The required measure of the interior angle of the given irregular convex hexagon is equal to 135 degrees.
The sum of the exterior angles of any polygon, including a hexagon, is always 360 degrees.
Each exterior angle of a convex polygon is supplementary to its corresponding interior angle.
Sum of each exterior angle and its corresponding interior angle is always 180 degrees.
Let x be the measure of the sixth exterior angle of the hexagon, then the sum of all six exterior angles is,
⇒ 360 = 5a + x
where a is the measure of each of the other five exterior angles.
Rearrange this equation to solve for x,
⇒ x = 360 - 5a
Since each exterior angle is supplementary to its corresponding interior angle,
x + a = 180
Substituting x = 360 - 5a into this equation, we get,
⇒ 360 - 5a + a = 180
Simplifying this equation, we get,
⇒4a = 180
⇒ a = 45
Each of the other five exterior angles has a measure of 45 degrees.
The sum of each interior angle and its corresponding exterior angle is 180 degrees,
so the measure of each interior angle of the hexagon is,
180 - 45 = 135 degrees.
Therefore, the measure of the interior angle of the irregular convex hexagon is 135 degrees.
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A large container holds 4 gallons of chocolate milk that has to be poured into bottles. Each bottle holds 2 pints.
If the ratio of gallons to pints is 1: 8,
bottles are required to hold the 4 gallons of milk.
Answer:
64 Bottles
Step-by-step explanation:
that is the procedure above
What is the difference of 620 and 89.7?
Answer: 530.3
Step-by-step explanation:
Difference means to subtract
620-89.7=530.3
Answer:
530.3
Step-by-step explanation:
You want to subtract 620-89.7. If you want to use the standard algorithm you have 620.0-89.7. You "borrow" from the 2 in the tens place, then "borrow" from the ones place. To subtract 10-3 tenths. Then you subtract the ones place which is 9-9=0 ones. Now you subtract 62-8=53 tens. So you have 530.3 as the difference.
1) Name 2 decimals whose sum is less than 1.
The decimals whose sum is less than 1 are 0.4 and 0.5.
How to illustrate the expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
As an illustration, the expression x + y has the terms x and y with an addition operator between them. In this case, the decimals whose sum is less than 1 are 0.4 and 0.5 as the sum is 0.9.
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Which is greater, 2 5/6 hours or 2.8 hours?
Answer:
2.8 hours
Step-by-step explanation:2.8 hours is greater because 2.8 hours is 3 hours and 20 minutes.
2 5/6 is not a full 3 hours, its just 2 hours and 50 minutes
Find f(g(3)) for the functions f(x) =3x+8 and g(x) =-x^3
We are given:
f(x) = 3x + 8
g(x) = -x³
__________________________________________________________
The Concept:
We have to find the values of f(g(3)), which means that we have to apply the function g() on 3 and apply the function f() on the value we get.
Finding f(g(3)):
Finding g(3):
g(x) = -x³
g(3) = -(3)³
g(3) = -27
Finding f(g(3)):
f(x) = 3x + 8
f(g(3)) = 3(g(3)) + 8
f(g(3)) = 3(-27) + 8
f(g(3)) = -81 + 8
f(g(3)) = -73
Hence, f(g(3)) = -73
A school band has `70` students.
`50\%` of them are sixth graders, `30\%` are seventh graders, and the rest are eighth graders.
How many band members are 6th graders and how many are 7th grader
Answer:
Step-by-step explanation: Half of 70 is 35 so there are 35 Sixth-grader and then you do 70 multiplied by 30% and get 21
Which equation descibes the pattern shown in the table?
What is the whole story about? An uncomfortable bed and Tell tale heart
answer →a murder most heinous and a narrator who fights his insanity
explanation: I read the book in cass
HELP!!!!!!!!!!!!!!!!!!!!!!!!
The recursive formula for f(n) is f(n) = 4.25 + f(n - 1), f(0) = 2.25.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let f(n) represent the total cost of shoe rentals for n games, hence:
The recursive formula for f(n) is f(n) = 4.25 + f(n - 1), f(0) = 2.25.
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Find the zeros and give the multiplicity of
F(x)= x^2(x^2+18x+81)
Answer:
Step-by-step explanation:
To find the zeros of F(x), we need to solve the equation F(x) = 0.
F(x) = x^2(x^2+18x+81)
The expression F(x) can be factored as:
F(x) = x^2(x+9)^2
So, the zeros of F(x) are x = 0 and x = -9, with a multiplicity of 2 for both.
The factor x^2 contributes to a zero of multiplicity 2, which means that the graph of F(x) touches the x-axis at x = 0 but does not cross it. The factor (x+9)^2 also contributes to a zero of multiplicity 2, which means that the graph of F(x) touches the x-axis at x = -9 but does not cross it.
To summarize, the zeros and their multiplicities for F(x) are:
x = 0 (multiplicity 2)
x = -9 (multiplicity 2)
A manufacturing process has a 70% yield, meaning that 70% of the products are acceptable and 30% are defective. If three of the products are randomly selected, one after the other, find the probability that all of them are acceptable. Consider these as independent.
Answer:
\(Probability = 34.3\%\)
Step-by-step explanation:
Given
Represent acceptable with A and defective with D
\(A = 70\%\)
\(B = 30\%\)
Required
Determine the probability that three selected are acceptable
This can be represented as:
\(Probability = AAA\)
Substitute values for A
\(Probability = 70\% * 70\% * 70\%\)
\(Probability = 34.3\%\)
The outside diameter of an electrical conduit is 6.3 centimeters. The thickness of the conduit is 0.4 centimeter. Find the inside diameter of the conduit. Carry the answer to one decimal place.
Answer:
5.5 cm
Step-by-step explanation:
You want the inside diameter of a conduit with an outside diameter of 6.3 cm and a wall thickness of 0.4 cm.
WallsThere is a wall at each end of the inner diameter, so it will differ from the outside diameter by twice the wall thickness:
6.3 cm - 2×0.4 cm = 5.5 cm
The inside diameter is 5.5 cm.
A pair of equations is shown below:
y=7x- 8
y= 5x-2
Part A: Explain how you will solve the pair of equations by substitution or elimination. Show all the steps and write the solution. (5 points)
Part B: If the two equations are graphed, at what point will the lines representing the two equations intersect? Explain your answer. (5 points
Answer:
x=3, y=13. (3, 13).
Step-by-step explanation:
7x-8=5x-2
7x-5x-8=-2
2x-8=-2
2x=-2+8
2x=6
x=6/2=3
y=5(3)-2=15-2=13
Answer:
given y=7x-8 i
y=5x-2 ii
Step-by-step explanation:
equating equation i and ii which is i=ii
7x-8=5x-2
7x-5x= -2+8
2x=6
x=6÷2
x=3
now
putting the value of xbin equation i
y=7x-8
y=7×3-8
y=21-8
y=13
hence the value of x and y is 3 and 13 respectively
Find the value of L that Will Maximize the profit Q=L²e^0.01L
The minimum profit occurs at L = 0, where Q = 0.
To find the value of L that maximizes the profit Q = L²\(e^{(0.01L)\).
We need to differentiate Q with respect to L and find the critical points where the derivative equals zero.
Then we can determine whether each critical point is a maximum or a minimum by examining the second derivative.
Testing for critical points:Q = L²\(e^{(0.01L)\)
Q' = \(2Le^{(0.01L)\) + \(0.01 L^2e^{(0.01L)\)
= 0(2L + 0.01L²) \(e^{(0.01L)\)
= 0L (critical point) or 200 \(e^{(0.01L)\)
= 0 (extraneous, ignore)
2L + 0.01L² = 0L(2 + 0.01L) = 0L = 0 or L = -200 (extraneous, ignore)
The only critical point is at L = 0.
Testing for maximum or minimum:Q'' = \(2e^{(0.01L)\) + 0.02Le^(0.01L) + 0.0001L²\(e^{(0.01L)Q''(0)\)
= \(2e^{(0)\) = 2Since Q''(0) > 0,
The critical point at L = 0 is a minimum.
Therefore, there is no value of L that maximizes the profit.
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The values of L that will maximize the profit are 0 and -200
Finding the value of L that will maximize the profitFrom the question, we have the following parameters that can be used in our computation:
\(Q = L\²e^{0.01L\)
Differentiate the function
So, we have
\(Q' = \frac{L \cdot (L + 200) \cdot e^{0.01L}}{100}\)
Set the equation to 0
\(\frac{L \cdot (L + 200) \cdot e^{0.01L}}{100} = 0\)
Cross multiply
\(L \cdot (L + 200) \cdot e^{0.01L} =0\)
When expanded, we have
L = 0, L + 200 = 0 and \(e^{0.01L} =0\)
When solved for L, we have
L = 0 and L = -200
Hence, the values of L are 0 and -200
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A survey of 800 randomly selected adults in a certain country found that 82% believed that
protecting the rights of those with unpopular views is a very important component of a strong
democracy.
a. Verify the Central Limit Theorem conditions.
b. Find a 95% confidence interval for the proportion of adults in the country who believe that
protecting the rights of those with unpopular views is a very important component of a strong
democracy.
c. Would a 90% confidence interval based on this sample be wider or narrower than the 95%
interval? Give a reason for your answer.
a) the Central Limit Theorem conditions are met. b) The 95% confidence interval for the proportion of adults who believe in protecting the rights of those with unpopular views is approximately 0.7934 to 0.8466.
c) . A 90% confidence interval would be wider than the 95% interval
How to Verify the Central Limit Theorem conditions.To verify the Central Limit Theorem (CLT) conditions, we need to check the following:
1. Random Sampling: The survey states that 800 adults were randomly selected, which satisfies this condition.
2. Independence: We assume that the responses of one adult do not influence the responses of others. This condition is met if the sample is collected using a proper random sampling method.
3. Sample Size: To apply the CLT, the sample size should be sufficiently large. While there is no exact threshold, a common rule of thumb is that the sample size should be at least 30. In this case, the sample size is 800, which is more than sufficient.
Therefore, the Central Limit Theorem conditions are met.
b. To find a 95% confidence interval for the proportion of adults who believe in protecting the rights of those with unpopular views, we can use the formula for calculating a confidence interval for a proportion:
CI = p ± z * √(p(1-p)/n)
where:
- p is the sample proportion (82% or 0.82 in decimal form).
- z is the z-score corresponding to the desired confidence level. For a 95% confidence level, the z-score is approximately 1.96.
- n is the sample size (800).
Calculating the confidence interval:
CI = 0.82 ± 1.96 * √(0.82(1-0.82)/800)
CI = 0.82 ± 1.96 * √(0.82*0.18/800)
CI = 0.82 ± 1.96 * √(0.1476/800)
CI = 0.82 ± 1.96 * √0.0001845
CI ≈ 0.82 ± 1.96 * 0.01358
CI ≈ 0.82 ± 0.0266
The 95% confidence interval for the proportion of adults who believe in protecting the rights of those with unpopular views is approximately 0.7934 to 0.8466.
c. A 90% confidence interval would be wider than the 95% interval. The reason is that as we increase the confidence level, we need to account for a larger margin of error to be more certain about the interval capturing the true population proportion. As a result, the interval needs to be wider to provide a higher level of confidence.
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A parachute is describing at rate of 28 feet per minute find the total change of altitude of the parachuter after 4 mins
A parachute is describing at rate of 28 feet per minute find the total change of altitude of the parachuter after 4 mins.
112 feet
Evaluate -x+23y if x=9 and y=2
Answer:
The answer is 37
whats 2 2/9 times 2 1/5
Answer:
1/45
Step-by-step explanation:
Answer:
8/45
Step-by-step explanation:
2 * 2/9 * 2 * 1/5
2 * 2.9 * 2/5
2 * 2*2/9*5
=8/45
Please help me understand this handwriting can some pls re write and label I DONT UNDERSTAND CURSIVE :(
Answer:
7:01
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Conditions " humanitarian groups Salahiel 1-1-1, 1-1-2, 1-2-3 1-R-5, 2-L-2, 2-L-3, 2-14, 2-1-5, 2-RI
Flores 1-30
Munting 1-2-4
Gumbon 1-1-3 CDP 1-1-3
Status oppose ending 742 Montoya 1-1, 1-2, 1-3
federal courts challenge
Gamboa 1-R-2 Custom 1-7
CDP 1-L-36, 1-2-4
de Vogue 1-2-1, 2-1-5, 2-L-6
7 expulsions at boders
root causes textul Amer.
Cop 1-L-34, 1-1-2, 1-R-4
Border Report 1-2
CDP 1-R-2, 1-R-3 Montoya 1-8
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Hopes this helps :)
(8)
Tricia used 2 bags of sugar to bake some cupcakes.
She used of another bag of sugar to make some macaroons.
How many bags of sugar did she use altogether?
bags of sugar
Answer:
She used 3.
Step-by-step explanation:
You have 2 bags.
You have another bag.
You use all of them.
How many did you use altogether?
3.
Tricia used 2.5 bags of sugar altogether.
What is an expression?In mathematics, an expression is a combination of numbers, variables, operators, and/or functions that represents a mathematical quantity or relationship. It can be as simple as a single number or variable, or it can be more complex, involving multiple terms and operations.
Tricia used 2 bags of sugar to make cupcakes and used 1/2 of another bag of sugar to make macaroons.
Therefore, the total amount of sugar she used is:
2 + 1/2 = 2.5 bags of sugar.
So, The number of bags Tricia used was 2.5 bags of sugar altogether.
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Help meee I don’t understand
The graph of the function f(x) = (x-4)(x + 1) is shown
below.
Which statement about the function is true?
O The function is increasing for all real values of x
where
x < 0.
O The function is increasing for all real values of x
where
x < -1 and where x > 4.
O The function is decreasing for all real values of x
where
-1
O The function is decreasing for all real values of x
where
x < 1.5.
The statement that is true regarding the function f(x) = (x-4)(x + 1) is that the function is increasing for all real values of x where x < -1 and where x > 4. So, the option is: O The function is increasing for all real values of x where x < -1 and where x > 4.
Explanation: Given function is:f(x) = (x - 4) (x + 1). The graph of the given function is shown below: As it is visible from the graph, the function is decreasing for all real values of x where x lies between -1 and 4 (inclusive).
The turning point of the function is x = -0.5, which is the x-coordinate of the vertex of the parabola. Also, we see that the vertex is the minimum point of the parabola and the y-coordinate of the vertex is -4.25. This means that f(x) ≥ -4.25 for all x. The function is increasing for all real values of x where x < -1 and where x > 4.
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Polygon A is similar to Polygon B.
Find the perimeter of Polygon B.
24
A
PA = 128
15
B
PB = [?]
Answer:
\(P_{B}\) = 80
Step-by-step explanation:
given 2 similar figures with ratio of sides = a : b
then ratio of perimeters is also a : b
here ratio of sides = 24 : 15 = 8 : 5
the ratio of perimeters is also 8 : 5
then by proportion
\(\frac{ratioA}{P_{A} }\) = \(\frac{ratioB}{P_{B} }\) , that is
\(\frac{8}{128}\) = \(\frac{5}{P_{B} }\) ( cross- multiply )
8 \(P_{B}\) = 5 × 128 = 640 ( divide both sides by 8 )
\(P_{B}\) = 80
Refer to the given terms . A pattern defines the relationship between the first two terms . Determine the relationship and identify the missing term of the second pair , such that both the pairs are analogous . AZP : ZAR :: TXK :
The missing term in the second pair is YUL.
To determine the relationship between the first two terms, let's analyze the given pattern: AZP : ZAR.
If we look closely, we can observe that each letter in the first term is shifted one position forward in the alphabet to form the corresponding letter in the second term.
So, applying the same pattern to the second pair (TXK), we need to shift each letter one position forward in the alphabet:
T + 1 = U
X + 1 = Y
K + 1 = L
Therefore, the missing term in the second pair is YUL.
The analogy between the pairs is that each letter in the first term is shifted one position forward in the alphabet to form the corresponding letter in the second term.
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What is the range of the function shown on the graph
Answer:
-2<=y<=-7
Step-by-step explanation:
(h+3)2 find the square. Simplify your answer.
(h+3)² simplified is:(h+3)² = h² + 6h + 9
What is binomial?
Binomial refers to a type of probability distribution that describes the number of successes in a fixed number of independent trials.
The expression (h+3)² is a binomial squared. When we square a binomial, we use the formula:
(a+b)² = a² + 2ab + b²
where a and b are any numbers or variables. In this case, our binomial is (h+3), so we can use the formula with a=h and b=3:
(h+3)² = h² + 2h3 + 3²
The first term, h², comes from squaring the h in the binomial. The second term, 2h3, comes from multiplying the two terms in the binomial together and then doubling the result. Finally, the third term, 3^2, comes from squaring the 3 in the binomial.
Simplifying the expression, we can combine like terms. We have h² as the first term, 23h as the second term, and 3^2 as the third term. 23h is equal to 6h, so we can rewrite it as:
(h+3)² = h² + 6h + 9
And that is the simplified form of the expression (h+3)².
Therefore, (h+3)² simplified is:(h+3)² = h² + 6h + 9
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in a bag if marbles 1/2 are blue 1/6 are green 1/12 are yellow you pick a marble with out looking what color marble are you most likely going to choose
Answer: Blue
Step-by-step explanation:
Half of the entire freaking bag is blue,it states it in the question.If there is so many,unless by pure blind luck you will get that.
I hope it helps!
PLS HELO THANK YOUUUUU
Answer:
divide 500 by 125.
You get 4x = 568
Answer is 142
Happy Learning
Answer:
142
Step-by-step explanation:
For accounting purposes, the value of assets (land, buildings, equipment) in a business are depreciated at a set rate per year. The value, V(t) of $537,000 worth of assets after t years, that depreciate at 17% per year, is given by the formula V(t) = Vo(b)t. What is the value of Vo and b, and when rounded to the nearest cent, what are the assets valued at after 9 years?
a
Vo = $537,000, b = 0.17, and the value after 9 years is $0.45
b
Vo = $537,000, b = 0.83, and the value after 9 years is $100,386.92
c
Vo = $537,000, b = 1.17, and the value after 9 years is $98,291.76
d
Vo = $537,000, b = 0.83, and the value after 9 years is $91,290.00
Answer:
I think it is D
Step-by-step explanation:
The sum of three consecutive even integers is
312. Find the Integers.
Answer:
104, 105, 106
Step-by-step explanation:
Consider three consecutive integers. If the first is x then the second is 1 more than x (or x+1) and the third is x+2
The sum of these three integers is x + x+1 + x+2 and is known to be 312, so
x + x+1 + x+2 = 312, gather like terms
3x + 3 = 312, subtract 3 from both sides
3x = 309, divide both sides by 3
x = 104, so the integers are
104, 105, 106