The following statement which are true are Kayla's opportunity cost to go to the movie is $9.50 and Tara's total cost of attending the movie is $50.5, option B, D.
Tara earns $8.50 per hour
She is scheduled to work for 4 hours
Total earnings=$8.50 × 4
=$34
Tara's opportunity cost of attending the movie instead of working is $34
Since, a ticket cost $9.50
And she always spend about $7 on snacks
Tara's total cost of going to the movies = opportunity cost of attending the movie + cost of tickets + cost of snacks
=$34 + $9.50 + $7
=$50.5
Opportunity cost refers to the cost of satisfying a want at the expense of another want. It can also be called REAL COST or TRUE COST.
Therefore,
2. Kayla's opportunity cost to go to the movie is $9.50
4. Tara's total cost of attending the movie is $50.5
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Complete question:
Tara earns $8.50 an hour (after taxes) at the pizza place. She is scheduled to work four hours this afternoon. However, her friend Kayla called and asked her if she wants to go to the movie. A ticket to the movie costs $9.50. In addition, she always spends about $7 on snacks.
Which of the following statement are true? Select all that apply.
1. Tara's opportunity cost if she goes to work instead of the movie is $34.
2. Kayla's opportunity cost to go to the movie is $9.50.
3. There is no opportunity cost for Tara to go to the movie.
4. Tara's total cost of attending the movie is $50.5
5. Tara's opportunity cost if she goes to the movie instead of working is $34
How much money does the average professional football fan spend on food at a single
football game? That question was posed to 60 randomly selected football fans.
The sampled results show that the sample mean was $70. 00 and prior sampling
indicated that the population standard deviation was $17. 50.
Use this information to create a 95 percent confidence interval for the population mean.
The 95 percent confidence interval for the population mean is $65.59 to $74.41.
To calculate a 95% confidence interval for the population mean, we will use the sample mean, population standard deviation, and sample size provided. The formula for the confidence interval is:
CI = X ± (Z * (σ / √n))
Where:
- X is the sample mean, $70.00
- Z is the Z-score for a 95% confidence interval, 1.96
- σ is the population standard deviation, $17.50
- n is the sample size, 60
CI = $70.00 ± (1.96 * ($17.50 / √60))
Calculate the margin of error:
Margin of Error = 1.96 * ($17.50 / √60) ≈ $4.41
Now, calculate the confidence interval:
Lower Limit = $70.00 - $4.41 ≈ $65.59
Upper Limit = $70.00 + $4.41 ≈ $74.41
So, the 95% confidence interval for the population mean is approximately $65.59 to $74.41.
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Identify all the lines on the graph with unit rates that are less than 2 and greater than the unit rate of the relationship in the table. X y
7 8
14 16
21 24
The only line on the graph with a unit rate less than 2 is the horizontal line passing through y=8.
To identify the unit rates on the graph, we need to find the slope of the line connecting each pair of points. We can use the formula:
slope = (change in y) / (change in x)
For example, the slope between the first two points (7,8) and (14,16) is:
slope = (16-8) / (14-7) = 8/7
Similarly, we can find the slopes for the other pairs of points:
- between (7,8) and (21,24): slope = (24-8) / (21-7) = 16/14 = 8/7
- between (14,16) and (21,24): slope = (24-16) / (21-14) = 8/7
Notice that all three slopes are equal, which means the graph represents a line with a constant unit rate of 8/7.
To find lines with unit rates less than 2, we need to look for steeper lines on the graph. Any line with a slope greater than 2/8 (or 1/4) will have a unit rate greater than 2.
One way to see this is to note that a slope of 2/8 means that for every 2 units of increase in y, there is 8 units of increase in x. This is equivalent to saying that the unit rate is 2/8 = 1/4. If the slope is greater than 2/8, then the unit rate is greater than 1/4, and therefore greater than 2.
Looking at the graph, we can see that the steepest line has a slope of 2/3, which means it has a unit rate of 2/3. Therefore, any line with a slope greater than 2/3 will have a unit rate greater than 2, and any line with a slope less than 2/3 will have a unit rate less than 2.
To summarize:
- The graph represents a line with a constant unit rate of 8/7.
- Any line with a slope greater than 2/3 has a unit rate greater than 2.
- Any line with a slope less than 2/3 has a unit rate less than 2.
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Determine which two statements contradict each other.
-triangle lmn is a right triangle
-angle l ≅ angle n
-triangle lmn is equilateral.
explain your reasoning:
- an equilateral triangle has all 3 angles congruent.
-triangle lmn must have the right angle at m , not l or n .
-a right triangle cannot also be an isosceles triangle.
-equilateral triangles have 60 degree angles, so none are right.
The two contradictory statements are "triangle LMN is a right triangle" and "triangle LMN is equilateral."
An equilateral triangle has all three sides and angles congruent. Therefore, if triangle LMN is equilateral, all angles in the triangle must be congruent and equal to 60 degrees. However, the statement "triangle LMN is a right triangle" implies the presence of a 90-degree angle, which contradicts the requirement for all angles to be 60 degrees in an equilateral triangle.
Additionally, the statement "angle L ≅ angle N" suggests that angles L and N are congruent. In an equilateral triangle, all angles are congruent, so if angles L and N are congruent, it further supports the claim that triangle LMN is equilateral.
In conclusion, the statement "triangle LMN is a right triangle" contradicts the statement "triangle LMN is equilateral" because a right triangle cannot be equilateral.
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Which is the closest to the volume of the solid figure formed from the net?
I'm sorry, but I cannot answer your question without a net or a description of the solid figure. Can you please provide more information or context?
x+y=112
y=x-58
using elimination
PLEASE HELP ME!!!!
Answer:
x=85
y=27
;)
Step-by-step explanation:
x+y=112
y=x-58
add 58 to the other side
58+y=x
Subtract y
x-y=58
x+y=112
Now if we add these we get
2x=170
x=85
Then if we substitute 85 in x+y=112
85+y=112
112
-85
____
27
Check your Answer on
y=x-58
27=85-58
27=27
This is the Answer
Please DM me if I should reexplain THANK YOU!
Hope this helps!
Amanda wants to add 6732 and 4975 how can Amanda use mental math to add the numbers is Amanda answer correct explain
she can add each number one by one , and whenever she needs to carry numbers over. She can add them to the already existing numbers. she cna check with a calculator
Please help it due soon and the answer is meant to be in kg
Answer: 20 kg
Step-by-step explanation:
You follow the line of best fit until 50cm
Then you trace across and look at the x-axis.
There you will find that the dog will be 20kg at 50cm using the line of best fit.
an engineer for an electric company is interested in the mean length of wires being cut automatically by machine. the desired length of the wire is 12 feet. it is known that the standard deviation in the cutting length is .15 feet, suppose the engineer decided to estimate the mean length to within .025 with 99% confident. what sample size is needed?
According to the given standard deviation, the engineer would need a sample size of at least 75 wires to estimate the mean length to within 0.025 feet with 99% confidence.
To estimate the mean length of the wires being cut, the engineer needs to determine the sample size needed to achieve a certain level of confidence and level of precision. In this case, the engineer wants to estimate the mean length to within 0.025 feet with 99% confidence. This means that there is a 99% chance that the true population mean falls within the estimated range.
To determine the sample size needed, the engineer can use a formula that takes into account the desired level of confidence, level of precision, and the standard deviation of the population. The formula is:
n = (z² x s²) / E²
Where:
n = sample size needed
z = z-score for desired level of confidence (99% = 2.58)
s = standard deviation of the population (0.15 feet)
E = level of precision (0.025 feet)
Plugging in the values, we get:
n = (2.58² x 0.15²) / 0.025²
n = 74.83 ≈ 75
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Color the stars, so it is unlikely impossible to choose a red one.
The Nielsen Company surveyed 371 owners of Android phones and found that 200
of them planned to get another Android as their next phone. What is the lower
bound for the 95% confidence interval for the proportion of Android users who plan
to get another Android?
The lower bound for the 95% confidence interval for the proportion of Android users who plan to get another Android phone is 0.463 .
It can be evaluated applying the formula
Lower Bound = Sample Proportion - Z-Score × Standard Error
Here
Sample Proportion
= 200/371 = 0.539
Z-Score = 1.96 (for a 95% confidence interval)
Standard Error = √[(Sample Proportion * (1 - Sample Proportion)) / Sample Size]
= √[(0.539 × (1 - 0.539)) / 371]
= 0.045
Therefore,
Lower Bound = 0.539 - 1.96 × 0.045 = 0.463
A confidence interval is a known as the specified range of values that is prone to contain an unknown population area with a certain degree of confidence.
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Let f(x)= x⁴ - 6x³ - 60x² + 5x + 3. Find all solutions to the equation f'(x) = 0. As your answer please enter the sum of values of x for which f'(x) = 0.
The answer is 2, which represents the sum of the values of x for which f'(x) = 0.
How to find critical points?To find the critical points of f(x), we need to find the derivative of f(x):
f(x) = x⁴ - 6x³ - 60x² + 5x + 3f'(x) = 4x³ - 18x² - 120x + 5Setting f'(x) = 0 and solving for x, we get:
4x³ - 18x² - 120x + 5 = 0We can use the Rational Root Theorem to find possible rational roots of the equation. The possible rational roots are:
±1, ±5/4, ±3/2, ±5, ±15/4, ±3, ±15, ±1/4We can use synthetic division or long division to check which of these roots are actually roots of the equation. We find that the only real root is x = 5/4, and it has multiplicity 2.
The sum of the values of x for which f'(x) = 0 is simply the sum of the critical points of f(x). In this case, we only have one critical point: x = 5/4.
5/4 + 5/4 = 10/4 = 2.We first find the derivative of the given function and set it equal to zero to find the critical points. We use the Rational Root Theorem to find the possible rational roots of the equation, and then we use synthetic division or long division to check which of these roots are actually roots of the equation. In this case, we find that the only critical point of the function is x = 5/4 with multiplicity 2.
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Using the driver's speed in feet per second, 72.08, how far did her car travel during her reaction time?
round your answer to two decimal places.
To answer this question, we need to know the driver's reaction time. Let's assume the reaction time is 1.5 seconds, which is a typical average for most drivers.
To find how far the car traveled during the reaction time, we can use the formula:
distance = speed × time
Plugging in the given speed of 72.08 feet per second and the assumed reaction time of 1.5 seconds, we get:
distance = 72.08 ft/s × 1.5 s
distance = 108.12 ft
Therefore, the car traveled 108.12 feet during the driver's reaction time. Rounded to two decimal places, the answer is 108.12.
For items A and B, us this data set of the price, in dollars, of a milkshake at five different restaurants:4,2,9,14,6. If necessary, round your answer to the nearest tenth of a unit. Decimal answers must round to tenth place.
(I need help, quick!)
Answer:
I'm assuming that A and B are two different items, and you want me to work with the same data set for both items. Here are the calculations:
1. Mean price of milkshake:
To find the mean price of a milkshake, you need to add up all the prices and divide by the total number of prices:
(4 + 2 + 9 + 14 + 6) / 5 = 7
Therefore, the mean price of a milkshake is $7.
2. Median price of milkshake:
To find the median price of a milkshake, you need to put the prices in order from lowest to highest:
2, 4, 6, 9, 14
The median is the middle value. Since there are five values, the middle value is the third value, which is 6.
Therefore, the median price of a milkshake is $6.
3. Mode of price of milkshake:
To find the mode of the price of a milkshake, you need to find the price that appears most frequently in the data set. In this case, there is no price that appears more than once, so there is no mode.
Therefore, there is no mode for the price of a milkshake.
I hope that helps! Let me know if you have any further questions.
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Find (a) the lateral area and (b) the surface area of the prism.
In this prism, lateral Area = 858.54 m² and surface area = 890.54 m².
Firstly, we will find the lateral area of the prism by applying the formula:
Lateral area = perimeter × height
Perimeter = sum of all the sides of prism
= 4 + 8 + 8.94 = 20.94 m
Lateral Area = 20.94 * 41 = 858.54 m²
Now, we have to find the surface area of the prism.
Surface area = Lateral Area + 2 × ( Base Area)
Base Area = the area of a triangle with sides 4, 8, and 8.94.
Now, we will calculate the area of the triangle
Firstly, we will find s for calculating the area of triangle and then apply the formula.
s = ( 4 + 8 + 8.94)/2 = 10.47 m
Area of triangle = [tex]\sqrt{ (10.47 (10.47 - 4)(10.47 - 8)(10.47 - 8.94))}[/tex]
= [tex]\sqrt{(10.47 (6.47)(2.47)(1.53))}[/tex]
= 16 m²
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Correct question:
Use formulas to find the lateral area and surface area of the given prism. Round your answer to the nearest whole number. The figure is not drawn to scale. The bases are right triangles.
What is the electron arrangement of an Al³+ ion?
A. 2,8
B. 2,3
C. 2, 8, 3
D. 2, 8, 8
Correct option is A)
The arrangement of electrons in different energy levels around a nucleus is called electronic configuration. The periodicity in properties of elements in any group is due to repetition in the same valence shell electronic configuration after a certain gap of atomic numbers such as 2, 8, 8, 18, 18, 32.
The atomic number of Al is 13 and its electronic configuration is 2, 8, 3. So, the electronic configuration of [tex]\text{Al}^3+[/tex] is 2,8.
a,b,c are prime numbers.
Find a,b,c that sastify the equation: a^4 + b^4 + c^4 + 54 = 11abc
The prime number values of a, b and c that satisfy the equation a⁴ + b⁴ + c⁴ + 54 = 11abc are a = 3, b = 2, and c = 5.
Let's consider the equation a⁴ + b⁴ + c⁴ + 54 = 11abc. Due to the fact that the total of four even numbers is also even, the left-hand side is always even. As a result, since 2 is the only even prime, one of the factors a, b, or c must be 2 for 11abc to likewise be even.
Let's examine each instance,
Case 1: a = 2
Substituting a = 2 into the equation, we get,
16 + b⁴ + c⁴ + 54 = 22bc
b⁴ + c⁴ - 22bc + 38 = 0
Since b and c are primes, they must be odd. Let b = 3 and c = 5, we have,
3⁴ + 5⁴ - 2235 + 38 = 0
81 + 625 - 330 + 38 = 0
Case 2: b = 2
Substituting b = 2 into the equation, we get,
a⁴ + 16 + c⁴ + 54 = 22ac
a⁴ + c⁴ - 22ac + 70 = 0
Since a and c are primes, they must be odd. Let a = 3 and c = 5, we have,
3⁴ + 5⁴ - 2235 + 70 = 0
Case 3: c = 2
Substituting c = 2 into the equation, we get,
a⁴ + b⁴ + 16 + 54 = 22ab
a⁴ + b⁴ - 22ab + 70 = 0
However, for any odd number x, x⁴ mod 16 = 1, which means that a⁴ and b⁴ are both corrosponds to 1 mod 16. So, as the conclusion, a = 3, b = 2, and c = 5.
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Verify that the function
f(x) = -4x^2 + 12x - 4 In x attains
an absolute maximum and absolute minimum
on [1/2, 2].
Find the absolute maximum and minimum
values.
The function f(x) = -4x² + 12x - 4 attains an absolute maximum of 3 at x = 1/2 and an absolute minimum of -8 at x = 2 on the interval [1/2, 2].
To help you verify and find the absolute maximum and minimum values of the function f(x) = -4x² + 12x - 4 on the interval [1/2, 2].
Step 1: Find the critical points by taking the derivative of f(x) and setting it to 0.
f'(x) = -8x + 12
Step 2: Solve f'(x) = 0 to find critical points.
-8x + 12 = 0
x = 3/2
Step 3: Evaluate the function f(x) at the critical point and the interval's endpoints.
f(1/2) = -4(1/2)^2 + 12(1/2) - 4(1/2) = 3
f(3/2) = -4(3/2)^2 + 12(3/2) - 4(3/2) = 1
f(2) = -4(2)^2 + 12(2) - 4(2) = -8
Step 4: Compare the function values and determine the absolute maximum and minimum values.
The absolute maximum value is 3 at x = 1/2.
The absolute minimum value is -8 at x = 2.
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The table shows the number of different categories of books that Mrs. Hoover, the librarian, sold at the book fair on Thursday.
If Mrs. Hoover sells 50 books at the book fair on Friday, which prediction for Friday is NOT supported by the data in the table?
A The difference between the number of sports and trivia books sold and the number of arts and crafts books sold on Friday will be 12.
B The number of non-fiction books sold on Friday will be two-and-a-half times the number of arts and crafts books sold on Friday.
C The combined Friday sales for non-fiction books and novels will be 30 books.
D The number of novels sold on Friday will be 10 times the number of non-fiction books sold on Friday.
The prediction that is not supported by the data is option B: "The number of non-fiction books sold on Friday will be two-and-a-half times the number of arts and crafts books sold on Friday."
How to explain the dataWe can see from the table that on Thursday, 7 sports and trivia books and 19 arts and crafts books were sold, for a difference of 12.
On Thursday, 13 non-fiction books and 19 arts and crafts books were sold. If we assume that the same ratio will hold on Friday, then we can predict that the number of non-fiction books sold will be (19/2)*2.5 = 23.75, which is not a whole number. Therefore, this prediction is not supported by the data.
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Mario's Pizzeria offers 2 types of crust and 6 different kinds of toppings. They assigned each side of the coin to a type of pizza crust and each number on the number cube to a topping. If Mario's makes a one-topping pizza, what is the probability that the coin flipped and the cube rolled will describe the pizza crust and topping combination they just made? Express the answer as a decimal rounded to the nearest thousandth
To determine the probability of the coin flip and the cube roll describing the pizza crust and topping combination made at Mario's Pizzeria, we need to consider the total possible outcomes of these events.
There are 2 types of crust, so the coin has 2 sides (heads for one crust type and tails for the other). For the toppings, there are 6 options, represented by the numbers 1 to 6 on the number cube.
First, we find the total possible outcomes by multiplying the number of crust options (2) by the number of topping options (6):
Total possible outcomes = 2 crust options * 6 topping options = 12 combinations
Since there is only one specific combination that Mario's Pizzeria just made, the probability of the coin flip and the cube roll describing this specific combination is:
Probability = 1 (specific combination) / 12 (total possible outcomes)
To express this as a decimal rounded to the nearest thousandth, divide 1 by 12:
Probability ≈ 0.083
So, the probability that the coin flipped and the cube rolled will describe the pizza crust and topping combination that Mario's Pizzeria just made is approximately 0.083, or 8.3%.
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Two lines meet at a point that is also the vertex of an angle set up and solve an appropriate equation for x and y.
Both vertical angles measure 90 degrees, and the adjacent angles each measure 90 degrees as well.
When two lines intersect at a point, we can use the properties of vertical and adjacent angles to set up and solve equations relating to their measures. This can help us find missing angles or verify that two angles are congruent.
When two lines intersect at a point, they form two angles. These angles are called vertical angles, and they are always congruent. In addition, the two lines also form two pairs of adjacent angles, each pair of which adds up to 180 degrees.
Let's consider an example to understand this concept better. Suppose we have two lines AB and CD that intersect at point P. If angle APD measures x degrees, then angle BPC also measures x degrees because they are vertical angles. Similarly, angle APB and angle CPD are adjacent angles, and their sum is 180 degrees. If angle APB measures y degrees, then angle CPD also measures y degrees.
Therefore, we can set up the following equation:
x + y = 180
This equation relates the measures of the adjacent angles formed by the two lines. We can solve for one variable in terms of the other by rearranging the equation:
y = 180 - x
This equation gives us the measure of one angle in terms of the measure of the other. We can substitute this expression into the equation for the vertical angles to get:
2x = 180
Solving for x, we find that x = 90.
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I need help with this real quick please
First, using the Pythagorean theorem, we get the hypotenuse = 12.
sin = opposite/hypotenuse = [tex]\frac{6\sqrt{3} }{12} = \frac{\sqrt{3} }{2}[/tex]
cos = adjacent/hypotenuse = [tex]\frac{6}{12} =\frac{1}{2}[/tex]
tan = opposite/adjacent = [tex]\frac{6\sqrt{3} }{6} = \sqrt{3}[/tex]
csc = hypotenuse/opposite = [tex]\frac{12}{6\sqrt{3} } =\frac{2}{\sqrt{3} }[/tex]
sec = hypotenuse/adjacent = [tex]\frac{12}{6} =2[/tex]
cot = adjacent/opposite = [tex]\frac{6}{6\sqrt{3} } = \frac{1}{\sqrt{3} }[/tex]
Express the quantity "14 revolutions per second" in radians per second. Write your answers in terms of pi
14 revolutions per second can be expressed as 28π radians per second.
A radian is an angle whose corresponding arc in a circle is equal to the radius of the circle. A revolution is a full rotation, or a complete, 360-degree turn.
1 revolution per second is expressed as 2π radians per second.
To calculate the number of radians in 14 revolutions per second, we have to multiply 2π by 14.
14 revolutions per second = 14 * 2π
= 28π radians per second
Thus, the answer to the given question comes out to be 28 π radians per second
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A triangle has base b and height h. The base is doubled. Complete the description of how the height
must change so that the area remains the same. Complete the explanation of the reasoning.
The area of the original triangle is - 0,6 2. The area of the new triangle is
$(201)2 =
-0,1 2. Therefore, the height must be
This must equal the original area,
(select)
When the base of a triangle is doubled, the height must be halved to maintain the same area. This is because the area of a triangle is proportional to the product of its base and height. Area of the new triangle is b₁h₂.
Given that a triangle has base b and height h, and the base is doubled. We need to find how the height must change so that the area remains the same.
The area of the original triangle is (1/2) b₁h₁.
Let's assume that the original base is b₁ and the original height is h₁.
Now, the base is doubled, so the new base is 2b₁.
Using the formula for the area of a triangle, we can find the area of the new triangle as
Area of the new triangle = (1/2) × base × height
= (1/2) × 2b₁ × h₂
= b₁h₂
where h₂ is the new height of the triangle.
Since we want the area of the new triangle to be equal to the area of the original triangle, we can equate the two expressions for the area
b₁h₁ = b₁h₂
Simplifying, we get
h₂ = h₁/2
Therefore, the height must be halved when the base is doubled to keep the area of the triangle constant.
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--The given question is incomplete, the complete question is given
" A triangle has base b and height h. The base is doubled. Complete the description of how the height
must change so that the area remains the same. Complete the explanation of the reasoning.
The area of the original triangle is (1/2) b₁h₁. The area of the new triangle is 1/2 (2b₁)h₂ =_____ This must equal the original area (1/2) b₁h₁. Therefore, the height must be_____"--
(1 point) Assuming that y is a function of x, differentiate x^6y^9 with respect to x. dy Use D for dy/dx in your answer. d/dx (x^6y^9) =
To differentiate x^6y^9 with respect to x, we will use the product rule. The product rule states that the derivative of a product of two functions is the derivative of the first function multiplied with the second function, plus the first function multiplied with the derivative of the second function.
Step 1: Identify the functions
Function 1 (u): x^6
Function 2 (v): y^9
Step 2: Find the derivatives
u' (du/dx): Differentiate x^6 with respect to x, which gives 6x^5
v' (dv/dx): Differentiate y^9 with respect to x, which gives 9y^8 * (dy/dx) = 9y^8D (since D = dy/dx)
Step 3: Apply the product rule
d/dx (x^6y^9) = u'v + uv'
= (6x^5)(y^9) + (x^6)(9y^8D)
= 6x^5y^9 + 9x^6y^8D
So, the derivative of x^6y^9 with respect to x is 6x^5y^9 + 9x^6y^8D.
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Find the missing dimension of the cone.
the volume is 1/18π and the radius is 1/3. find the height.
Answer:
h = 3/2
Step-by-step explanation:
Volume of cone formula: V = 1/3 π r²h
We are given volume and the radius so we can plug in those values
1/18π = 1/3 π (1/3)²h
1/18π = 1/3 π 1/9 h
Multiply the fractions on the right side:
1/18π = 1/27πh
Multiply both sides by reciprocal of 1/27 (which is 27)
3/2π = πh
Divide both sides by π
h = 3/2
Hope this helps!
Solve the inequality for x 4x-1 grater then -5
The solution of the inequality 4x-1 grater then -5 is x > -1
Solving the inequality for x
From the question, we have the following parameters that can be used in our computation:
4x-1 grater then -5
Express properly
so, we have the following representation
4x - 1 > -5
Add 1 to both sides of the inequality
so, we have the following representation
4x > -4
Divide both sides by 4
x > -1
Hence, the solution of the inequality is x > -1
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Write the decimal form of 129275775
Answer: 129275775.0
Step-by-step explanation:
129275775.0
whenever there is a whole number, the decimal is at the end of the number.
Simplify (7/2 x 5/3) + (1/6 x 3/2) - (12/8 x 4/3)
Give proper step by step explanation
Answer:
To simplify the given expression:
(7/2 x 5/3) + (1/6 x 3/2) - (12/8 x 4/3)
Step 1: Simplify the fractions within the parentheses first.
(35/6) + (1/4) - (48/24)
Step 2: Find a common denominator for all three terms. The least common multiple of 6, 4, and 24 is 24.
(35/6 x 4/4) + (1/4 x 6/6) - (48/24 x 1/1)
Step 3: Simplify the numerators using the common denominator.
(140/24) + (6/24) - (48/24)
Step 4: Combine the like terms.
98/24 or 4 1/6
Therefore, the simplified form of the expression is 4 1/6.
If there were a 10 percent tax on every pack of cigarettes John bought between age 22 and age 70, how much tax revenue would be raised from John's cigarette purchases? How might such tax money be used to help reduce smoking rates?
Using one cigarette packet per day with the cost of $ 5.50 tax revenue would be raised from John's cigarette purchases is $9,636.
What is Tax revenue:Tax revenue is the income received by the government from the taxation of individuals, businesses, and other entities.
Taxes are mandatory payments imposed on income, goods and services, property, and other items, which are collected by the government to finance public goods and services such as infrastructure, education, healthcare, and defense.
To solve the given problem, assume the cost of a cigarette packet and find the total revenue that can be generated.
Here we have
There was a 10 percent tax on every pack of cigarettes John bought between the age of 22 and age 70
To calculate the tax revenue raised from John's cigarette purchases between ages 22 and age 70, we need to know how many packs of cigarettes he bought during that period.
Let's assume that John bought an average of one pack of cigarettes per day or 365 packs per year.
The difference Between the ages of 22 and age 70 = 70 - 22 = 48 years
Hence, John would have bought cigarettes for 48 years, so the total number of packs he bought would be:
365 packs/year x 48 years = 17,520 packs
If there were a 10% tax on each pack, the tax revenue would be:
0.10 x $5.50 (average cost of a pack of cigarettes in the US)
= $0.55 tax per pack
$0.55 tax per pack x 17,520 packs = $9,636 in tax revenue
This is an estimate, as it does not take into account any variations in the price of cigarettes over time or across different regions.
Reducing smoking rates:As for how much tax money could be used to reduce smoking rates, there are several options.
One possibility is to invest the revenue in smoking cessation programs and public health campaigns to educate people about the risks of smoking and help them quit.
The money could also be used to fund research into developing new treatments for tobacco addiction or to support medical research into the health effects of smoking.
Therefore
Using one cigarette packet per day with the cost of $ 5.50 tax revenue would be raised from John's cigarette purchases is $9,636.
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FY varies directly as X & Y equals eight when X equals eight what is the value of X when Y equals four?
The calculated value of X when Y equals four is four
Calculating the value of X when Y equals four?From the question, we have the following parameters that can be used in our computation:
Y varies directly as X &Y equals eight when X equals eightUsing the above as a guide, we have the following:
y = kx
Where
k = constant of variation
When Y equals eight when X equals eight, we have
8k = 8
So, we have
k = 1
This means that the equation is
y = 1 * x
Evaluate
y = x
When the value of y is 4, we have
4 = x
This gives
x = 4
Hence, the value of X when Y equals four is four
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If FY varies directly as X, we can write the equation as:
FY = kX
where k is the constant of variation. To find the value of k, we can use the fact that "Y equals eight when X equals eight":
8 = k(8)
Simplifying this equation, we get:
k = 1
Now we can use this value of k to find the value of X when Y equals four:
4 = 1X
Solving for X, we find that
X = 4
Therefore, when Y equals four, X equals 4 as well...