The measure of an exterior angle at the fifth vertex is 62°.
A pentagon has 5 straight sides. The shape must also be closed.
A convex pentagon has no angles pointing inwards, and no internal angles can be more than 180°.
When all angles are equal and all sides are equal it is regular, otherwise, it is irregular.
The sum of exterior angles is 360°.
To know the angle of the fifth vertex add the remaining four vertexes and subtract from the sum of exterior angles.
Given 4 vertexes of the pentagon are 83°, 83°, 26°, and 46°.
By adding these we get a total of 238°
Fifth vertex=360°-238°
Fifth vertex=62°
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of 4
Workers in an office of 40 staff were asked their favourite type of take-away.
The results are summarised in the table.
Take-away
Pizza
Curry
Fish & chips
Kebab
Other
What fraction of a person is one degree?
Give your answer in its simplest form.
Frequency
4
4
8
5
19
Angle
a
b
C
d
e
Workers in an office of 40 staff were asked their favourite type of take- away.1/9 bit of a person is one degree.
What's Fraction?
An element of a total is a bit. The number is represented mathematically as a quotient, where the numerator and denominator are resolve. Both are integers in a simple bit. A bit appears in the numerator or denominator of a complex bit. The numerator of a proper bit is lower than the denominator.
The magnitude of an angle is measured using a unit of dimension. In magnitude, 1 degree is original to1/360 of a full gyration.
Degree 1 – direct.
Degree 2 – quadratic.
Degree 3 – boxy.
Degree 4 – quartic( or, if all terms have indeed degree, biquadratic)
Given that;
total workers = 40
Bit of a person = 1 degree
we know that 360 ° = 40 person
so for 1 degree = 40/360 = 1/9
Hence,1/9 bit of a person is one degree.
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is the system linear or non-linear? you need to justify your answer. b) is the system time-varying or time-invariant? you need to justify your answer. c) is the system causal or not causal? you need to justify your answer. d) find the impulse response function of the system
The given system is :
a) Linear
b) Time-invariant
c) Casual
d) Impulse response function is h(n) = 2δ(n-1) + δ(n-2).
a) Linear: A system is considered linear if it satisfies the superposition principle, meaning that if the inputs x1(n) and x2(n) produce outputs y1(n) and y2(n), respectively, then the output of the system to a weighted sum of inputs is equal to the weighted sum of the outputs. In this system, 2x(n-1) and x(2n) are both linear operations, and the sum of two linear operations is also a linear operation. Therefore, this system is linear.
b) Time-invariant: A system is considered time-invariant if the output is not dependent on the current time, but only on the input and its previous values. In this system, the coefficients 2 and 1 do not change with time, and the system does not depend on the current time. Therefore, this system is time-invariant.
c) Causal: A system is considered causal if the output only depends on the present and past inputs, and not on future inputs. In this system, x(2n) only depends on the past and present inputs, and x(n-1) only depends on past inputs. Therefore, this system is causal.
d) Impulse response function: The impulse response function of the system can be found by taking the unit impulse as the input, solving for the output and normalizing it.
h(n) = 2δ(n-1) + δ(n-2)
where δ(n) is the unit impulse function and h(n) is the impulse response function of the system.
Correct Question :
y(n) = 2x(n-1) + x(2n). is the system linear or non-linear? you need to justify your answer. b) is the system time-varying or time-invariant? you need to justify your answer. c) is the system causal or not causal? you need to justify your answer. d) find the impulse response function of the system
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6. Oliver runs a mile in 6 minutes. He left his house and
ran 2 miles North, 3 miles east, then ran back to his
house. What was the total time of Oliver's run?
Oliver runs a mile in 6 minutes. He runs 2 miles North and 3 miles east, so the total distance he ran is 2 + 3 = 5 miles.
Since he ran the same distance back to his house, the total distance he ran is 52 = 10 miles.
Since he runs a mile in 6 minutes, the total time of Oliver's run was 106 = 60 minutes.
Therefore, Oliver's total run time is 60 minutes.
Consider the following data representing the price of refrigerators (in ollars).
1388, 1384, 1152, 1085, 1352, 1162, 1229, 1464, 1412, 1258, 1475, 1329, 1376, 1122, 1468, 1443, 1283, 1182, 1207,
1310, 1178
Class
1080-1149
1150-1219
1220-1289
1290-1359
1360-1429
1430-1499
Step 7 of 7: Compute the cumulative frequency of the second class.
In this case, the cumulative frequency of the second class would be the number of prices in the data set that fall within the range of $1150 and $1219 plus the cumulative frequency of the first class.
What is the cumulative frequency?Cumulative frequency is a running total of the frequencies of a data set. It is used to keep track of how many observations fall within a certain range of values. It is the sum of the frequencies of all the classes up to a certain point.
The second class is 1150-1219 which means it includes the price of refrigerators that fall within the range of $1150 and $1219. To find the cumulative frequency of the second class, you would need to count the number of prices in the data set that fall within that range and add it to the cumulative frequency of the previous class.
In this case, the cumulative frequency of the second class would be the number of prices in the data set that fall within the range of $1150 and $1219 plus the cumulative frequency of the first class. Since the cumulative frequency of the first class is not provided, we cannot calculate the cumulative frequency of the second class without more information.
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David knows a phone call to a friend costs 25 cents for the first 3 minutes and 10 cents for additional minute. Write a liner equation and calculate how long does he make a phone call if he spends $10
PLEASE HELP
If David spends $10, he may call for 50 minutes.
As per the data given in the above question are as bellow,
Let x represent the duration of David's phone calls.
The following linear equation can be used to express the call's cost:
Price = x + (x - 3) (0.10)
By setting the equation's value to 10 and finding the value of x, we can determine how long David will talk on the phone if he spends $10:
10 = 0.25x + (x-3)(0.10) (0.10)
The right side of the equation is first made simpler:
10 = 0.25x + 0.10x - 0.30
Next, we may combine related words as follows: 10 = 0.35x - 0.30
10 plus 0.30 equals 0.35x when applied to both sides.
Consequently, x = 50. David talks on the phone for 50 minutes.
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nine percent of americans have rh-negative o blood type. in a random sample of 200 americans, what is the probability that the sample proportion with rh-negative o blood types will be less than 12% (round off to second decimal place)?
The probability that the sample proportion with rh-negative o blood types will be less than 12% is 0.93.
According to the question,
91 pts nine percent of Americans have rh-negative o blood type.
In a random sample of 200 Americans, what is the probability that the sample proportion with rh-negative o blood types will be less than 12% = ?
by Using central limit theorem,
P(p cap < p) = P(Z<p cap-p/√p(1-p)/n)
so,
P(p cap < 0.12) = P(Z<0.12-0.09/√(0.09×0.91/200)
= P(Z<1.4825)
= 0.9309 (from Z table)
= 0.93 (Rounded to second decimal place)
so, The probability that the sample proportion with rh-negative o blood types will be less than 12% is 0.93.
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Find the missing length of the figure.
x=
mm
The measure of the missing length in the figure, found using Pythagorean Theorem is; x = 37 mm
What is Pythagorean Theorem?Pythagorean Theorem states the relationship between the lengths of the sides of a right triangle. According to Pythagorean Theorem, the sum of the squares of the leg lengths of a right triangle is equivalent to the square of the length of the hypotenuse side.
Please find attached a possible figure in the question, obtained from a similar question posted on the website.
The 13 mm side hypotenuse length of the right triangle on the left indicates a other leg length of the right triangle can be found using Pythagorean Theorem as follows;
Square of the length of the hypotenuse side = Sum of the square of the length of the other two sides
13² = 5² + (second leg length)²
The second leg length of the right triangle on the left = √(13² - 5²) = 12
The 12 mm leg length of the right triangle on the left indicates that the leg length of the right triangle on the right which correspond with the 12 mm leg length on the left is 12 mm
The length of the hypotenuse of the right triangle on the right, which is the missing length, x is therefore;
x² = 12² + 35² = 1369
The measure of the missing length x is therefore;
x = √(1369) = 37
The missing length in the figure is; x = 37 mm
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Can someone help me asap please?
By Interception of a point f(x) = 3.75b + 25 and this we get the Value 3.75.
How do you find the interception of a point?A line's x-intercept and y-intercept are the points at which the x- and y-axes cross, respectively.In order to locate the point or points of intersection, we must solve the equation f(x) = g. (x). We shall learn the x value(s) of the intersection point(s) from the solution of this equation. Once we have determined the value for x, we may use it to solve one of the original equations to determine the value of y.Examples :
f(x) = 3.75b + 25
Axis interception points of 3.75b + 25:
X intercepts:(-20 / 3,0),
Y intercepts : (0.25)
Slope of 3.75b + 25: 3.75.
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There must be some reason why Hot Dog sausages are sold in packets of 10 and the bread rolls
in packets of 12: I bought just enough packets of each to have the same number of each.
How many items were on the receipt?
There must be some reason why Hot Dog sausages are sold in packets of 10 and the bread rolls in packets of 12: I bought just enough packets of each to have the same number of each therefore the number of items which were on the receipt is eleven (11).
What is Multiplication?This is referred to as an operation that represents the basic idea of repeated addition of the same number and will be used to get the same number of each in this scenario.
Since Hot Dog sausages are sold in packets of 10 and the bread rolls in packets of 12, to get the same number of each will be to look for values which when multiplied will give the same number which are 6 and 5 respectively to give equal number of 60 each. therefore the number of items on the receipt will be 6+5 = 11.
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A dot plot shows the number of pizza sold at a local restaurant each day one week. One Columbia of dots on the plot is much taller than the others explain what that means in the context of the data and of percents
If one column of dots on the dot plot is much taller than the others, it means that on that particular day, the restaurant sold significantly more pizzas than on the other days of the week.
A dot plot is a simple graphical representation of data where each data point is represented by a dot or mark above a number line. In this context, the dot plot shows the number of pizzas sold at a local restaurant each day for one week. The height of the column of dots represents the number of pizzas sold on that particular day.
If one column of dots is much taller than the others, it means that on that particular day, the restaurant sold significantly more pizzas than on the other days of the week. This could be due to a variety of reasons such as a special promotion, a holiday, or just a generally busy day.
Understanding which days are the busiest for the restaurant can help the management make decisions such as staffing levels, inventory management, and marketing strategies. For example, if a particular day of the week is consistently the busiest, the restaurant may want to offer a special promotion or discount on that day to attract more customers.
In terms of percents, if for example, the restaurant sold 100 pizzas on the day with the tallest column of dots, and the next highest day sold 60 pizzas, the day with 100 pizzas would be 166.6% higher than the day with 60 pizzas. It indicates the significance of the difference between the two days in terms of sales.
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Question 9 (2 points)
Lily threw a ball. The balls equation that demonstrated its height and velocity is:
h(x) = -16x² + 3x + 35
What was the initial height that she threw the ball from?
The initial height of the ball is the y-intercept of the function. The initial height she threw the ball from was 35.
Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax² + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient, and 'c' is called the absolute term of f (x).
The function is as follows:
h(x) = -16x² + 3x + 35
Substitute the value of x = 0.
So, we have:
h(0) = -16(0)² + 3(0) + 35
Evaluate the exponent
h(0) = -16(0) + 3(0) + 35
Evaluate the products
h(0) = 0 + 0 + 35
Evaluate the sum
h(0) = 35
Hence, the initial height she threw the ball from was 35.
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Question
During this same time, the digital print manager tracked the number of visits to the website's
homepage. He found that before launching the new marketing plan, there were 4,800 visits. Over the
course of the next 5 weeks, the number of site visits increased by a factor of 1. 5 each week.
Write an equation to model the relationship between the number of weeks, x, and the number of site
visits, f(x).
Enter the correct answer in the box by replacing the values of a and b.
TT
a а в
sin cos tan sin-'costan-
9
+
o
2 Δ Ο
Σ
U OD
A
yo
>
다
1
5
2
CSC sec cotlog log in
|
4800(0. 081)
f(x) = 4800 * 1.5^x is the equation to model the relationship between the number of weeks, x, and the number of site visits.
It is said that the number of visits increased by a factor of 1.5 each week, which means it multiplied by 1.5 every week.
So the equation can be modeled as:
f(x) = 4800 * 1.5^x
Where x is the number of weeks and f(x) is the number of site visits.
Note that this equation is only valid for the number of weeks after the new marketing plan has been launched, since before that the number of visits was 4,800.
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Write two expressions (with at least two terms each) that when added together have a sum of -4n + 6.
(Please answer immediately, worth 25 points and i'll mark brainliest)
The two expressions that add to get a sum of - n + 6 are
A. (-6n) + (6 + 2n) and
B. (- 10n + 2) + (6n + 4)
Now, According to the question:
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
The expression is :
-4n + 6
Now the expression as
A. (-6n) + (6 + 2n)
After adding, we have;
(-6n) + (6 + 2n) = -6n + 6 + 2n
= - 4n + 6
B. (- 10n + 2) + (6n + 4)
After adding we have;
(- 10n + 2) + (6n + 4) = - 10n + 2 + 6n + 4
= - 4n + 6
Hence, The two expressions that add to get a sum of - n + 6 are A. (-6n) + (6 + 2n) and B. (- 10n + 2) + (6n + 4)
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L2.10.2 Quiz: Some Guidelines for Problem Solving
Question 4 of 6
What are some steps you might take after coming to a solution? Check all
that apply.
A. Create a logical name for the variable.
B. Gather your resources.
C. Write down the facts.
D. Draw a diagram.
E. Present your answer with units.
4
OF. Double-check that your answer satisfies the equation.
Some steps you might take after coming to a solution include all of the following:
A. Create a logical name for the variable.
E. Present your answer with units.
What is a problem solving process?In Computer technology and Mathematics, a problem solving process can be defined as a systematic approach that is used typically for identifying and determining the optimal and effective solution to a particular problem.
Generally speaking, you must ensure that a logical name for the given variable is created after developing a solution to any mathematical or scientific problem.
In conclusion, the final answer (solution) must be presented with the correct and appropriate unit of measurement.
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Simplify the expression
Answer: -1.9d + 5.4h - 13
Step-by-step explanation:
write an equation:
an addition equation with one variable that has a solution of 3
Answer:
x + 5 = 8
Step-by-step explanation:
x + 5 = 8
Subtract 5 from both sides.
x + 5 - 5 = 8 - 3
x = 3
Answer: x+5=8
Step-by-step explanation:
1/2x + 3 = 4
What does x equal?
In the given diagram, what are angles 1 and 7 called?
simplify. 1.4x−5x+4−x+3 Enter your answer by filling in the boxes. Use decimal form when necessary.
A large container holds 8 gallons of water. It begins leaking at a constant rate. After 32 minutes the container has 6 gallons left. At what rate is the water leaking. Express answer as a positive value.
Answer:
1/16 gallons per minute
Step-by-step explanation:
The water level drops from 8 gallons to 6 gallons in 32 minutes
The volume of water that has leaked is 8 - 6 = 2 gallons
Since this volume of water has leaked in 32 minutes, rate of leak
+ 2/32 = 1/16 gallons per minute
Write an equation of the parabola that satisfies the conditions.
Vertex: (3, 3); y-intercept: (0, -6)
The equation of the parabola with the given vertex and y-intercept is:
y = -(x - 3)² + 3
How to Write an Equation of a Parabola with a Given Vertex and Y-intercept?The equation of a parabola in vertex form is given by:
y = a(x - h)² + k
Where (h, k) is the vertex of the parabola, and a is a nonzero constant. To find the equation of the parabola that satisfies the given conditions, we can use the vertex and the y-intercept to find the values of a, h, and k.
The vertex of the parabola is (3, 3), so h = 3 and k = 3. The y-intercept of the parabola is (0, -6), which means that when x = 0, y = -6. Substituting these values into the equation of the parabola, we get:
y = a(x - 3)² + 3
When x = 0, y = -6. Plugging in the value of x and y, we get
-6 = a(0 - 3)² + 3
-6 = 9a + 3
-9 = 9a
a = -1
Therefore, the equation of the parabola that satisfies the given conditions is:
y = -(x - 3)² + 3
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Help Me Please!!!!!
Homework!
A graph of the solution of this inequality w ≤ 200 is shown in the image attached below.
How to graph the inequality?In this exercise, we would solve the given inequality by making w the subject of formula as follows;
w/-10 ≤ -20
By multiplying both sides of the inequality by -10, we have the following:
-10 × w/-10 ≤ -20 × -10
w ≤ 200
Next, we would use an online graphing calculator to plot the inequality as shown in the graph attached below. Additionally, the circle on the number line (graph) is closed because of the less than or equal to (≤) symbol.
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PLEASE HELP!!!
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
A pyramid has a regular hexagonal base with side lengths of 4 and a slant height of 6. Find the total area of the pyramid.
T. A. =
The total area of the pyramid is (24√3 + 72) square units or 113.57 square units.
What is a hexagonal pyramid?A hexagonal pyramid is a 3D design in which the base is hexagonal and the faces or sides are isosceles triangles, which come together to form the hexagonal pyramid at the summit of the pyramid. A hexagonal pyramid has six sides on the base and six isosceles triangles on the sides.
Given a hexagonal pyramid,
base length = 4
slant height = 6
area of pyramid = sum of the area of the base to the lateral area
area of pyramid = A(base) + A(lateral)
Area of base = 3√3/2*(a²)
a = base length = 4
Area of base = 3√3/2*(4²)
Area of base = 24√3 square units
now lateral area or area of triangular faces,
lateral area = 6*1/2*b*h
h = height of triangle = 6
b = base of triangle = 4
lateral area = 6*1/2*4*6
lateral area = 72 square units
total area = A(base) + A(lateral)
total area = (24√3 + 72) square units
Total area = 113.57 square units.
Hence the area of the pyramid is (24√3 + 72) square units or 113.57 square units.
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can anyone tell how to do this in confused
Answer:
Step-by-step explanation:=2/11+10/5
=10/55+110/55
=120/55
=24/11
A heat source generates heat at a rate of 70. 0 W (1 W = 1J/s). How much entropy does this produce per hour in the
surroundings at 28. 5 °C? Assume the heat transfer is reversible.
The entropy produced by the heat source is 2.17 J/K per hour.
In order to calculate the amount of entropy produced by a heat source, we need to use the formula for entropy change: ΔS = Q/T,
where Q is the amount of heat transferred and T is the temperature of the surroundings in kelvins.
To convert the temperature to Kelvin, we add 273.15 to the temperature in degrees Celsius.
In this case, the heat source generates 70.0 W of heat and the temperature of the surroundings is 28.5 °C.
So, to find the entropy change per hour, we need to multiply the power generated by the time:
ΔS = (70.0 W) * (3600 s/h) / (28.5+273.15)
This calculation results in approximately 2.17 J/K * h or 2.17 J/K per hour.
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Please help me with my math homework! It’s due soon!
Answer:
The slope of the line is -2.
Step-by-step explanation:
Rise/Run
you have 2 points on the graph since this is a negative slope you start on the top point
you count straight down up to your next point and you should get 8.
then you count to the right to your next point and should get 4.
that would give you 8/4 as your slope.
8/4 simplified is 2.
The slope is 2
A right rectangular prism measures 12 cm tall, 8 cm long, and 5 cm wide.
A manufacturer would like to double the surface area of this prism. What should be the height of the new prism so that its surface area is doubled?
Enter your answer, to the nearest tenth, in the box.
cm
Answer:
24
Step-by-step explanation:
12*8*5 =480 current surface
double = 960
so make the 12 into 24 height.
done
A
Solve for x.
x =
10
x = 4
x = 5
x = 2
10
4
2
E
B
X
Determine whether the underlined number is a statistic or a parameter. In a study of all 1506 seniors at a college, it is found that 65% own a television. Choose the correct statement below. a. Parameter because the value is a numerical measurement describing a characteristic of a population. b. Statistic because the value is a numerical measurement describing a characteristic of a sample.
c. Parameter because the value is a numerical measurement describing a characteristic of a sample. d. Statistic because the value is a numerical measurement describing a characteristic of a population.
The correct statement is parameter because the value is a numerical measurement describing a characteristic of a population.
A parameter is a numeric value that describes a population feature in probability and statistics. It is a fixed value that is typically unknown and used to define or describe a probability distribution. The population's mean, variance, and standard deviation are a few examples of parameters.
Typically, these parameters are calculated using statistical techniques like maximum likelihood estimation from a sample of data. One can learn something about the entire population from a parameter. In the case of a given question, this implies that after asking everyone in that group, one will know something. All 1506 seniors at college were included in the survey and it was discovered that 65% of them own a television.
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This question has two parts. First, answer Part A. Then, answer Part B.
Part A
Select the correct choices to complete the sentence.
TICKETS Jamal has $40 to buy tickets to a performance for himself and his friends. If he buys a $10 membership, he can buy tickets for $5 each. How many tickets can he buy while remaining within his budget?
Part A
If x represents the number tickets Jamal purchases, write an inequality that represents the situation.
, 1 of 4.
Select Choice
+, 2 of 4.
Select Choice
x , 3 of 4.
Select Choice
, 4 of 4.
Select Choice
Part B
Select the correct choices to complete the sentence.
Part B
Solve the inequality.
x , 1 of 2.
Select Choice
, 2 of 2.
Select Choice
Within his budget, he can still purchase 6 tickets. The inequality is 40 < 5x + 10.
Unitary method: what is it?The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
In light of the query
With his $40, Jamal may get tickets for himself, his friends, and a show.
If he spends $10 to join a membership,
Money remaining = $40 - $10 = $30
Now he may purchase the ticket at $5 apiece.
Now, tickets that he may purchase while staying within his budget found using utilizing the unitary technique.
Tickets= $30 / $5
Tickets = 6
As a result, he may purchase the remaining 6 tickets for his budget.
A:
Number of tickets = x
Hence, the inequality is 40 < 5x + 10.
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