The answer for it is diagram B because it does not cross or have parallel lines
In a spring, the tension (Tnewtons) is directly proportional to its extension ( x cm). When the tension is 150 newtons, the extension is 6 cm. (a) Find a formula for T' in terms of x. T = AD
The formula for tension (T) in terms of extension (x) is T = 25x.
The given statement is T = kx, where T is the tension, x is the extension, and k is the proportionality constant.
To solve this problem, we need to find the value of k. We can do that by substituting the given values of T and x into the equation:
T = kx
150 = k×6
k = 25
Therefore, the formula for tension (T) in terms of extension (x) is T = 25x.
To learn more about the proportional relationship visit:
brainly.com/question/12917806.
#SPJ1
50 Points! Multiple choice algebra question. Photo attached. Thank you!
the object will fall a distance of 1024 feet in 8 seconds. So the answer is (C) 1024 ft.
what is distance ?
Distance is a scalar quantity that refers to the total length traveled by an object or person, without considering the direction. It is a measure of the path length between two points, usually measured in units such as meters (m), feet (ft), or kilometers (km).
In the given question,
The formula t = √(d/16) relates the time t (in seconds) it takes an object to fall a distance d (in feet) to the acceleration due to gravity, which is approximately 32.2 feet per second squared.
To find how far the object will fall in 8 seconds, we can rearrange the formula to solve for d:
t = √(d/16)
t² = d/16 (Squaring both sides)
d = 16t² (Multiplying both sides by 16)
Substituting t = 8 into the formula, we get:
d = 16(8)² = 1024
Therefore, the object will fall a distance of 1024 feet in 8 seconds.
So the answer is (C) 1024 ft.
To know more about distance, visit:
https://brainly.com/question/15172156
#SPJ1
Use the word factor product quotient in sum to describe the parts of five minus M divided by N -2-8 times M plus N
The parts of the expression in terms of factor, product, quotient, and sum are:
Factor- (5 - M)/(N - 2)
Product- 8 * M
Quotient- (5 - M)/(N - 2)
Sum- (5 - M)/(N - 2) + N - 8 * M - 2
Explain expression
An expression is a mathematical phrase that contains numbers, variables, and/or mathematical operations. It can be simplified or evaluated using mathematical rules and principles.
What is meant by quotient?
The quotient is the result obtained when one quantity is divided by another, usually represented as a whole number, fraction, or decimal. It is a fundamental concept in mathematics.
According to the given information
The given expression is:
(5 - M)/(N - 2) - 8 * M + N
We can break it down into the following parts using the words factor, product, quotient, and sum:
Factor: (5 - M)/(N - 2)
Product: 8 * M
Quotient: (5 - M)/(N - 2)
Sum: (5 - M)/(N - 2) + N - 8 * M - 2
To know more about expression visit
brainly.com/question/17775178
#SPJ1
Firefighters have a 52-foot extension ladder. In order to reach 48 feet up a building, how far away from the building should the foot of
the ladder be placed?
OA. 36 feet
OB. 20 feet
OC.28 feet
OD.32 feet
Manny's grocery store has a rectangular logo for their business that measures 1.9 meters long with an area that is exactly the maximum area allowed by the building owner.
Create an equation that could be used to determine L, the unknown side length of the logo.
Drag each number to the correct location on the table.
Complete a two-way frequency table using the given probability values.
The complete table as determined from the given probabilities is given below:
X Y Total
A 40 28 68
B 38 54 92
Total 78 82 160
What is the probability P(A|B)?P(A|X) means the conditional probability of A given X has occurred. In this case, 40/92 means out of 92 times X occurred, A occurred 40 times.
P(B) means the marginal probability of B, which is the total probability of B occurring regardless of whether A occurred or not. In this case, 78/160 means out of 160 trials, B occurred 78 times.
The row and column totals are calculated by adding up the corresponding values.
The grand total is the sum of all the values in the table.
Learn more about probability at:
brainly.com/question/13604758
#SPJ1
Full Question:
Although part of your question is missing, you might be referring to this full question:
See the attached image.
Evaluate the indefinite integral given below.
The indefinite integral when evaluated has a solution of 2cot(2x⁵ - 5x) + C
Evaluating the indefinite integralFrom the question, we have the following parameters that can be used in our computation:
The integral of (10 - 20x⁴)csc²(2x⁵ - 5x)
³
This can be expressed as
∫(10 - 20x⁴)csc²(2x⁵ - 5x) dx
The above is a complex expression
So, we make use of a graphing tool to evaluate the solution
Using a graphing tool, we have
Step 1:
[tex]\frac{4\cos(10x)\sin(4x^5) - 4\sin(10x)\cos(4x^5)}{sin^2(4x^5) - 2\sin(10x)\sin(4x^5) + cos^2(4x5) - 2\cos(10x)\cos(4x5)+ \sin^2(10x) + \cos^2(10x)} + C[/tex]
When simplified, we get
2cot(2x⁵ - 5x) + C
hence, the solution is 2cot(2x⁵ - 5x) + C
Read more about derivatives at
https://brainly.com/question/5313449
#SPJ1
Determine how many integer solutions there are to
x₁ + x₂ + x3 + x₁ = 20, if
0≤x₁ < 3, 0≤ x₂ < 4, 0≤x3 <5, 0≤x4 < 6
Based on the information given, there are a total of 118 solutions.
How many possible solutions are there?This is a problem of solving a Diophantine equation subject to some conditions. Let's introduce a new variable y4 = 20 - (x1 + x2 + x3 + x4). Then the problem can be restated as finding the number of solutions to:
x1 + x2 + x3 + y4 = 20
Subject to the following conditions:
0 ≤ x1 < 3
0 ≤ x2 < 4
0 ≤ x3 < 5
0 ≤ y4 < 6
We can solve this problem using the technique of generating functions. The generating function for each variable is:
(1 + x + x^2) for x1
(1 + x + x^2 + x^3) for x2
(1 + x + x^2 + x^3 + x^4) for x3
(1 + x + x^2 + x^3 + x^4 + x^5) for y4
The generating function for the equation is the product of the generating functions for each variable:
(1 + x + x^2)^3 (1 + x + x^2 + x^3 + x^4 + x^5)
We need to find the coefficient of x^20 in this generating function. We can use a computer algebra system or a spreadsheet program to expand the product and extract the coefficient. The result is: 1118
Learn more about solutions in https://brainly.com/question/30665317
#SPJ1
Answer: This problem involves finding the number of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints. We can use the stars and bars method to solve this problem.
Suppose we have 20 stars representing the sum x₁ + x₂ + x3 + x₁. To separate these stars into four groups corresponding to x₁, x₂, x₃, and x₄, we need to place three bars. For example, if we have 20 stars and 3 bars arranged as follows:
**|**||
then the corresponding values of x₁, x₂, x₃, and x₄ are 2, 4, 6, and 8, respectively. Notice that the position of the bars determines the values of x₁, x₂, x₃, and x₄.
In general, the number of ways to place k identical objects (stars) into n distinct groups (corresponding to x₁, x₂, ..., xₙ-₁) using n-1 separators (bars) is given by the binomial coefficient (k+n-1) choose (n-1), which is denoted by C(k+n-1, n-1).
Thus, the number of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints is:
C(20+4-1, 4-1) = C(23, 3) = 1771
However, this count includes solutions that violate the upper bounds on x₁, x₂, x₃, and x₄. To eliminate these solutions, we need to use the principle of inclusion-exclusion.
Let Aᵢ be the set of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints, where xᵢ ≥ mᵢ for some integer mᵢ. Then, we want to find the cardinality of the set:
A = A₀ ∩ A₁ ∩ A₂ ∩ A₃
where A₀ is the set of all non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20, and Aᵢ is the set of solutions that violate the upper bound on xᵢ.
To find the cardinality of A₀, we use the formula above and obtain:
C(20+4-1, 4-1) = 1771
To find the cardinality of Aᵢ, we subtract the number of solutions that violate the upper bound on xᵢ from the total count. For example, to find the cardinality of A₁, we subtract the number of solutions where x₂ ≥ 4 from the total count. To count the number of solutions where x₂ ≥ 4, we fix x₂ = 4 and then count the number of solutions to the equation x₁ + 4 + x₃ + x₄ = 20 subject to the constraints 0 ≤ x₁ < 3, 0 ≤ x₃ < 5, and 0 ≤ x₄ < 6. This count is given by:
C(20-4+3-1, 3-1) = C(18, 2) = 153
Similarly, we can find the cardinalities of A₂ and A₃ by fixing x₃ = 5 and x₄ = 6, respectively. Using the principle of inclusion-exclusion, we obtain:
|A| = |A₀| - |A
Step-by-step explanation:
What is the slope intercept of -2 and y-intercept (0,2)?
Answer:
The slope-intercept form of the equation of a line is:
y = mx + b
where m is the slope and b is the y-intercept.
We are given that the y-intercept is (0,2), which means that the value of b is 2.
We are also given that the slope is -2, which means that the value of m is -2.
Substituting these values into the slope-intercept form, we get:
y = -2x + 2
Therefore, the slope-intercept form of the equation of the line is y = -2x + 2.
Step-by-step explanation:
Answer:
that is correct just to give you feedback on that
Please anwser the question i will reward brainlest.
Answer:
2((3(4) + 4(7) + 3(7)) = 2(12 + 28 + 21) = 2(61) = 122 square meters
Describe what happens as the number of sides of the bases of a prism increases.
THIS IS NOT COLLEGE LEVEL IT IS MIDDLE SCHOOL
Answer:
As the number of sides of the bases of a prism increases, the shape of the prism becomes more complex and closer in form to a cylinder. For example, a prism with two identical polygonal bases, such as a rectangular prism or a triangular prism, will have a more blocky or pyramidal shape. However, as the number of sides of the base increases, the shape of the prism becomes more cylindrical and less pyramidal in appearance. This is because the more sides a polygon has, the more closely it approximates a circle, and the cross-section of the prism becomes more circular in shape.
When the number of sides of the base of a prism increases, the prism becomes more like a cylinder.
Draw and label a rectangular prism that has a surface area of 96 square meters
There are 2 sides.
First side is 12 by 2 so you would multiply them together which is 24 and since there is another side the same length multiply by 2 which is 48.
Second side small side is 2 by 4 so multiply them together which is 8 and since there is another side the same demension multiply 8 by 2 which is 16.
The last side is 12 by 4 so again multiply them together which is 48. Multiply it by two since there is another side with same dimension which is 96.
Now do 48 + 16 + 96 (the answer gotten after finding the areas for each sides and their identicals) which is 160 ft²
The label for rectangular prism that has a surface area of 96 square meters is in the attached image.
Mohawk Skywalkers are iron workers who helped build skyscrapers, bridges, and other structures for over 120 years. Which of the following is a statistical question about the Mohawk Skywalkers?
A. How many construction sites has each of the current Mohawk Skywalkers worked on in their lifetime?
B. How many New York City skyscrapers were built with the help of Mohawk Skywalkers?
C. How many generations of the Martin family have worked as Mohawk Skywalkers?
D. How many Mohawk Skywalkers helped build the Empire State Building?
How many construction sites has each of the current Mohawk Skywalkers worked on in their lifetime? is a statistical question about the Mohawk Skywalkers. Option A.
What are statistical questions?A statistical question is a question that can be answered by collecting and analyzing data. It involves variability and asks about the distribution of a population, rather than just a single value or specific instance.
Option A is a statistical question because it asks about the variability of the number of construction sites each of the current Mohawk Skywalkers worked on in their lifetime.
Option B is also a statistical question as it asks about the distribution of New York City skyscrapers built with the help of Mohawk Skywalkers.
Option C is not a statistical question because it asks for a specific value, the number of generations of the Martin family who have worked as Mohawk Skywalkers, which does not involve variability or a population.
Option D is not a statistical question as it asks for a specific value, the number of Mohawk Skywalkers who helped build the Empire State Building, which does not involve variability or a population.
More on statistical questions can be found here: https://brainly.com/question/29257078
#SPJ1
Keilantra's math teacher plots student grades on their weekly quizzes against the
number of hours they say they study on the pair of coordinate axes and then draws
the line of best fit. What does the slope of the line represent?
The slope of the line of best fit provides valuable information about the relationship between the two variables being plotted and can be used to make predictions about future data points or to identify patterns and trends in the data.
What is the slope?
The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).
The slope of the line of best fit on a scatter plot represents the rate of change between the two variables being plotted.
In the case of Keilantra's math teacher, the slope of the line of best fit between student grades on weekly quizzes and the number of hours they say they study represents the change in grades for every additional hour of studying.
For example, if the slope is positive (i.e., the line slopes upward from left to right), it indicates that as the number of hours studied increases, the average grade on the quiz tends to increase as well.
On the other hand, if the slope is negative (i.e., the line slopes downward from left to right), it indicates that as the number of hours studied increases, the average grade on the quiz tends to decrease.
Therefore, the slope of the line of best fit provides valuable information about the relationship between the two variables being plotted and can be used to make predictions about future data points or to identify patterns and trends in the data.
To learn more about the slope visit:
https://brainly.com/question/3493733
#SPJ1
Substitute the supplied value and simplify both sides of the equation, if necessary. Then decide if the supplied value is or is not a solution.
m + 2(m + 1) = 14 {4}
The left-hand side simplifies to 14, and the right-hand side is also 14. Therefore, the equation is true when m = 4.
What is LHS and RHS?"LHS = RHS" stands for "left-hand side equals right-hand side". It is a notation commonly used in mathematics to show that two expressions are equal to each other.
Define Substitution?In mathematics, to substitute means to replace a variable or expression in an equation or function with a specific value or expression.
To substitute the value 4 for m in the given equation, we replace every occurrence of m:
m + 2(m + 1) = 14
4 + 2(4 + 1) = 14
4 + 2(5) = 14
4 + 10 = 14
14 = 14
14 is the result of simplifying the left and right sides, respectively. Consequently, when m = 4, the equation is accurate.
So, the value 4 is a solution to the given equation.
To know more about Substitution visit:
https://brainly.com/question/29051233
#SPJ1
Substitute the supplied value and simplify both sides of the equation, if necessary. Then decide if the supplied value is or is not a solution.
m + 2(m + 1) = 14 {4}
The equation simplifies to 14 = 14, which is a true statement.
What is the purpose of the equation?In mathematics, an equation is defined as a set of numbers that contains operations and may contain a variable. Equations are used to solve for these unknown variables using various operations such as addition, subtraction, multiplication and division.
Replacing m by 4, we get:
m + 2 (m + 1) = 14
4 + 2 (4 + 1) = 14
4 + 2(5) = 14
4 + 10 = 14
14 = 14
The equation simplifies to 14 = 14, which is a true statement. Therefore, the given value 4 is a solution to Eq.
Learn more about Equations here
https://brainly.com/question/29657992
#SPJ1
the data on the graph show the foot lengths and forearm lengths for a group of people. the line of best fit for the data is shown. use equation on the line of best fit to re-edit the length of a persons forearm if the length of their is 8 inches
The length of a person’s forearm if the length of their foot is 8 inches.
Define linear equation!A linear equation is an equation that describes a straight line on a graph. It is an algebraic equation that involves two variables, usually x and y, and can be written in the form of y = mx + b, where m is the slope of the line and b is the y-intercept.
The slope of a line is the measure of the steepness of the line, or how much it rises or falls for a given change in x. It can be calculated as the change in y divided by the change in x between any two points on the line.
The y-intercept is the point where the line crosses the y-axis, or the value of y when x is zero.
Let
x ----> Length of Foot in inches
y ----> Length of Forearm in inches
we have
y=1.11x-0.83
For x=8 in
To find y, change the value of x in the linear equation.
y=1.11(8)-0.83=8.05in
To know more about slope visit:
brainly.com/question/3605446
#SPJ1
The complete question is :
The data on the graph show the foot lengths and forearm lengths for a group of people. The line of best fit for the data is shown. Use the equation of the line of best fit to predict the length of a person’s forearm if the length of their foot is 8 inches.
A graph is labeled as Foot Length versus Forearm Length. The horizontal axis is labeled as Length of Foot left parenthesis inches right parenthesis and the vertical axis is labeled as Length of Forearm left parenthesis inches right parenthesis. The values on the horizontal axis range from 0 to 15 in increments of 1 and the values on the vertical axis range from 0 to 15 in increments of 1. Several points are scattered throughout the graph and a line is shown which passes between these points and the equation of the line is labeled as y equals 1 decimal point 1 1 x minus 0 decimal point 8 3.
A.8.88 inches
B.6.94 inches
C.9.16 inches
D.8.05 inches
Dorothy Wagner is currently selling 40 "I ♥ Calculus" T-shirts per day, but sales are dropping at a rate of 4 per day. She is currently charging $7 per T-shirt, but to compensate for dwindling sales, she is increasing the unit price by $1 per day. How fast, and in what direction, is her daily revenue currently changing?
The rate at which her daily revenue is currently changing and the direction of the change is; Her revenue is currently increasing at $12 per day
What is the rate of change of a function?The rate of change of a function is the rate at which the output of the function changes per unit change in the input of the function.
Let x represent the number of days, therefore;
The number of T-shirts Dorothy sells, y = 40 - 4·x
The price at which she sells the T-shirts = 7 + x
Therefore, Dorothy's daily revenue, R(x) = (40 - 4·x) × (7 + x) = 12·x - 4·x² + 280
The rate of change of her daily revenue can be obtained from the derivative of the revenue function as follows;
The rate at which her daily revenue is therefore;
R'(x) = d(R(x))/dx = 12 - 8·x
The rate at which her revenue is changing currently can be obtained from the rate function by plugging in x = 0, as follows;
R'(0) = 12 - 8×0 = 12
Her revenue is changing at a rate of $+12 per day.
The positive value of the rate, 12, indicates that her revenue is increasing at $12 per day
Learn more on the rate of change of a function here: https://brainly.com/question/20066447
#SPJ1
Hannon Company makes swimsuits and sells these suits directly to retailers. Although
Hannon has a variety of suits, it does not make the All-Body suit used by highly skilled
swimmers. The market research department believes that a strong market exists for thistype of suit. The department indicates that the All-Body suit would sell for approximately $100. Given its experience, Hannon believes the All-Body suit would have the following manufacturing costs
Direct materials $ 25
Direct labor 30
Manufacturing overhead 45
Total costs $100
Instructions
(a) Assume that Hannon uses cost-plus pricing, setting the selling price 20% above its
costs. (1) What would be the price charged for the All-Body swimsuit? (2) Under what
circumstances might Hannon consider manufacturing the All-Body swimsuit given this approach?
(b) Assume that Hannon uses target costing. What is the price that Hannon would charge the retailer for the All-Body swimsuit?
(c) What is the highest acceptable manufacturing cost Hannon would be willing to incur to produce the All-Body swimsuit, if it desired a profit of $20 per unit? (Assume target costing.)
Hannon's maximum allowable production cost for the All-Body swimsuit is $80 if it wants to make a profit of $20 per unit.
Given data ,
a)
Using cost-plus pricing, the selling price is set 20% above the costs.
Selling price=Costs+(Costs x Markup)
Selling price=$100 + ($100x0.20)
Selling price=$100+$20
On simplifying the equation , we get
Selling price=$120
The price charged for the All-Body swimsuit would be$120.
Hannon might consider manufacturing the All-Body swimsuit under the cost-plus pricing approach if the market demand is strong enough to justify the selling price of $120 and if Hannon can efficiently produce and sell the swimsuit to generate profits.
(b)
Using target costing, the price charged by Hannon to the retailer is determined by subtracting the desired profit per unit from the target selling price.
Target selling price=$100 (given)
Desired profit per unit=$20 (given)
Price charged to retailer=Target selling price - Desired profit per unit
Price charged to retailer=$100-$20
On simplifying the equation , we get
Price charged to retailer=$80
The price that Hannon would charge the retailer for the All-Body swimsuit under target costing is$80.
(c)
To determine the highest acceptable manufacturing cost for the All-Body swimsuit under target costing, we subtract the desired profit per unit from the target selling price.
Target selling price=$100 (given)
Desired profit per unit=$20 (given)
Highest acceptable manufacturing cost=Target selling price-Desired profit per unit
Highest acceptable manufacturing cost=$100-$20
Highest acceptable manufacturing cost=$80
Hannon would be ready to spend up to $80 in manufacturing costs to develop the All-Body swimsuit if it wanted to make $20 each unit.
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ1
7
Assignment Active
Describing Exponential Functions
Which statements describe the function f(x) = 3()*? Check all that apply.
Each successive output is the previous output divided by 3.
As the domain values increase, the range values decrease.
The graph of the function is linear, decreasing from left to right.
Each successive output is the previous output multiplied by 3.
The range of the function is all real numbers greater than 0.
The domain of the function is all real numbers greater than 0.
The correct statements regarding the exponential function 3(1/3)^x is given as follows:
Each successive output is the previous output divided by 3.As the domain values increase, the range values decrease.The range of the function is all real numbers greater than 0.How to define an exponential function?An exponential function has the definition presented as follows:
y = ab^x.
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.The function for this problem is given as follows:
f(x) = 3(1/3)^x.
The parameter b is of 1/3 < 1, hence:
Each successive output is the previous output divided by 3.The function is decreasing.The range is all real values greater than 0, as a = 3 is positive and the function has an horizontal asymptote at y = 0.
More can be learned about exponential functions at brainly.com/question/2456547
#SPJ1
PLEASE HELP! An ethanol railroad tariff is a fee charged for shipments of ethanol on public railroads. An agricultural association publishes tariff rates for railroad-car shipments of ethanol. Assuming that the standard deviation of such tariff rates is $1200, determine the probability that the mean tariff rate of 400 randomly selected railroad-car shipments of ethanol will be within $80 of the mean tariff rate of all railroad-car shipments of ethanol. Interpret your answer in terms of sampling error. The probability is what?
(Round to three decimal places as needed.) Thanks!
If an ethanol railroad tariff is a fee charged for shipments of ethanol on public railroads. The probability is: 84.6%.
How to find the probability?In this case, we have:
Population standard deviation (σ): $1200
Sample size (n): 400
Margin of error (E): $80
The standard deviation of the sample mean can be calculated as:
σM = σ / √n = 1200 / √400 = 60
To find the probability that the sample mean is within $80 of the population mean, we need to find the z-scores for the upper and lower limits of the interval:
Lower limit: z = (mean - E - population mean) / σM = (-80) / 60 = -1.3333
Upper limit: z = (mean + E - population mean) / σM = 80 / 60 = 1.3333
Using a standard normal distribution table or calculator, we can find the area under the curve between these two z-scores:
P(-1.3333 < Z < 1.3333) = 0.8461
Therefore, the probability that the mean tariff rate of 400 randomly selected railroad-car shipments of ethanol will be within $80 of the mean tariff rate of all railroad-car shipments of ethanol is approximately 0.846 or 84.6%.
Interpretation: This means that if we take many samples of 400 railroad-car shipments of ethanol and calculate their mean tariff rates, about 84.6% of these means will be within $80 of the true mean tariff rate of all ethanol shipments. This also means that there is a sampling error of $80, which is the maximum amount by which the sample mean may differ from the population mean due to random sampling variability.
Learn more about probability here:https://brainly.com/question/13604758
#SPJ1
Let A and B be two events such that
P(A) = 1/5 While P(A or B) = 1/2
Let P(B) = P. For what values of P
are A and B independent?
elem algebra
I tried doing a question on my own, I didn't get it right :(
ANY HELP WILL BE GREAT, THANKSS
Answer:
the missing y coordinate is 2/5
Step-by-step explanation:
You are basically solving for y since you are missing the y coordinate
Since x=5 plug that in and you will get 5+5y=7
subtract 5 on both sides and you will get 5y=2
divide 5 on both sides and you will get 2/5
The circumference of the smaller circle is 25% of the circumference of the larger circle. Find the circumference of the larger circle. Round your answer to the nearest tenth
The circumference of the larger circle is approximately 9.4 units.
What is circumference?The circumference is the distance around the edge or boundary of a closed two-dimensional shape, such as a circle or an ellipse.
According to question:Let C be the circumference of the larger circle. Then the circumference of the smaller circle is 0.25C, according to the given information.
We know that the circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle. Therefore, we can write:
C = 2πr for the larger circle
0.25C = 2πr for the smaller circle
Dividing the second equation by 0.25, we get:
C = 8πr for the smaller circle
Now we can equate the two expressions for C and solve for r:
2πr = 8πr
6πr = C
r = C/(6π)
Finally, we can substitute this value of r into the expression for C in terms of r for the larger circle:
C = 2πr = 2π(C/(6π)) = (1/3)Cπ
Solving for C, we get:
C = (3/π)C
C = 3π ≈ 9.4 (rounded to the nearest tenth)
Therefore, the circumference of the larger circle is approximately 9.4 units.
To know more about circumference visit:
https://brainly.com/question/28757341
#SPJ1
A company sells snow globes made out of glass that are in the shape of hollow
spheres. Khloe measures the outer diameter of a snow globe to be 30 cm. If the glass
has a thickness of 0.35 cm, find the total volume of glass that makes up the globe.
Round your answer to the nearest hundredth if necessary. (Note: diagram is not
drawn to scale.)
The total volume of glass that makes up the snow globe is approximately 1,757.84 cubic centimeters.
What is the inner sphere?
The Inner Sphere is a region of interstellar space surrounding Earth to a radius of roughly 450 - 550 light-years, generally demarcated by the outer borders of the "Great Houses."
The outer sphere has a diameter of 30 cm, so its radius is 15 cm. The volume of the outer sphere is given by the formula:
V outer = (4/3)πr_outer³
V outer = (4/3)π(15 cm)³
V outer ≈ 14,137.17 cm³
The inner sphere has a diameter of 30 cm minus the thickness of the glass on both sides, so its diameter is:
30 cm - 2(0.35 cm) = 29.3 cm
Therefore, the radius of the inner sphere is:
r inner = 29.3 cm / 2 = 14.65 cm
The volume of the inner sphere is given by the formula:
V inner = (4/3)πr_inner³
V inner = (4/3)π(14.65 cm)³
V inner ≈ 12,379.33 cm³
Finally, the volume of glass that makes up the snow globe is the difference between the volumes of the outer and inner spheres:
V glass = V outer - V inner
V glass ≈ 1,757.84 cm³
Therefore, the total volume of glass that makes up the snow globe is approximately 1,757.84 cubic centimeters.
To know more about inner sphere visit:
brainly.com/question/31041676
#SPJ1
____ are characteristics of samples, whereas ______ are characteristic of populations.
AConcepts; statistics
BParameters; statistics
CStatistics; parameters
DParameters; estimations
What does the transformation f(x)
shrinks it horizontally
shrinks it vertically
ertically
stretches it horizontally
stretches it vertically
4
f(2x) do to the graph of f(x)?
The x-coordinates of all the points on the graph of f(2x) are half the x-coordinates of the corresponding points on the graph of f(x), which results in a horizontal compression or shrinking of the graph.
What is a graph?
In computer science and mathematics, a graph is a collection of vertices (also known as nodes or points) connected by edges (also known as links or lines).
The transformation f(2x) stretches the graph of f(x) horizontally by a factor of 1/2. In other words, the graph of f(2x) will be compressed horizontally compared to the graph of f(x).
To see why this is the case, consider the effect of replacing x with 2x in the expression for f(x). If we think of f(x) as a set of points in the xy-plane, then each point (x,y) on the graph of f(x) is transformed into the point (2x,y) on the graph of f(2x).
Therefore, this means that the x-coordinates of all the points on the graph of f(2x) are half the x-coordinates of the corresponding points on the graph of f(x), which results in a horizontal compression or shrinking of the graph.
To know more about graph check the below link:
https://brainly.com/question/19040584
#SPJ1
Find cos (A) I need help with this question
Answer:
[tex]\frac{8}{10}[/tex]
Step-by-step explanation:
[tex]cos(A) = \frac{adjacent}{hypotenuse} \\= \frac{AB}{AC}\\= \frac{8}{10}[/tex]
Answer:
Answer:
\frac{8}{10}
10
8
Step-by-step explanation:
\begin{gathered}cos(A) = \frac{adjacent}{hypotenuse} \\= \frac{AB}{AC}\\= \frac{8}{10}\end{gathered}
cos(A)=
hypotenuse
adjacent
=
AC
AB
=
10
8
Find the surface area of the following figure. Round your final answer to the nearest
tenth.
The surface area is approximately 41.7 square units.
The rectangle has dimensions 18 units by 6 units, so its area is:
A(rectangle) = l x h = 18 x 6 = 108 square units
The semicircle has a radius of 5 units, so its area is half that of a full circle:
A(semicircle)
= 1/2 x π x r²
= 1/2 x π x 5²
= 1/2 x 25π
= 12.5π
To find the total surface area, we need to add the areas of the rectangle and the semicircle. However, since the semicircle is attached to the top of the rectangle, we need to subtract the area of the portion of the circle that overlaps with the rectangle. This overlapping area is equal to the width of the rectangle (18 units) times half the circumference of the circle (1/2 x π x r), or:
A(overlap)
= w x 1/2 x π x r
= 18 x 1/2 x π x 5
= 45π
Therefore, the total surface area is:
Surface area = A(rectangle) + A(semicircle) - A(overlap) = 108 + 12.5π - 45π ≈ 41.7 square units
Rounding to the nearest tenth, the surface area is approximately 41.7 square units.
To know more about the surface area visit:
brainly.com/question/30945207
#SPJ1
Is (2, 3) a solution to this system of equations?
y = -2x + 7
y = x + 1
yes
no
Answer:
Yes.
Step-by-step explanation:
(2, 3) means we'll let x be 2 and y be 3. Let's solve both equations first:
y = -2x + 7
3 = -2(2) + 7
3 = -4 + 7
:. 3 = 3
Okay, so one half is proven. Let's do the other half now.
y = x + 1
3 = 2 + 1
3 = 3
:. (2,3) is a solution to the system of equations.