Question Prog
A regular pentagon ABCDE is shown.
Work out the size of angle x.
D
A
C
B
The value of the angle x of the given pentagon is: x = 36°
How to find the angle in the polygon?The formula to find the interior angle of a regular polygon is:
θ = 180(n - 2)/n
where n is number of sides of polygon
In this case we have a pentagon which has 5 sides. Thus:
θ = 180(5 - 2)/5
θ = 540/5
θ = 108°
Now, the sides of the pentagon are equal and as such the triangle formed ΔBDC is an Isosceles triangle where:
∠BDC = ∠DBC
Thus:
x = (180 - 108)/2
x = 72/2
x = 36°
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2. Indicate whether the following statement is sometimes true, always true or never true. Justify you response. "If f(x) is defined for all × ≤R, then f'(x) is also defined for all × = R." (2 mark
The statement "If f(x) is defined for all x ≤ R, then derivative f'(x) is also defined for all x = R" is sometimes true.
The first part states that "f(x) is defined for all x ≤ R." This means that the function f(x) is defined and exists for every value of x that is less than or equal to R. In other words, the function is defined in the interval (-∞, R].
The second part of the statement says that "f'(x) is also defined for all x = R." Here, f'(x) represents the derivative of the function f(x). It states that the derivative of f(x) exists and is defined at x = R.
The key point to consider is that the existence and differentiability of a function at a specific point are not dependent on the entire interval in which the function is defined. In other words, just because a function is defined for all x ≤ R does not necessarily mean that its derivative will be defined at x = R.
Therefore, it is possible for the statement to be true in some cases, where the derivative exists at x = R, but it is not always true. The truthfulness of the statement depends on the specific properties and behavior of the function f(x) and its derivative f'(x) in the vicinity of x = R.
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A projector is connected to your computer and projects onto a large wall. The projector enlarges what is on your computer screen by a scale factor of 325%. An image on your computer is inches long. What is the length of the projected image on your wall?
Is this always true, sometimes true, or never true?
Answer:
This statement is sometimes true
2) Rolling a single die 33 times, keeping track of the numbers that are rolled. A) Not binomial: the trials are not independent. B) Not binomial: there are more than two outcomes for each trial. C) Not binomial: there are too many trials. D) Procedure results in a binomial distribution
I am confused how they were able to get the constraints in ch6
problem 10P
In Chapter 6, Problem 10P, the constraints are derived based on the given problem scenario and the objective of the optimization problem. Without specific details about Problem 10P in Chapter 6, it is challenging to provide a precise explanation.
However, I can provide a general understanding of how constraints are typically formulated in optimization problems. In optimization problems, constraints are used to represent the limitations or restrictions on the decision variables. These constraints can arise from various sources, such as physical constraints, resource constraints, budget constraints, or technical constraints. To derive the constraints, you need to carefully analyze the problem statement and identify the conditions or limitations that must be satisfied. These conditions are then translated into mathematical inequalities or equations that relate the decision variables. For example, if the problem involves allocating limited resources among different activities, the constraints would represent the availability of those resources and ensure that the total allocation does not exceed the available amount. Similarly, if the problem involves production planning, constraints might include demand requirements, capacity limitations, or inventory constraints. In general, the process of formulating constraints requires careful consideration of the problem's requirements, objectives, and limitations. It often involves translating real-world constraints into mathematical expressions to create a well-defined optimization problem that can be solved using appropriate techniques.
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Felicia is a long-distance runner. She is able to run the first 2 hours of a training run at a certain rate. The rate at which she runs after her first 2 hours decreases for the remainder of her training run. On Monday, Felicia runs x hours, where x≥2. The average rate at which Felicia runs for the entire training run is represented by 13+6(x−2)x. What is the meaning of the parts of this rational expression in the context of the situation? Select from the drop-down menus to correctly complete each statement.
Answer:
total distance of Felicia's training run
first two hours x = 2....so we have
[ 13 + 6(2 - 2) ] / 2 = 13 / 2 = distance / rate = = 6.5 mph ⇒ "c"
distance covered in 4 hrs =
[13 + 6( 4 - 2) ] = 13 + 6(2) = 13 + 12 = 25 miles
But she ran 13 miles the first two hours
So....she must run 12 miles the last two hours ⇒ "c"
which variety of nonrandom sampling takes proportions into consideration?
a) convenience
b) judgment
c) quota
d) purposive
The variety of nonrandom sampling that takes proportions into consideration is: c) quota
Quota sampling is the variety of nonrandom sampling that takes proportions into consideration. In quota sampling, the researcher selects a specific number of participants from each subgroup of the population based on their proportion in the overall population. This ensures that the sample represents the different subgroups in the population proportionately.
In quota sampling, the researcher selects participants based on specific characteristics or proportions to ensure that the sample represents the target population accurately. The researcher sets quotas for different groups or segments based on known proportions or desired representation in the population.
For example, if a population consists of 60% males and 40% females, a quota sample might be designed to include the same proportions of males and females. The researcher would continue to select participants from each group until the quotas are met.
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NEED HELPP! (05.02 MC) Using logarithmic properties, what is the solution to log11(y + 8) + log114 = log1160? Show all necessary steps.
Using logarithmic properties, the solution to the given logarithmic equation is y = 7
Solving Logarithmic equationsFrom the question, we are to determine the solution to the given equation
The given equation is
\(log_{11}(y+8) + log_{11}(4) = log_{11}(60)\)
Applying the product law of logarithms, we get
\(log_{11}(y+8) \times (4) = log_{11}(60)\)
This gives
\(log_{11}(4y+32) = log_{11}(60)\)
Applying the equality law of logarithm, we get
\(4y + 32 = 60\)
\(4y = 60-32\)
\(4y =28\)
∴ y = 28/4
y = 7
Hence, the solution to the given logarithmic equation is y = 7
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the area of the shaded region is $78$ square inches. all angles are right angles and all measurements are given in inches. what is the perimeter of the non-shaded region?
The perimeter of the non-shaded region in the figure can be calculated to be 14 inches.
Given a figure.
The middle portion of the figure is not shaded.
It is required to find the perimeter of the non-shaded region.
It is given that:
The whole area of the shaded region = 78 inches²
The area of the small square which is situated at the bottom is:
Area of small square = 2 × 4
= 8 inches²
So, the area of the rest of the shaded area = 78 - 8
= 70 inches²
Now, the area of the whole region without the small square is:
Area = 10 × (10 - 2)
= 80 inches²
So, the area of the non-shaded region = 80 - 70
= 10 inches²
The width of the non-shaded rectangle is 2 inches.
So, length = 5 inches.
So, the perimeter is:
P = 2(5 + 2)
= 14 inches
Hence, the perimeter is 14 inches.
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The figure is given below.
URGENT!!!! ANSWER FAST!!!!!!
Answer:
Step-by-step explanation:
its the second one
Match the following expression 12(x-3)+18=4(3x-3) with the number of solutions below.
A.One solution?
B.No solution ?
Or
C.All solution?
Answer:
No Solution.
Step-by-step explanation:
12(x-3)+18=4(3x-3)
12x-36+18=12x-12
12x-12x-18=-12
-18=-12
no solution
What is the median for the following set of data?
5, 7, 8, 10, 12, 12
A.12
B.10
C.9
D.7
Answer:
C.)9
Step-by-step explanation:
You add up all your data to get 54 and divide by the amount of numbers you had in the data which was 6. So if you divide 54 by 6 you get 9.
Please help me get the answers for this
Answer:
B.
Step-by-step explanation:
Which function translates each point on the graph of y=mx+b so that the slope of the segment from the original point to the translated point is 43?
Answer:
s(x)=32mx+b
Step-by-step explanation:
It should be this
Suppose that each fn : R → R is continuous on a set A, and (fn)
converges to f∗ uniformly on A. Let (xn) be a sequence in A
converging to x∗ ∈ A. Show that (fn(xn)) converges to f∗(x∗)
If n > N, we have |fn(xn) − f∗(x∗)| ≤ |fn(xn) − f∗(xn)| + |f∗(xn) − f∗(x∗)| + |f∗(x∗) − fn(x∗)| < ε/3 + ε/3 + ε/3 = ε.
Suppose that each fn: R → R is continuous on a set A, and (fn) converges to f∗ uniformly on A.
Let (xn) be a sequence in A converging to x∗ ∈ A. Show that (fn(xn)) converges to f∗(x∗).Solution: Let ε > 0 be arbitrary.
We must show that there exists an index N such that if n > N, then |fn(xn) − f∗(x∗)| < ε. We know that (fn) converges uniformly to f∗ on A.
Hence, there exists an index N1 such that if n > N1, then |fn(x) − f∗(x)| < ε/3 for all x ∈ A.
Also, by continuity of f∗ at x∗, there exists a δ > 0 such that if |x − x∗| < δ, then |f∗(x) − f∗(x∗)| < ε/3.
Since (xn) converges to x∗, there exists an index N2 such that if n > N2, then |xn − x∗| < δ.
Let N = max{N1, N2}. Then, if n > N, we have |fn(xn) − f∗(x∗)| ≤ |fn(xn) − f∗(xn)| + |f∗(xn) − f∗(x∗)| + |f∗(x∗) − fn(x∗)| < ε/3 + ε/3 + ε/3 = ε.
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Which expressions are quadratic expressions? Check all that apply.
z2
2x + 7x – 10
2x2 + 9x – 7
500(0.25)t – 1
13x3 + 21x2 – 5
Answer:
Step-by-step explanation:
the quadratic expression is
2x^2+9x-7
this is the only one
Answer:
2x^2+9x-7
Step-by-step explanation:
Two straight lines are shown.
Answer:
(3,20)
Step-by-step explanation:
so O must be 0,0 and A is a midpoint of OB
This means B must be (14,12)
B is the midpoint of TS.
This means that the distance of SB is equal to the distance of BT.
This must mean that the coordinate of T must be (3,20)
O: (0,0) x coordinate increases by 7. y coordinate increases by 6.
A: (7,6)
B: (14,12)
S: (25,4) x coordinate decrease by 11. y coordinate increases by 8.
B: (14,12)
T: (3,20)
The coordinates of T are (3, 20).
What is Straight Line?A straight line is an endless one-dimensional figure that has no width.
From the figure, A is the midpoint of OB and B is the midpoint of TS
The coordinates of O are (0, 0) and Coordinates of A are (7,6)
We can find coordinate of B.
(7, 6)=(0+x/2, 0+y/2)
(7,6)=(x/2, y/2)
x/2=7 and y/2=6
x=14 y=12
So the coordinates of B are (14, 12)
Now we can find the coordinates of T.
(14, 12)=(X+25/2, Y+4/2)
X+25=28
x=3
Y+4=24
Y=20
So the coordinates of T are (3, 20)
Hence, the coordinates of T are (3, 20).
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Triangle ABC is similar to triangle EBD.
y
6
5
A
4
3
2
1
B
-6-5-4-3-2-1 1 2 3 4 5 6
NE
ED
-4
-5
-6+
which two transformations performed on triangle ABC and its image will prove triangle ABC and triangle EBD are similar?
dilation centered about the origin, with a scale factor of
A rotation of 90° clockwise about the origin
D.
2
B. rotation of 90° counter-clockwise about the origin
dilation centered about the origin, with a scale factor of
2
C. rotation of 270° clockwise about point C
F. dilation centered about point C. with a scale factor of 2
Answer: B
Step-by-step explanation: I did deh math ._.
b
Step-by-step explanation:
Okay soo its B its b its b its b
2x+2yequals 5, x-2y equals 3 find the solution set by using method elimination by substitution
The solution set of the given system of equations is {(8/3, -1/6)}.
We are given the following system of linear equations:
2x + 2y = 5 ...(1)
x - 2y = 3 ...(2)
We can use the method of elimination by substitution to solve this system. First, we solve equation (2) for x in terms of y:
x = 2y + 3
Substituting this value of x in equation (1), we get:
2(2y + 3) + 2y = 5
Simplifying the above expression, we get:
6y + 6 = 5
6y = -1
y = -1/6
Substituting this value of y in equation (2), we get:
x - 2(-1/6) = 3
x + 1/3 = 3
x = 8/3
Therefore, the solution set of the given system of equations is:
{(8/3, -1/6)}
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let p represenst "angke A is an obtuse angle" and q represent " the measure of angle A = 75 degrees. convert the symbolic statement to a sentence.
In this scenario, we are considering if-then statements. Looking at the given statement,
p = angle A is an obtuse angle
q = the measure of angle A = 75 degrees
A statement of if q, then p would be
q - p
where - is an arrow pointing to the right
Looking at the picture, the symbol before p represents negation. It tells us that
if q, then not p. By translation, the correct answer would be
If the measure of angle A = 75 degrees, then angle A is not an obtuse angle
A rectangle measures165inches by104inches. What is its area?
Answer:
17 160 inches
Step-by-step explanation:
Area = width x length
so 165 x 104 which is 17 160
Therefore, the area of the rectangle is 17 160 inches
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The curve formed by a quadratic equation is called a...?
Answer: The curve formed by a quadratic equation is called a PARABOLA
Step-by-step explanation:
Answer:
Parabola
Step-by-step explanation:
Plz help me I don't understand
Antonio pays y dollars per visit to his fitness center and he pays his bills every 3 months . In October he visited the gym 22 times in November he visited 25 times and in December he visits 19 times write and variable expression to represent how much he will have to pay for the last three months of last year. Evaluate the expression for y=2.50
nahhhh im goood. 6235736203274352
A single tractor-trailer driver is starting a new shift, intending to travel 450 miles from Charlotte, NC to Pittsburgh, PA. Estimating an average speed of 50 mph and abiding by the current HOS rules, what is the minimum number of clock hours (not driving hours) it will take him?
It will take a minimum of 10 clock hours (not driving hours) for the truck driver to travel 450 miles from Charlotte, NC to Pittsburgh, PA.
The current Hours of Service (HOS) rules for truck drivers stipulate that a truck driver cannot drive for more than 11 hours after 10 consecutive hours off duty.
Additionally, the driver is not allowed to drive beyond 14 hours after coming on duty.
The driver's shift includes both driving and non-driving time.
Therefore, it is necessary to consider the total amount of time spent on the job.
The truck driver will have to stop for rest breaks, refueling, or other reasons during the 450-mile journey to Pittsburgh, Pennsylvania. The driver is required to take a 30-minute break after eight hours of driving.
Therefore, the minimum number of clock hours (not driving hours) it will take the truck driver to travel the 450-mile distance from Charlotte, NC to Pittsburgh, PA is calculated as follows:
Time for the trip = (Distance ÷ Average Speed) + Breaks
Time for the trip = (450 ÷ 50) + (30 ÷ 60) × 2
Time for the trip = 9 + 1
Time for the trip = 10 clock hours
Therefore, it will take a minimum of 10 clock hours (not driving hours) for the truck driver to travel 450 miles from Charlotte, NC to Pittsburgh, PA.
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What are the 3 ways to name an angle?
There are three ways to name an angle--by its vertex, by the three points of the angle (the middle point must be the vertex), or by a letter or number written within the opening of the angle.
You can name a specific angle by using the vertex point, and three points on each of the angle's rays or by letter or number written. The name of the angle is simply the three letters representing those points, with the vertex point listed in the middle. You can also name angles by looking at their size. Right angles are 90 degrees. Acute angles are less than 90 degrees. Obtuse angles are greater than 90 degrees, but less than 180 degrees, which is a straight angle, or a straight line.
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Find the indefinite integral: S(-7secxtanx - 5sec²x)dx
The value of the indefinite integral: S(-7secxtanx - 5sec²x)dx is -7ln|sec(x) + tan(x)| - 5x + 5ln|sec(x)| + C
To integrate the expression S(-7sec(x)tan(x) - 5sec²(x))dx, we first use the identity sec²(x) = 1 + tan²(x) to rewrite the second term as -5 - 5tan²(x). Then we can split the integral into two parts as follows: S(-7sec(x)tan(x) - 5sec²(x))dx = -7Ssec(x)tan(x)dx - 5S(1 + tan²(x))dx = -7sec(x)dx - 5x - 5tan(x)dx
Now we can integrate each part separately. The integral of sec(x) is ln|sec(x) + tan(x)| + C, and the integral of tan(x) is ln|sec(x)| + C. Therefore, S(-7sec(x)tan(x) - 5sec²(x))dx = -7ln|sec(x) + tan(x)| - 5x + 5ln|sec(x)| + C where C is the constant of integration.
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Which statement must be true? arc r t ≅ arc u t ∠rqt ≅ ∠rst rq ⊥ qt rs ≅ st
The sides RS and ST are equal because they are the side of the congruent triangle that is RS ≅ ST. Then the correct option is D.
What is a circle?It is a locus of a point drawn equidistant from the center. The distance from the center to the circumference is called the radius of the circle.
In circle Q, ∠RQS ≅ ∠SQT.
In ΔRQS and ΔTQS
∠RQS ≅ ∠SQT (Given)
QS = QS (Common side)
RQ = QT (Radius of the circle)
The ΔRQS and ΔTQS triangles are congruent to each other. That is given as ΔRQS ≅ ΔTQS.
The sides RS and ST are equal because they are the side of the congruent triangle that is RS ≅ ST. Then the correct option is D.
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Answer:
D. rs≅st
Step-by-step explanation:
i did it
on the math portion of the sat, scores are roughly normal, with a mean of 500 and a standard deviation of 100. what percent of scores are above 400?
The percent of scores are above 400 is 84.13 percent.
Given that, mean \((\bar{x})\)=500 and the standard deviation \((\sigma)\)=100.
Standard deviation is the positive square root of the variance. Standard deviation is one of the basic methods of statistical analysis. Standard deviation is commonly abbreviated as SD and denoted by 'σ’ and it tells about the value that how much it has deviated from the mean value.
Here, from the normalization curve the proportion of SAT scores above 400 is
\((50+\frac{68.26}{2})\%\)
\(= 84.13 \%\)
Therefore, the percent of scores are above 400 is 84.13 percent.
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