Answer:
average speed = (55 + 70 + 525) / 6
= 650 / 6
= 108.33 km per hour
Step-by-step explanation:
first hour = 55 per hour.
= 55
second and third = 35 per hour.
= 70
fourth, fifth and sixth = 175 per hour.
= 525
average speed = (55 + 70 + 525) / 6
= 650 / 6
= 108.33 km per hour
what is the correct leaf unit if the 1st observation in a dataset was 0.014, assume values rounded to 3rd decimal?
Answer:
4
Step-by-step explanation:
You want to know the leaf unit corresponding to data value 0.014 when values are rounded to thousandths.
Leaf unitThe leaf unit for data values in a stem-and-leaf plot is the least-significant digit of the data value, when all data values are expressed to the same precision.
The least significant digit of 0.014 is 4. The leaf unit is 4.
<95141404393>
Let A be the subset of R³ given by A = {(x, y, z) =∈ R³ | x² + y² ≤ 4,0 ≤ z ≤ 4 − x² - y²} . Define the function f : A → R by f(x, y, z)= x+3y² + z. (a) Show that A is closed.
(b) Show that A is bounded
(c) Show that there is a point (x0, y0, z0) in A such that
f(x,y,z) ≤ f (x0, y0, z0)
for all (x,y,z) in A
(a) Show that A is closed:A set is said to be closed if it contains all of its limit points. It is equivalent to saying that a set is closed if it contains all of its accumulation points. A set that is not closed is called open.The set A = {(x, y, z) ∈ R³ | x² + y² ≤ 4,0 ≤ z ≤ 4 − x² - y²} can be expressed as the intersection of the paraboloid z = 4 − x² - y² and the cylinder x² + y² = 4. Now we can prove A is closed, which is equivalent to demonstrating that it includes all of its limit points.Let us assume that (x₀, y₀, z₀) is a limit point of A. If we can show that (x₀, y₀, z₀) is a point of A, we will have shown that A contains all of its limit points.Among other things, the following are implied by the condition (x, y, z) ∈ A:-4 ≤ x ≤ 4,-4 ≤ y ≤ 4,0 ≤ z ≤ 4 − x² - y².(x, y, z) is a limit point of A if and only if it satisfies all of the following conditions:-4 ≤ x ≤ 4,-4 ≤ y ≤ 4,0 ≤ z ≤ 4 − x² - y².And for each ε > 0, there is a point (x, y, z) ≠ (x₀, y₀, z₀) such that the Euclidean distance between (x, y, z) and (x₀, y₀, z₀) is less than ε (i.e., the point (x, y, z) is in the ε-neighborhood of (x₀, y₀, z₀). The distance between (x, y, z) and (x₀, y₀, z₀) is defined as follows:d = sqrt((x - x₀)² + (y - y₀)² + (z - z₀)²).Because ε > 0, d > 0. Then there exists a point (x, y, z) in A for which d < ε. There are two cases to consider in order to finish the proof:Case 1: If 0 < z₀ ≤ 4, then there exists a positive ε such that the 3D ball Bε((x₀, y₀, z₀)) of radius ε around (x₀, y₀, z₀) lies inside A. It is because there is a positive number δ for which Bδ((x₀, y₀, z₀)) lies in the intersection of z = 4 − x² - y² and cylinder x² + y² ≤ 4, and we can choose ε as the smaller of δ and z₀.Case 2: If z₀ = 0, then we must choose ε < 1. The reason for this is because there is an infinite sequence of points in A that converge to (x₀, y₀, z₀). The sequence is defined as follows:(x₁, y₁, z₁) = ((1/2)ε, (1/2)ε, 0),(x₂, y₂, z₂) = ((2/3)ε, (2/3)ε, ε/3),(x₃, y₃, z₃) = ((3/4)ε, (3/4)ε, ε/2),...,(xₙ, yₙ, zₙ) = ((n/(n + 1))ε, (n/(n + 1))ε, ε/(n + 1)),...Then, the point (x₀, y₀, z₀) is an accumulation point of the sequence. As a result, we have shown that A contains all of its limit points, implying that A is closed.(b) Show that A is bounded:A set is said to be bounded if it is contained in some ball of finite radius. In other words, a set A is bounded if there exists a positive real number r such that A is contained in the ball of radius r centered at the origin. A set that is not bounded is said to be unbounded.A is contained within the cylinder x² + y² ≤ 4, as well as above the plane z = 0 and below the plane z = 4 - x² - y², among other things. The upper surface of A is clearly bounded, since it lies within a circle of radius 2 and is parallel to the xy-plane. As a result, we must show that the bottom surface is bounded as well.Let (x, y, 0) be a point on the xy-plane. We will demonstrate that the point lies within a disk of radius 2, centered at the origin and lying on the xy-plane.The formula x² + y² ≤ 4, which describes the cylinder x² + y² ≤ 4, guarantees that (x, y) lies inside a circle of radius 2 centered at the origin. Furthermore, the formula 0 ≤ z ≤ 4 - x² - y² implies that z ≤ 4. As a result, (x, y, 0) is contained in a disk of radius 2 centered at the origin and lying on the xy-plane, with height bounded above by 4. As a result, the set A is bounded.(c) Show that there is a point (x₀, y₀, z₀) in A such that f(x,y,z) ≤ f(x₀,y₀,z₀) for all (x,y,z) in A:The function f(x, y, z) = x + 3y² + z is a continuous function defined on a closed, bounded set A. As a result, by the Extreme Value Theorem, there must be a point (x₀, y₀, z₀) in A at which f(x, y, z) is minimal.Therefore, for all (x, y, z) in A, we have:f(x, y, z) ≤ f(x₀, y₀, z₀).
Determine the annual percentage yield, or the effective interest rate, for $1200 invested at 6.63% over 8 years compounded daily. Round your answer to the nearest hundredth of a percent, if necessary. Answer
The annual percentage yield, or the effective interest rate, for $1200 invested at 6.63% over 8 years compounded daily is approximately 64.04%.
To determine the annual percentage yield, or the effective interest rate, for $1200 invested at 6.63% over 8 years compounded daily, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial investment)
r = the annual interest rate (6.63%)
n = the number of times interest is compounded per year (365 for daily compounding)
t = the number of years (8)
Plugging in the values, we have:
A = 1200(1 + 0.0663/365)^(365*8)
Calculating this, we get A ≈ $1,968.49.
To find the annual percentage yield, we need to find the interest earned:
Interest = A - P = $1,968.49 - $1200 = $768.49
Now, we can find the annual percentage yield using the formula:
Annual percentage yield = (Interest / P) * 100
Plugging in the values, we have:
Annual percentage yield ≈ ($768.49 / $1200) * 100 ≈ 64.04%
Therefore, the annual percentage yield, or the effective interest rate, for $1200 invested at 6.63% over 8 years compounded daily is approximately 64.04%.
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1/3 (x + 3)
I need a answer fast please
Answer:
\(\frac{1}{3}\) x + 1
Step-by-step explanation:
\(\frac{1}{3}\) (x + 3) ← multiply each term in the parenthesis by \(\frac{1}{3}\)
= \(\frac{1}{3}\) x + 1
a. What is the nth fraction in the following sequence? 2
1
, 4
1
, 8
1
, 16
1
, 32
1
,… b. What is the sum of the first n of those fractions? To what number is the sum getting closer and closer? Two forces, A=80 N and B=44 N, act in opposite directions on a box, as shown in the diagram. What is the mass of the box (in kg ) if its acceleration is 4 m/s 2
?
A)an = 2*2^(n-1)`. B) `The sum of the first n fractions is `2*(2^n - 1)`.
a. The sequence is a geometric sequence with the first term `a1 = 2` and common ratio `r = 2`.Therefore, the nth term `an` is given by:`an = a1*r^(n-1)`
Substituting `a1 = 2` and `r = 2`, we have:`an = 2*2^(n-1)`
b. To find the sum of the first n terms, we use the formula for the sum of a geometric series:`S_n = a1*(1 - r^n)/(1 - r)
`Substituting `a1 = 2` and `r = 2`, we have:`S_n = 2*(1 - 2^n)/(1 - 2)
`Simplifying:`S_n = 2*(2^n - 1)
`The sum of the first n fractions is `2*(2^n - 1)`.As `n` gets larger and larger, the sum approaches `infinity`.
Thus, the sum is getting closer and closer to infinity.
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X + 2x - 7/4=1 - x/2 -x ayudaaaaa
Answer:
|x| - |-x| = 0
Step-by-step explanation:
Answer:
no se
Step-by-step explanation:
no se
i predict i have 20 cents in my piggy bank. if i actually have 25 cents. what the percent error?
Answer:
Your percent error is 20% with the prediction of 20 cents in your piggy bank when the actual amount is 25 cents.
Step-by-step explanation:
The formula for percent error is (|predicted value - actual value|)/(actual value) * 100.
% Error = |(20 - 25)|/(25) * 100
= (|-5|)/25 * 100
= 5/25 * 100
= 20%
Answer:
The percent error is 20%
Step-by-step explanation:
The formula for percent error is:
PE = |Predicted Value - Real Value| / Real Value
PE = |20 - 25| / 25 × 100
PE = |-5| / 25 × 100
PE = 5/25 × 100
PE = 20%
given that Set B has n=50 data values and mean x
ˉ
=4. There are 50 data values in Set B, so we can let x 1
,x 2
,…,x 50
be the data values in the original Set B. Since the mean is equal to 10 we have the following. x
ˉ
4
(4)
= n
∑x
= x 1
+x 2
+…+x 50
=x 1
+x 2
+…+x 50
=x 1
+x 2
+…+x 50
The sum of all the data values in Set B is equal to 200. Given that Set B has 50 data values and a mean of 4, we can represent the data values as x₁, x₂, ..., x₅₀. The mean of the set i s equal to 4. This implies that the sum of all the data values is equal to 50 times the mean, which is 4.
The mean of a set of data is calculated by summing up all the data values and dividing by the total number of values. In this case, we have 50 data values and a mean of 4. So, we can express the mean as (x (bar)) = (x₁ + x₂ + ... + x₅₀) / 50. Multiplying both sides of the equation by 50, we get 50 (x (bar)) = x₁ + x₂ + ... + x₅₀. Since (x (bar)) is equal to 4, we can substitute it into the equation to obtain 50(4) = x₁ + x₂ + ... + x₅₀, which simplifies to 200 = x₁ + x₂ + ... + x₅₀. Therefore, the sum of all the data values in Set B is equal to 200.
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A set of data with 1200 numbers is normally distributed with a mean of 27 and a standard deviation of 4. How many numbers in the data would you expect to be between 23 and 31?
What numbers would be between 19 and 35 as well?
Help!
Step-by-step explanation:
The mean is 27 and the standard deviation is 4.
23 is 1 standard deviation below the mean, and 31 is 1 standard deviation above the mean. According to the empirical rule, 68% of the population is between -1 and +1 standard deviations.
68% of 1200 is 816.
19 is 2 standard deviations below the mean, and 35 is 2 standard deviations above the mean. According to the empirical rule, 95% of the population is between -2 and +2 standard deviations.
95% of 1200 is 1140.
What role do hypotheses play in scientific inquiry, and why are null hypothesis used sometimes?
A hypothesis is a testable guess about how a commodity works. It may be an idea, proposition, a possible medium of commerce, or a statement about an effect. A null hypothesis is a vaticination that there's no difference between groups or conditions or a statement or idea that can be falsified or proved wrong.
What's meant by a hypothesis in statistics?
In Statistics, a thesis is defined as a formal statement, which explains the relationship between the two or further variables of the specified population. It helps the experimenter to restate the given problem into a clear explanation for the outgrowth of the study.
Characteristics of hypothesis
The important characteristics of the hypothesis are
• The hypothesis should be short and precise
• It should be specific
• A hypothesis must be related to the being body of knowledge
• It should be able to verification
What's the Null hypothesis?
The null hypothesis is a kind of hypothesis that explains the population parameter whose purpose is to test the validity of the given experimental data. This thesis is either rejected or not rejected grounded on the viability of the given population or sample. In other words, the null hypothesis is a hypothesis in which the sample compliances effect by chance. It's said to be a statement in which the surveyors want to examine the data. It's denoted by H₀.
Hence a hypothesis is a testable guess about how a commodity works. It may be an idea, proposition, a possible medium of commerce, or a statement about an effect. A null hypothesis is a vaticination that there's no difference between groups or conditions or a statement or idea that can be falsified or proved wrong
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Solve the equation 3x3−28x2+69x−20=0 given that 4 is a zero of f(x)=3x³−28x²+69x−20 A) {4,−1,−5/3} B) {4,5,1/3} C) {4,1,5/3} D) {4,−5,−1/3}
The correct answer is A) {4, -1, -5/3}. The solutions to the equation 3x^3 - 28x^2 + 69x - 20 = 0 are x = 4, x = 1/3, and x = 5.
To find the solutions to the equation 3x^3 - 28x^2 + 69x - 20 = 0, we are given that 4 is a zero of the function f(x) = 3x^3 - 28x^2 + 69x - 20.
Given that 4 is a zero of f(x), we can use synthetic division to find the other zeros.
Using synthetic division with 4 as the zero, we have:
```
4 | 3 -28 69 -20
| 12 -64 20
------------------
3 -16 5 0
```
The result of the synthetic division gives us the reduced quadratic equation 3x^2 - 16x + 5 = 0.
To find the other zeros, we can solve this quadratic equation by factoring or using the quadratic formula:
3x^2 - 16x + 5 = 0
Factoring: (3x - 1)(x - 5) = 0
Setting each factor equal to zero, we have:
3x - 1 = 0 => x = 1/3
x - 5 = 0 => x = 5
Therefore, the solutions to the equation 3x^3 - 28x^2 + 69x - 20 = 0 are x = 4, x = 1/3, and x = 5.
The correct answer is A) {4, -1, -5/3}.
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What is (-3)^-9 times (-3)^5
Answer:
1/80 or 0.01234568
Step-by-step explanation:
Exponentiation: (-3) ^ (-9) = -5.08052634253E-5 = -1/
19683
Exponentiation: (-3) ^ 5 = -243
= -1/
19683
* (-243) = -1 · (-243)/
19683 · 1
= 243/
19683
= 1 · 243/
81 · 243
= 1/
81
What is 50 percent of 62? 0.31 3.1 31 310
Answer:
\(\Huge \boxed{\mathrm{31}}\)
Step-by-step explanation:
50 percent of 62 is also one half of 62.
62 × \(\frac{1}{2}\) = 31
Answer:
50 is 31% of 62.
Step-by-step explanation:
To solve this, we need to set up our problem like this, since percentages are written with %, and add up to 100%.
\(\frac{62}{x} =\frac{100}{50}\)
Next, we flip the denominators with the numerators so that the x ends up on the top.
\(\frac{x}{62}=\frac{50}{100}\)
Finally, we can see that 50/100 is 1/2, so to solve x/62, we have to divide 62 by 2 to get our answer.
62 ÷ 2 = 31
Our answer is 31%.
Suppose we have a neighborhood of n houses. For any two houses we pick, there is a road between them. (a) The landlord wants to cut maintenance costs by removing some of the roads. Let k be the minimum number of roads he can remove such that the neighborhood is still connected (every house can be walked to from every other house) and there are no cycles. Determine the value of k as an expression in terms of n. Then indicate how to remove the minimum number of roads from the neighborhood such that the requirements are satisfied. (b) Suppose now instead that the landlord wants to remove houses. Let ℓ be the minimum number of houses that must be removed such that the neighborhood is still connected and has no cycles. Removing a house also removes the roads it is connected to. Determine the value of ℓ as an expression in terms of n. Then indicate how to remove the minimum number of houses from the neighborhood such that the requirements are satisfied
a) ℓ is equal to the number of leaf nodes in the graph. If we have n nodes in the graph, then the maximum number of leaf nodes that we can have is n-1 (when the graph is a tree).
b) k = (n-1) - (number of connected components).
To remove the minimum number of roads from the neighborhood such that the requirements are satisfied, we need to remove bridges.
Explanation:
Part a) To begin with, it is stated that we have a neighborhood of n houses. For any two houses we pick, there is a road between them. The landlord wants to cut maintenance costs by removing some of the roads. Let k be the minimum number of roads he can remove such that the neighborhood is still connected (every house can be walked to from every other house) and there are no cycles.
To find the minimum number of roads that he can remove, such that the neighborhood is still connected and there are no cycles, let us start by finding the total number of roads required for a connected neighborhood with n houses, where every house can be walked to from every other house.
We can use the formula for the minimum number of edges required for a connected graph, which is given by (n-1).
Thus, for n houses, we need n-1 roads.
But we have n houses and for any two houses we pick, there is a road between them.
Therefore, the total number of roads in the neighborhood is greater than or equal to n-1.
Suppose the landlord removes k roads. This means that there will be multiple disconnected components and to keep the neighborhood connected, we need to add edges between these components.
Thus, k is equal to the number of edges that need to be added to get a connected graph.
Therefore,
k = (n-1) - (number of connected components).
To remove the minimum number of roads from the neighborhood such that the requirements are satisfied, we need to remove bridges. Bridges are roads which if removed, increase the number of connected components. Removing a bridge will never create a cycle. Thus, we can start by identifying bridges and then removing them.
Part b)
Suppose now instead that the landlord wants to remove houses. Let ℓ be the minimum number of houses that must be removed such that the neighborhood is still connected and has no cycles.
Removing a house also removes the roads it is connected to. Determine the value of ℓ as an expression in terms of n. Then indicate how to remove the minimum number of houses from the neighborhood such that the requirements are satisfied.
To remove the minimum number of houses from the neighborhood such that the requirements are satisfied, we can start by finding the number of nodes that we can remove while keeping the graph connected.
Let G be a connected graph with n nodes. If we remove a node v from G along with its incident edges, then the graph will be disconnected into components.
However, if v is a leaf node (a node with degree 1), then we can remove the node and its incident edge without disconnecting the graph. If G has no leaf nodes, then it must have a cycle. Removing any node from a cycle will break the cycle and create at least one leaf node.
Thus, to remove the minimum number of nodes, we need to identify the leaf nodes and remove them until no more leaf nodes are left. The minimum number of nodes that can be removed without disconnecting the graph is equal to the number of leaf nodes in the graph.
Therefore, ℓ is equal to the number of leaf nodes in the graph. If we have n nodes in the graph, then the maximum number of leaf nodes that we can have is n-1 (when the graph is a tree).
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4x+5-x=10+3x+4
solution
Answer:
9
Step-by-step explanation:
4x-x=3x
3x±5=10±3x±4
10±4=14
14±3x
3x±5=14±3x
3x-3x=14-5
3x-3x=0
14-5=9
If the radius is 5 what is the length of arc LM?
Answer:
100/360 * 2\(\pi\)5
1000\(\pi\)/360 = 25\(\pi\)/9 = 8.722
Step-by-step explanation:
Amy and Stephanie were playing a number game. Amy picked a number and told Stephanie that if she added 7 to her number and multiplied the sum by 2 it would equal 4 which equation could Stephanie use to find the number 4
Answer:
2(n+7)=4
Step-by-step explanation:
n is the number
Anna is getting a new puppy. The dog bed is $19.49, but it is 15% off. The dog
bed also has a 7.5% sales tax. What is the final price of the dog bed?
A. $17.81
B. $19.12
C. $22.05
D. $20.43
By using percentage, it can be calculated that-
Final price of dog bed = $17.81
What is percentage?Suppose there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.
Percentage, which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.
As an illustration, 1% of 1,000 chickens is equal to 1/100 of 1,000, or 10 birds, and 20% of the quantity is equal to 20% of 1,000, or 200. These relationships can be generalized as x = PT/100 where x is the quantity equal to a specific percentage P of T and T is the total reference quantity selected to represent 100%. As a result, T is 1,000, P is 1, and x is determined to be 10 in the case for 1 percent of 1,000 chickens.
For example, 3% means \(\frac{3}{100}\). Here, 3 is expressed as a fraction of 100
Price of a dog bed = $19.49
Rate of discount = 15%
Price after discount = $(\(19.49 - \frac{15}{100}\times 19.49\)) = $16.5665
Rate of sales tax = 7.5%
Final price of dog bed = $(\(16.5665 - \frac{7.5}{100}\times 16.5665\)) = $17.81
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HELP ME FOR POINTS AND BRAINETEST
Answer:
71.8 = 7 x 10 + 1 x 1 + 8 x 0.1
7.018 = 7 x 1 + 1 x 0.01 + 8 x 0.001
0.718 = 7 x 0.1 + 1 x 0.01 + 8 x 0.001
Step-by-step explanation:
___________________________________________________________
Number 1 \(>See Below<\)
\(The\;second\;one,\; 7 *10+1*1+8*0.1\)
___________________________________________________________
Number 2 \(>See\;Below<\)
\(The\;third\;one, 7*1+1*0.01+8*0.001\)
___________________________________________________________
Number 3 \(>See\;Below<\)
\(The\;fourth\;one,\;7*0.1 + 1 * 0.01 + 8 * 0.001\)
___________________________________________________________
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\(\left[\begin{array}{ccc}Thanks,\;JustSomeIdiot.\end{array}\right]\)
The ale price of every item in a tore i 85% of it regular price
1. The regular price of a backpack i $30 what’ it’ ale price?
2. The ale price of a occer ball i $15. 30 what’ it regular price?
3. The ale price of a jacket i $21. 08 what’ it regular price?
The sale price of the backpack is $25.5, the sale price of the soccer ball is $13.005, and the sale price of one jacket is 17.918.
Given:
The sale price of every item in a store is 85 percent of its regular price.
1. The regular price of a backpack is $30.
Then, the sale price = 85% of (the regular price of a backpack )
= 0.85 x ($30)
= $25.5
Hence, the sales price of the backpack = $25.5
2. The regular price of a soccer ball is = $15.30
The sale price of the soccer ball is 85% of its regular price.
Therefore, the sale price = 85% of $15.30
= $13.005
So, the sale price of the soccer ball is $13.005.
3. The regular price of a jacket is $21. 08
The sale price of a jacket is 85% of its regular price.
Therefore, the sale price = 85% of $21. 08
= $17.918
So, the sale price of a jacket is $17.918.
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If Log 4 (x) = 12, then log 2 (x / 4) is equal to A. 11 B. 48 C. -12 D. 22
Answer:
\(\huge \boxed{\mathrm{D. \ 22}}\)
Step-by-step explanation:
\(\mathrm{log_4 (x)=12}\)
Make the base 4 from both sides.
\(\mathrm{4^{log_4 (x)}=4^{12}}\)
Simplify the equation.
\(\mathrm{x=16777216}\)
\(\mathrm{log_2 (\frac{x}{4} )}\)
Let x = 16777216
\(\mathrm{log_2 (\frac{16777216}{4} )}\)
\(\mathrm{log_2 (4194304)}\)
Evaluate.
\(22\)
Answer:
\(log_2(\frac{x}{4} )=22\)
which is your answer "D"
Step-by-step explanation:
If \(log_4(x)=12\) this means that : \(x=4^{12}\) based in the definition of logarithm.
And this exponential expression can also be written using that \(4=2^2\):
\(x=4^{12}=(2^2)^{12}=2^{24}\)
so now we know what x is with base 2 (which is needed for the second expression:
\(log_2(\frac{x}{4} )=?\)
And this also can be written in exponent form (using the unknown "?" we need to find) as:
\(2^?=\frac{x}{4} \\x=4\,*\,2^?\\x=2^2\,*\,2^?\\x=2^{2+?}\)
Since we know the value of x in base 2 (from our first analysis), then:
\(x=2^{2+?}=2^{24}\\then\\2+?=24\\?=22\)
Therefore,
\(log_2(\frac{x}{4} )=22\)
Karamo is currently 5 feet and 3 inches tall. His father is 5 foot 11 inches, his mother is 5 foot 7 inches, and his older brother is 5 foot 9 inches. If Karamo’s adult height will be the average of his 3 family members’ heights, how many more inches will he grow?
Answer:
Karamo is currently 5 feet and 3 inches tall, which is 63 inches. His father is 5 foot 11 inches, which is 71 inches. His mother is 5 foot 7 inches, which is 67 inches. His older brother is 5 foot 9 inches, which is 69 inches. The average of these heights is 67 inches. Therefore, Karamo will grow 4 more inches to reach his adult height.
Step-by-step explanation:
please help me guys
Step-by-step explanation:
midpoint : it is the point in the middle marking half of the total distance.
therefore,
1)
EV = LE = LV/2
10 = 5m
m = 2
2)
LR = RO = LO/2
n + 4 = 12
n = 8
3)
LER and LVO are similar triangles. that means they have the same angles, and the ratio of one corresponding pair of lines or sides between both triangles is the same for all corresponding line pairs.
we know e.g. LE/LV = 1/2.
the same ratio applies then to ER/VO = 1/2 = 18/20p.
18/20p = 1/2
18 = 20p/2
2×18 = 20p
36 = 20p
p = 36/20 = 9/5 = 1.88888888888...
4)
VL = 2×EL = 2×10 = 20
5)
LO = 2×RO = 2×12 = 24
6)
as we have already calculated for 3) :
VO = 36
7)
36 + 20 + 24 = 80
8)
10 + 12 + 18 = 40
9)
remember, the and angles in similar triangles.
LVO = 52°
10)
all angles around a single point in one side of a line are together 180°.
in this case there are 2 angles around E : LER and VER.
VER = 180 - LER = 180 - 52 = 128°
Step-by-step explanation:
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A red candle is 8 inches tall and burns at a rate of 7
10 inch per hour.
A blue candle is 6 inches tall and burns at a rate of 1
5 inch per hour.
After how many hours will both candles be the same height?
After four hours, the height of the candles will be the same.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
A red candle has an 8-inch height and burns at a 7/10-inch per hour rate. A 6-inch tall blue candle burns at a rate of 1/5 inch per hour.
Let x be the number of hours and y be the height.
y = -0.70x + 8 ...1
y = -0.20x + 6 ...2
From equations 1 and 2, then we have
- 0.20x + 6 = - 0.70x + 8
(0.70 - 0.20)x = 8 - 6
0.50x = 2
x = 4 hours
After four hours, the height of the candles will be the same.
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common factors of 14y^3+7y
Answer:
7y
Step-by-step explanation:
The greatest common factor of 14y³+7y is 7y, because
14y³+7y=7y(2y²+1)
A recipe uses 3 eggs for every 8 cups of flour. What is the ratio of eggs to flour in the recipe?
8 to 3
StartFraction 3 over 8 EndFraction
3 to 11
8:3
Answer:
3 to 8
Step-by-step explanation: It cannot be further simplified so 3 eggs to 8 cups or 3:8 ratio
A dump truck dumps gravel, forming a conical pile. The volume of the pile increases at a rate of 5 cubic feet per second. The height of the cone is related to the radius by h = 4r. The . volume of the cone is given by V = 1/3πhr2. Find the rate of change of the radius of the cone when the radius is 16 feet. The radius is changing at feet per second. Find the rate of change of the radius of the cone when the radius is 20 feet. The radius is changing at feet per second.
When the radius is 16 feet, the rate of change of the radius of the cone is approximately 0.00124 feet per second.
When the radius is 20 feet, the rate of change of the radius of the cone is approximately 0.00157 feet per second.
To find the rate of change of the radius of the cone, we need to differentiate the volume formula with respect to time.
Let's calculate it step by step.
Given:
Volume of the cone: V = (1/3)πhr^2
Height of the cone: h = 4r
Rate of change of volume:
dV/dt = 5 ft^3/s
First, let's substitute the expression for the height into the volume formula:
V = (1/3)π(4r)(r^2)
V = (4/3)πr^3
Now, we can differentiate the volume formula with respect to time:
dV/dt = (4/3)π(3r^2)(dr/dt)
5 = (4/3)π(3r^2)(dr/dt)
Next, we can simplify the equation:
5 = 4πr^2(dr/dt)
Now, we can solve for dr/dt by rearranging the equation:
dr/dt = 5 / (4πr^2)
To find the rate of change of the radius when the radius is 16 feet, we substitute r = 16 into the equation:
dr/dt = 5 / (4π(16)^2)
dr/dt = 5 / (4π(256))
dr/dt ≈ 0.00124 ft/s
Therefore, when the radius is 16 feet, the rate of change of the radius of the cone is approximately 0.00124 feet per second.
To find the rate of change of the radius when the radius is 20 feet, we substitute r = 20 into the equation:
dr/dt = 5 / (4π(20)^2)
dr/dt = 5 / (4π(400))
dr/dt ≈ 0.00157 ft/s
Therefore, when the radius is 20 feet, the rate of change of the radius of the cone is approximately 0.00157 feet per second.
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Stone runs 1 mile five times a week. How many miles does 4 he run each week? Write the equation you would use to solve. Then, fill in the grid with your answer. Tip: Fill in your answer as a fraction greater than 1.
The number of miles in 4 weeks is 20 mules
How to determine the number of milesFrom the question, we have the following parameters that can be used in our computation:
Stone runs 1 mile five times a week
This means that the rate is
Rate = 1 mile * 5 per week
So, we have
Rate = 5 miles per week
For 4 weeks, we have
Distance = 5 * 4
Evaluate
Distance = 20 miles
Hence, the distance is 20 miles
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A group of friends eats at a restaurant. the bill is 105.97. the group leaves a 18% tip the tax is 6.125%. What is the tip
Answer:
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Step-by-step explanation:
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The winner of the local triathlon swam 0.5 miles, biked 15 miles and ran 2.5 miles. He finished the race in 54 minutes. For the entire triathlon, what was his average speed in miles per hour?
Answer:
15 or 15.546
Step-by-step explanation:
you add all the numbers then divide by 54
Based on the information given, the speed is 20 miles per hour.
From the information given, the winner of the local triathlon swam 0.5 miles, biked 15 miles and ran 2.5 miles and he finished the race in 54 minutes.
Note that 54 minutes = 0.9 hour.
The speed will be:
= (0.5 + 15 + 2.5) / 0.9
= 18/0.9
= 20 miles per hour.
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