 pm:
From 8 am to 9 am: temperature increases by 2 degrees Celsius
From 9 am to 10 am: temperature increases by 2 degrees Celsius
From 10 am to 11 am: temperature increases by 2 degrees Celsius
From 11 am to 12 pm: temperature increases by 2 degrees Celsius
Therefore, the temperature at 12 pm will be:
-5 + 2 + 2 + 2 + 2 = -5 + 8 = 3 degrees Celsius
Now, we need to calculate how much the temperature will increase from 12 pm to 11:30 am:
From 12 pm to 1 pm: temperature increases by 2 degrees Celsius
From 1 pm to 2 pm: temperature increases by 2 degrees Celsius
From 2 pm to 3 pm: temperature increases by 2 degrees Celsius
From 9 pm to 10 pm: temperature increases by 2 degrees Celsius
From 10 pm to 11 pm: temperature increases by 2 degrees Celsius
From 11 pm to 11:30 pm: temperature increases by 1 degree Celsius
Therefore, the temperature at half past 11 will be:
3 + 2 + 2 + 2 + 1 = 10 degrees Celsius
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What is the inequality shown?
The total cost of producing a type of car is given by
C(x)=25000−40x+0.02x^2, where x is the number of cars produced. How
many cars should be produced to incur minimum cost?
The corporation should make 1000 of a certain sort of car in order to reduce production cost using minimal cost function and derivatives.
Finding the value of x that minimizes the cost function will help us determine the optimal number of automobiles to construct. [tex]C(x) = 25000 - 40x + 0.02x^2[/tex].
The derivative of C(x) with respect to x can be taken, set to zero, and then the value of x can be determined.
[tex]C'(x) = -40 + 0.04x = 0 0.04x = 40 \sx = 1000[/tex]
Hence, when 1000 cars are created, the least cost is incurred. We can check the second derivative of C(x) at x = 1000 to make sure this is a minimum.
[tex]C''(x) = 0.04 > 0[/tex]
The fact that the second derivative is positive demonstrates that the minimum of C(x) occurs at x = 1000.
As a result, the corporation should make 1000 of a certain sort of car in order to reduce production costs. Cost is reduced to $21000 at this manufacturing level.
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Suppose you have been tasked with regulating a single monopoly firm that sells 50-pound bags of concrete. The firm has fixed costs of $10 million per year and a variable cost of $3 per bag no matter how many bags are produced.
the optimal price and quantity for the bags of concrete should be amount $100 and 10,000 bags, respectively. This combination would yield a total economic surplus of $500,000.
Q = 10,000 - 100P
Where Q is the quantity of bags and P is the price per bag.
The goal of the regulation is to maximize total economic surplus.
To maximize total economic surplus, the optimal price and quantity for the bags of concrete should be determined. The total economic surplus for this situation can be calculated by finding the area of the triangle formed between the demand curve and the price line.
The optimal price is calculated by setting the demand equation equal to zero, giving P = 100.
The optimal quantity is calculated by substituting the optimal price into the demand equation, giving Q = 10,000.
The total economic surplus is calculated by finding the area of the triangle formed between the demand curve and the price line, which is (100*10,000)/2 = $500,000 amount.
Therefore, the optimal price and quantity for the bags of concrete should be $100 and 10,000 bags, respectively. This combination would yield a total economic surplus of $500,000.
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I NEED HELP! pleaseeee!
The length of the rectangle is 63 cm and the Breadth of the rectangle is 12 cm, for this, we have to know something about rectangles.
What is a rectangle?Rectangle, It is a plane shape, as opposed to a square, with four(4) straight sides and four(4) right angles, particularly one(1) with uneven neighboring sides.
Square, A square is a regular quadrilateral in Euclidean geometry, which means that it has four(4) equal(same) sides and four(4) equal angles. It can alternatively be explained as a rectangle with two(2) neighboring sides that are of equal(same) length.
Given, Perimeter = 150 cm, Length, l = 5b+3 , Breadth = b
150 = 2(5b + 3 + b)
150 = 2(6b +3)
6b +3 = 75
6b = 72
b = 12 cm, So l = 63 cm (By putting the b value in the l equation
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If the triangles shown at the right are similar,
what is the value of x?
Answer:
28.235
Step-by-step explanation:
10/34 = x/96
960= 34x
960/34= x
x= 28.235
What is the solution to this equation? -2x + 15 = 30
After simplifying we get, the solution to the equation as -2x + 15 = 30 is x = -7.5.
To solve the equation -2x + 15 = 30, we need to isolate the variable x on one side of the equation. We can do this by performing the same operation on both sides of the equation to maintain its balance.
First, we will subtract 15 from both sides of the equation to get:
-2x + 15 - 15 = 30 - 15
Simplifying the left-hand side and the right-hand side of the equation, we obtain:
-2x = 15
Next, we will divide both sides of the equation by -2 to isolate x:
-2x/-2 = 15/-2
Simplifying, we get:
x = -7.5
Therefore, the solution to the equation -2x + 15 = 30 is x = -7.5.
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4.02 Lesson Check Arithmetic Sequences (8)
Answer:
[tex]a_9= -134[/tex]
Step-by-step explanation:
Us the formula for arithmetic sequence
[tex]a_n = a_1 + d(n -1)[/tex]
where
[tex]\rm\:a_n=\:nth\:term\\\:d\:=\:common\:difference\\n\:=\:number\:of\:terms[/tex]
Given
[tex]a_1 = -38\\d = - 12\\n = 9[/tex]
[tex]a_9 = -38 -12(9 - 1) \\\\a_9 = -38 - 12(8)\\\\a_9= -38 - 96\\\\a_9= -134[/tex]
Consider the first five terms of the following sequence. 2, 6, 18, 54, 162,. Of The sequence defines a function, what is a reasonable domain and range of the function?A. Domain: {1, 2, 3, 4, 5, …}; Range: {2, 6, 18, 54, 162, …}Domain: {1, 2, 3, 4, 5, …}; Range: all real numbers. Domain: all real numbers; Range: {2, 6, 18, 54, 162, …}D. Domain: all real numbers; Range: all real numbers
The reasonable domain and range of the function is option (A) Domain: {1, 2, 3, 4, 5, …}; Range: {2, 6, 18, 54, 162, …}.
The sequence appears to be an exponential sequence with a common ratio of 3. That is, each term is obtained by multiplying the previous term by 3.
If this sequence defines a function, a reasonable domain would be the set of positive integers starting from 1 since the sequence begins with the first term being 2.
The range of the function appears to be the set of positive powers of 3 since each term is a power of 3 multiplied by the initial term, 2. Therefore, a reasonable range would be the set {2, 6, 18, 54, 162, ...}.
Therefore, the correct option is (A) Domain: {1, 2, 3, 4, 5, …}; Range: {2, 6, 18, 54, 162, …}.
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the 12-foot bed of a dump truck loaded with heavy stone must rise to an angle of 36 degrees before the stone will spill out. Approximately how high must the front of the bed rise (x) to unload?
The approximate height of the front bed 8.1ft
What is trigonometry?
The study of the relationships and characteristics of angles, triangles, and the trigonometric functions is the focus of the mathematic branch known as trigonometry (sine, cosine, tangent, cotangent, secant, and cosecant). It entails using algebraic methods and geometric principles to solve problems involving triangles and angles, such as measuring angles, computing triangle sides and angles, and analysing periodic events like waves and oscillations.
We use trigonometry to solve the problem
we have
tan (36) = opposite side/ adjacent side
tan(36) = opposite side / 12
Opposite side = tan(36) *12
Opposite side = 8.1 ft
Hence, the approximate height of the front bed 8.1ft
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ronsapa ar
9. Two distinct lines, l and m, are each perpendicular to the same line n.
Explain why & and m are parallel lines. (Lesson 1-6)
When two distinct lines, l and m, are each perpendicular to the same line n, it means that the two lines have the same angle of rotation in relation to n.
What is angle?An angle is a figure formed by two lines or rays diverging from a common point. It is measured in degrees, with a full circle representing 360 degrees. Angles are used to describe the direction and orientation of objects, as well as to measure the size of an area or the relationship between two lines. Angles are an important part of mathematics, used in problems such as geometry, trigonometry and calculus.
This angle is equal to 90 degrees, meaning that the two lines are parallel to one another.
Parallel lines are lines that never intersect and are always the same distance apart. This is the case for l and m because both lines are perpendicular to the same line n and, thus, have the same angle. Therefore, the two lines are parallel to one another, meaning that they will never cross and will always remain the same distance apart.
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The account balance on April 1st is $50.51. On April 15th a payment of $15.00 is made. On April 25th a purchase of $19.27 is made. The annual rate is 18%.
What is the unpaid balance? What is the finance charge using the unpaid balance method? What is the new balance?
Unpaid balance = $
Finance charge = $
New balance = $
In response to the stated question, we can state that The new balance is equation therefore $55.59.
What is equation?An equation is a mathematical assertion that establishes the equality of two expressions that are joined together by the equals sign ('='). For example, 2x – 5 = 13. 2x-5 and 13 are examples of expressions. The letter '=' connects the two expressions. A mathematical formula is called an equation if it contains two algebraic expressions on either side of the equal sign (=). It shows how the right and left formulas are equivalent to one another. Any formula will result in L.H.S. = R.H.S. (left side = right side).
We must ascertain the balance that is still owing after the payment and purchase transactions have been executed in order to calculate the unpaid balance.
The balance drops to $35.51 on April 15 ($50.51 - $15.00), a reduction of $15.00.
The account balance climbs to $54.78 ($35.51 + $19.27) on April 25.
The remaining balance is $54.78 as a result.
$44.29 * (0.18 / 365) * 30 = $0.81
The finance fee is therefore $0.81.
We combine the outstanding balance and the finance charge to determine the new balance:
$54.78 + $0.81 = $55.59
The new balance is therefore $55.59.
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In how many ways can 6 people be seated in a row of 9 chairs
There are 60,480 ways to seat 6 people in a row of 9 chairs using the multiplication principle of counting.
There are 9 choices for the first person, 8 choices for the second person (since one chair is already taken), 7 choices for the third person, and so on. Therefore, the total number of ways 6 people can be seated in a row of 9 chairs is:
[tex]9 * 8 * 7 * 6 * 5 * 4 = 60,480[/tex]
So there are 60,480 ways to seat 6 people in a row of 9 chairs.
To count the number of ways 6 people can be seated in a row of 9 chairs, we can use the multiplication principle of counting.
First, we consider the number of choices for the first person. Since there are 9 chairs and the order in which the people are seated matters, there are 9 choices for the first person. Once the first person is seated, there are 8 chairs remaining for the second person to choose from, since one chair is already taken. Therefore, there are 8 choices for the second person. Continuing in this way, there are 7 choices for the third person, 6 choices for the fourth person, 5 choices for the fifth person, and 4 choices for the sixth person.
To find the total number of ways to seat 6 people in a row of 9 chairs, we multiply the number of choices at each step together. Hence, the total number of ways is:
[tex]9 * 8 * 7 * 6 * 5 * 4 = 60,480[/tex]
So there are 60,480 ways to seat 6 people in a row of 9 chairs.
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The complete question is:
How many different arrangements are possible for 6 persons to sit in a row of 9 chairs?
a) 6720
b) 60480
c) 30
d) 346