Each base angle 72 degrees is the measure of the vertex angle of an isosceles triangle if the measure of the base angle is 36
For any triangle, the three angles always add to 180 degrees.
In an isosceles triangle, the base angles are the same measure. For now we don't know what they are, so let's call them x. The vertex angle is 36.
Adding the three angles (x, x, and 36) and setting that equal to 180 will help us find the value of x.
x+x+36 = 180
2x+36 = 180
2x+36-36 = 180-36 .... subtract 36 from both sides
2x = 144
2x/2 = 144/2 .... divide both sides by 2
x = 72
This triangle has two base angles of 72 each and the vertex angle of 36. As a check, the three angles should add up to 180
72+72+36 = 144+36 = 180
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the radius of a circle is increasing at a constant rate of 5 meters per second. at the instant when the radius of the circle is 1010 meters, what is the rate of change of the area? round your answer to three decimal places.
the radius of a circle is increasing at a constant rate of 5 meters per second, so the rate of change of the area is [tex]100\pi m/sec^{2}[/tex]
How is the rate of change calculated?Divide the y-value change by the x-value change to determine the rate of change. When analyzing changes in observable parameters like average speed or average velocity, finding the average rate of change is extremely helpful.
Suppose the radius of circle be r.
now, [tex]\frac{dr}{dt} = 5 m/sec[/tex]
And, area of circle is [tex]\pi r^{2}[/tex]
[tex]\frac{dA}{dy} = 2\pi r\frac{dr}{dt},[/tex] differentiate both sides with respect to t,
[tex]\frac{dA}{dt} |_{r=10} = 2\pi (10)(5)[/tex]
= [tex]100\pi m/sec^{2}[/tex]
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Someone help me please
The required solutions are as follows,
(a) The distance between A and B is 480 KM.
(b) Kenzi drove 60 km more than Jafar.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
a]
1 cm = 200 km,
Distance between A and B = 2.4 cm = 2.4 [200 km]
= 480 km
b]
Jafar drove for (A to B) = 480 km
Kenzi drove for B to C = 2.7 [200] = 540 km
Difference = 540 - 480 = 60km
Thus, the required solutions are as follows,
(a) The distance between A and B is 480 KM.
(b) Kenzi drove 60 km more than Jafar.
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cost $210. tax rate 12%. What is the total cost
Answer: $235.2
Step-by-step explanation:
We just multiply 210 by 12%
which gives us 25.2
Then we just add 25.2 + 210 = 235.2
Identify the parent function for the function g(x) = (x − 2)^3 from its function rule. Then graph g and identify what transformation of the parent function it represents.
NEED ASAP
The transformation from the parent function f(x) = x³ is a translation to the right by 2 units
How to describe the transformation from the parent function?From the question, we have the following function that can be used in our computation:
g(x) = (x − 2)³
To determine the parent function, we leave only the variable in the expression
So, we have
f(x) = x³
Next, we determine the transformation
We have the transformation to be from f(x) = x³ to g(x) = (x − 2)³
This means the function is translated right by 2 units
Hence, the transformation is 2 unit right
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What are the 3 types of proofs?.
The 3 types of proofs are the proof by induction, direct proof and the proof by contradiction.
Proof is a logical or mathematical argument that shows that the given statement is true.
Though proofs might later on be proven wrong and/or have exceptions.
The three types of proof are:
(i) Proof by Induction
(ii) Direct Proof
(iii) Proof by Contradiction
Proof by Induction:
Proof by induction is the proof in which we generalize a particular for the entire equation.
In the inductive step we generalize the conclusion from the basis, where we prove the equation for a particular value for the entire theorem or equation.
On solving this, if the answer observed follows the theorem used then it is proven
Proof by Contradiction:
In this type of proof we take a contradicting equation to the one that has to be proven. If this equation when further solved turns out to be false or untrue, the equation is considered proven.
Direct Proof:
In the direct proof we assume that the given equation or theorem, to be proven is correct. We then go on to slow the question with the given assumption. If the on solving the answer comes out to be correct, we say that the theorem has been proven.
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list the two types of sampling procedures group of answer choices causation and exact sampling precise and imprecise sampling probability and nonprobability sampling statistical and linear sampling large and small size sampling
The correct answer is Probability and non probability sampling procedure.
There are two distinct exits from sampling procedures.
There are two types of sampling: probability sampling and non-probability sampling.
In probability sampling each population has equal and independent chance to comes in the study . There are various types of probability samplings technique exists . These are simple random sampling , stratified random sampling, cluster sampling , systematic random sampling etc.
In non probability sampling the samples are selected on the basis of personal biasness, judgments and preferences. Judgemental sampling , quota sampling, dimensional sampling etc comes under this type of sampling procedure.
So here the correct answer is
Option -E- Probability and non probability sampling procedure.
Except it all other options are wrong.
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find the area of the shaded region under the standard normal distribution to the right of the given z-score. round your answer to three decimal places.
The area of shaded region is 0.171.
Given z-score is z = 0.95.
We have to calculate P(z > 0.95).
We can write this as
P(z > 0.95) = 1 - P(z < 0.95)
From the z-table we know that
P(z < 0.95) = 0.828
We will put this value in above equation, we get
P(z > 0.95) = 1 - 0.828
Therefore
P(z > 0.95) = 0.171.
Z-score tables are very useful in determining the probabilities of normally distributed random variables. The z-score standardizes the normally distributed variable to make any normal distribution fit into the standard normal distribution.
The z-score is calculated using the random variable, the mean, and standard deviation of a particular normal distribution of variables.
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for each group in the following list, find the order of the group and the order of each element in the group. what relation do you see between the orders of the elements of a group and the order of the group?
The relation which we see between the orders of the elements of a group and the order of the group is smallest positive power.
G = U(20), order of each element of G = ?
The smallest positive power of an element that gives you your identity is the order of the element in a group. Three instances are covered: complex numbers, a 2x2 rotation matrix, and real number elements of finite order.
G = U(20) = {1,3,7,9,11,13,17,19}
⇒ 3° ≡ 1, 3¹ ≡ 3, 3² ≡ 9, 3³ ≡ 7, 3¹ ≡ 1(20)
∴ order of 3 = 4
7⁴ ≡ 1 (mod 20) → order (7) = 4
9² ≡ 1 (mod 20) → order (9) = 2
11² ≡ 1 (mod 20) → order (11) = 2
13² ≡ 9(mod 20) → 13⁴ ≡ 81(mod 20) → 13⁴ ≡ 1 (mod 20)
⇒ order (13) = 4
order 07 = 4
17 ≡-3(mod 20) ⇒ 17² ≡ yy (mod 20)
⇒ 17⁴ ≡ 81 (mod 20) ≡ 1 (mod 20) ⇒
19 = -1 (mod 20)
19² ≡ 1 (mod 20) ⇒ order (19) = 2
Hence we get the requires answer.
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find an equation of the line tangent to the curve at the point corresponding to the given value of t. x=t^2-23, y=t^3 + t; t=5
The equation of the line tangent to the curve at the point corresponding to the given value of t.
x = t²-23 and y = t³ + t, at t = 5 is
38x - 5y + 574 = 0
Given, a curve with the points represented by
x = t²-23 and y = t³ + t, at t = 5
we have to find an equation of the line tangent to the curve at the given point on the curve.
so, the given point is (x , y) = (5² - 23 , 5³ + 5)
(x , y) = (2 , 130)
Now, the slope of the curve at that point be,
dy/dx = (3t² + 1)/(2t)
dy/dx = 76/10
Now, on using the slope-intercept form, we get
(y - 130)/(x - 2) = 38/5
5(y - 130) = 38(x - 2)
5y - 650 = 38x - 76
38x - 5y + 574 = 0
Hence, the equation of the line tangent to the curve at the point corresponding to the given value of t.
x = t²-23 and y = t³ + t, at t = 5 is
38x - 5y + 574 = 0
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a firm has two plants(x and y) producing the same product which sells for $12 each. fixed costs are $5,000/year at plant x and $7,000/year at plant y and variable costs are $3.00/unit and $2.00/unit for x and y, respectively. the total profit at x and y are equal when the volume of each plant(units) is: group of answer choices 1,500 2,000 500 none of the above 1,000
A firm has two plants (X and Y) producing the same product which sells for $12 each. The total profit at plant X and plant Y are equal if the volume of each plant is 2,000 units.
To solve the problem, first translate the given problem into equations.
The formula for profit is:
profit = revenue from sales - total cost
total cost = fixed cost + variable cost
revenue = selling price x number of units sold
Let:
x = the number of units sold in plant X
y = the number of units sold in plant Y
From the problem, we can conclude:
Profit X = profit Y
x = y
Profit X = 12x - (5000 + 3x) (equation 1)
Profit Y = 12 y - (7000 + 2y) (equation 2)
Substitute y = x into equation 2
Profit Y = 12 x - (7000 + 2x)
Hence,
12x - (5000 + 3x) = 12 x - (7000 + 2x)
3x - 2x = 7000 - 5000
x = 2,000
Therefore, total profit at plant X and plant Y are equal if the volume of each plant is 2,000 units.
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pope john paul ii's 1979 visit to this eastern bloc nation, his homeland, drew millions of followers and helped spark a decade-long underground movement against the communist government.
In June 1979, the Pope travelled to Poland for the second time.
The foundation of the Solidarity trade union, which was a crucial force in the overthrow of Communism in eastern Europe, was reportedly set in motion as a result of this journey, which some historians claim was the most important of all his travels.
John Paul paid visits to Warsaw, Gniezno, Kraków, Nowy Targ, Auschwitz, and Jasna Gora while in Poland. Millions of fans attended the nine-day tour.
His visit to his homeland drew millions of followers and helped spark a decade-long underground movement against the communist government.
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Here is a circle with a center Z and some line segments and curves joining points on the circle. Complete the table by identifying each segment or curve as a radius, diameter, or neither and explaining your reasoning.
Which formula should be used to correctly calculate the monthly mortgage payment? m = p startfraction left-bracket r (1 minus r) superscript n baseline right-bracket over (1 r) superscript n baseline endfraction m = p startfraction left-bracket r (1 r) superscript n baseline right-bracket over left-bracket (1 r) superscript n baseline minus 1 right-bracket endfraction m = p startfraction r over left-bracket (1 r) superscript n baseline minus 1 right-bracket endfraction m = p startfraction left-bracket r (1 r) superscript n baseline right-bracket over (n r) endfraction
The correct formula to calculate monthly mortgage payment on a loan is [tex]M= P\frac{ [R(1+R)^n]}{[(1+R)^n-1]}[/tex]
Where, M is the total monthly payment
P is the total amount of loan
R is the interest rate
N is the total time
The primary advantage of a mortgage loan is that, unlike most other loans, you can get one without giving up ownership of your house to anybody else and at extremely low interest rates. The monthly mortgage repayment is symbolized by the mortgage payment. The standard four components of a mortgage payment are principal, interest, taxes, and insurance. The principal, term, and interest rate of the mortgage loan, as well as other factors, influence the monthly mortgage payment. The monthly mortgage payment can be calculated using the aforementioned formula or a financial calculator online.
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I went into a store with a 70% off sign on the door. I found a pair of pants that were originally $49.99 for $30.00 I didn't think this was 70% off so I had to make sure. What were the real percentage off?
Using percentage to calculate the actual amount, we found out that the real percentage were off.
PercentagePercentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
In this case, we have to find 70% of the original price and see if it's true.
70% of $49.99 will be;
70 / 100 = x / 49.99
0.7 = x / 49.99
x = 49.99 * 0.7
x = 34.993
The new price is supposed to be $34.99 and not $30
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A sales position needs to be filled. There are two candidates available. The first candidate has 10 years of experience and can sell 10 units a week making a $3,000 profit per week for the company. He is asking for $80,000 salary. The second candidate has one year of experience and can sell eight units a week making a $2,400 profit for the company. He is asking for $45,000 salary. What candidate would make the company the most money their first year of employment?.
The candidate that would make the company the most money in their first year of employment is Candidate B
Which candidate would make more money?The amount of profit that a candidate can make for the company is:
= ( Number of weeks in year x Profit per week ) - Salary for the year
We shall assume 48 working weeks in a year.
The amount of money made by Candidate A would be:
= ( 48 x 3, 000 ) - 80, 000
= $64, 000
The amount of money made by Candidate B is:
= ( 48 x 2, 400 ) - 45, 000
= $70, 200
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consider the random experiment to tossing two fair coins. what is the total number of outcomes of the random experiment?
Using Random Experiment of tossing two coin ,
the total number of outcomes of the random experiment is 4 .
Random Experiments:
Specifically, random experiments are the process of observing uncertainties. After the experiment, you will know the result of the random experiment. The results are the results of random experiments.
Sample Space: The set of all possible outcomes is called the sample space. Therefore, in the context of random experiments, the sample space is our universal set.
Random Experiment: Flip a Coin
Sample space , S={Head, Tail} or usually written as {H,T}.
When you repeat a random experiment several times, each is called a trial.
In the coin toss example, each trial is either heads or tails.
we have given a random experiment of tossing two fair coins then,
sample space, S = {HH, HT, TH, TT} = 4
So, the total number of randomized experiment outcomes is 4.
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I really need help to get this done, please.
The circle is partitioned into 9 parts and arc GH is only one of the parts, therefore, the length of arc GH is a ninth of the circumference of the circle which has the radius as a factor.
The ratio of the measure of arc length GH to the radius, r, where r = n is [tex]\frac{2\cdot \pi}{9}[/tex]What is the circumference of a circle?The circumference of a circle is the perimeter of the circle which is equal to the product of twice the radius and π.
The circumference of the circle is C = 2·π·r
The circle is divided into 9 parts
The arc GH is the arc to one part of the circle
The length of the arc GH = 2·π·r/9
The ratio of the arc GH to the radius, r = n is therefore;
When r = n,
Measure of arc length [tex]\widehat{GH}[/tex] = 2·π·n/9
Ratio of [tex]\widehat{GH}[/tex] to r = n is obtained using the formula;
[tex]Ratio = \dfrac{Measure \ of \ arc\ length \ GH }{n}[/tex]
[tex]\dfrac{\dfrac{2\cdot \pi\cdot n}{9} }{n} = \dfrac{2\cdot \pi }{9}[/tex]
The ratio of the measure of arclength GH to the radius (r = n) is [tex]\dfrac{2\cdot \pi }{9}[/tex]Learn more about the measure of an arc of a circle in geometry here:
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The perimeter of a rectangle is 96 yards and the length is 14 yards more than the width what are the dimensions of the rectangle
Answer:
17 yards and 31 yards.
Step-by-step explanation:
Since length is 14 more than width, lets call width: w and length: w+14
So perimeter is 96 so: 2w+2(w+14)=96
2w+2w+28=96 so 4w+28=96
4w=68 and finally w=17
So 17 yards and 31 yards.
max is a function that expects two int parameters and returns the value of the larger one.
Two variables , population1 and population2, have already been defined and associated with intvalues.
Write an expression (not a statement!) whose value is the larger of population1 andpopulation2 by calling max.
max(population1, population2)
The larger of population1 and population2 by calling max.
max(population1, population2)
Since the function max returns a large integer among two integers, max(population1,population2) will give us the large one among population1 and population2. Now if we compare that value with population2 using another max, then that will provide us with the large among maximum (population1,population2) i.e it will be the largest among these three variables.
Therefore the required expression will be:
max(population1,population2).
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Annika's flight to Ottawa took 45 min. The bus ride to the airport took 3 h. Write a ratio to compare the time on the bus to the time on the plane.
A boy is mowing a rectangular lawn 40 ft. Long and 30 ft. Wide. He has cut all of it except for a rectangle that is 20 ft. Long and 15 ft. Wide. What fractional part of the lawn remains uncut?.
The fractional part of the lawn remains uncut = 1/4.
In this question, we have been given a boy is mowing a rectangular lawn 40ft long and 30ft wide.
He has cut all of it except for a rectangle that is 20ft long and 15ft wide.
The area of the rectangular lawn:
40 x 30 = 1200 sq. ft.
And the area of the uncut part of lawn would be:
20 x 15 = 300 sq. ft.
The fractional part of the lawn that remains uncut would be,
300 / 1200 = 1/4
Therefore, 1/4 part of the lawn remains uncut.
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A fancy bed and breakfast inn has 5 rooms, each with a distinctive color-coded decor. One day 5 friends arrive to spend the night. There are no other guests that night. The friends can room in any combination they wish, but with no more than 2 friends per room. In how many ways can the innkeeper assign the guests to the rooms?
A. 2100
B. 2220
C. 3000
D. 3120
E. 3125
In 2220 ways the innkeeper can assign the guests to the rooms i.e. Option B is correct.
As per the question,
Number of rooms = 5Number of friends = 5The rooms are distinctive colour-coded decor i.e. the rooms have to be distinct.There are Five friends and Five rooms,
⇒ 0 rooms of 2, 5 rooms of 1
⇒ 1 room of 2, 3 rooms of 1
⇒ 2 rooms of 2, 1 room of 1
Guests can be allotted rooms by the innkeeper as
1, 1, 1, 1, 1, 1, 2, 2, or 1, 1, 1, 2
To assign ( 1, 2, 2 ) = ways to assign guests to the rooms × ways to assign frequencies to rooms= 5 × ( 4 2 ) × ( 5 2 ) ( 3 2 )
To assign ( 1, 2, 2 ) = ways to assign guests to the rooms × ways toassign frequencies to rooms
= 5 × 4 × 3! ( 5 2 )
To assign ( 1, 1, 1, 1, 1 ) = 5!Total number of ways ( N ) = To assign ( 1, 2, 2 ) + To assign ( 1, 2, 2 ) +
To assign ( 1, 1, 1, 1, 1 )
= 5 × ( 4 2 ) × ( 5 2 ) ( 3 2 ) + 5 × 4 × 3! ( 5 2 ) +
5!
= 5 × ( 4 2 ) × ( 5 2 ) ( 3 2 ) + 120 ( 5 2 ) + 120
N = 2220 ways
Therefore, The innkeeper can assign guests to the rooms in 2220 ways with no more than two friends per room i.e. option B is valid.
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What is a parent in a graph?.
The parent graph is the graph of a relatively simple function.
Graph:
Graph refers the diagram that represents the variation of a variable in comparison with that of one or more other variables.
Given,
Here we need to define the parent in a graph.
Parent function refers the simplest form of a given family of functions.
Here by transforming the function in various ways, the graph can be translated, reflected, or otherwise changed.
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Andres is a high school basketball player. In a particular game, he made some two point shots and some free throws (worth one point each). Andres made a total of 12 shots altogether and scored a total of 16 points. Determine the number of two point shots andres made and the number of free throws he made.
The total number of free throws shots Andres made was 8 and the total number of two point shots Andres made was 4.
First, let us understand the variables:
Any number, vector, matrix, function, its argument, set, or one of its elements can be specifically represented by a variable.
Let x and y be the quantity of shorts.
x is the number of attempts at the free throw line.
y is the quantity of two-point attempts.
According to the question, we have;
x + 2y = 16 ............equation 1
x + y = 12 ............equation 2
From equation 2 we can take out the value of x;
x = 12 - y ............equation 3
substituting the value of x in equation 1, we will get;
(12 - y) + 2y = 16
12 - y + 2y = 16
12 + y = 16
y = 16 - 12
y = 4
putting the value of y in equation 3, we will get
x = 12 - 4
x = 8
Thus, the total number of free throws shots Andres made was 8 and the total number of two point shots Andres made was 4.
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there are 200 sixth-graders in a school. 170 of them want to take geometry, 175 of them want to take algebra, what is the least number of 6th graders who want to take part in both classes?
The least number of 6th graders who want to take part in both classes is 145.
The intersection of sets A and B is the set of all the elements which are common to both A and B. The intersection of sets is denoted by the symbol '∩'. Hence, we can write the intersection of A and B as A ∩ B.
The number of graders that want to take geometry is 170.
The number of graders that want to take algebra is 175.
A ∩ G= n(A) + n(G) -( AUB)
=175+170-200
= 345-200
= 145
Therefore, the least number of 6th graders who want to take part in both classes is 145.
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A urvey of 100 tudent wa taken concerning their knowledge of foreign
language. The reult were a follow: How many tudent do NOT know any of
the three language?
30 know French
19 know German
16 know Spanih
2 know both French and Spanih
12 know both French and German
7 know both German and Spanih
8 Know all three language
There are 48 such students who did not know any of the three languages.
Given,
Since we have given that
Number of students were taken for survey n(U)= 100
Number of students who know French n(F) = 30
Number of students who know German n(G) = 19
Number of students who know Russian n(R) = 16
Number of students who know both French and Russian n(F∩ R) = 11
Number of students who know both German and French n(G ∩ F) = 12
Number of students who know both Russian and German n(R ∩ G) = 6
Number of students who know all three languages = 4
So, n(F∪G∪R)=n(F)+n(G)+n(R)-n(F∩G)-n(F∩R)-n(G∩R)+n(F∩G∩R)
n(F∪G∪R)=30+19+16-12-11-6+4
n(F∪G∪R)=52
So, the number of students who do not know any of the three languages is
[tex]n ( F ∩ G ∩ R )' = n (U) - n ( F ∩ G ∩ R )\\n ( F ∩ G ∩ R )' = 100- 52\\\\n ( F ∩ G ∩ R )' = 48[/tex]
Hence, there are 48 such students who did not know any of the three languages.
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Review the process chart given below. Assume that an ankle injury patient is willing to pay for both operation and inspection steps. Which of these statements is true? a. Value-added time is less than 50% of cycle time. b. Value-added time is more than 50% of cycle time. c. Value-added time is exactly 50% of the time.
If an ankle injury patient is willing to pay for both operation and inspection steps, Value-added time is less than 50% of cycle time
The ankle injury is under 1.5 times as much pressure with each stride .
In an avergae we travel 1000 miles on foot annully.
Over 14.2 million visits to doctors is due to ankle injuries every year.
However only 15% of the total injuries results in fractures.
Therefore, if an ankle injury patient is willing to pay for both operation and inspection steps, the statements which is true is Value-added time is less than 50% of cycle time
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What are the parts of graph of a rational function?.
The parts of graph of a rational function is the asymptotes and the intercepts of the graph.
The graph of a rational function is a hyperbola
The asymptote is a line or curve that acts as the limit of another line or curve. For example, a descending curve that approaches but does not reach the horizontal axis is said to be asymptotic to that axis, which is the asymptote of the curve whereas the intercept of the graph is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis
Therefore, The asymptotes and the intercepts of the graph are the parts of graph in case of a rational function.
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i walk around the perimeter of a regular hexagonal ornamental pond. Through how many degrees do I turn at each corner? and altogether?
The number of degrees of each turn made in the regular hexagonal pond is: 120°.
Altogether is 720°.
What is a Hexagonal Shape?A hexagonal shape is a six (6) sided polygon that has 6 interior angles.
The sum of all interior angles of an x-sided polygon can be calculated as:
(n - 2)180.
To find the sum of all the interior angles of the hexagonal pond, substitute the n = 6 into (n - 2)180:
(6 - 2) × 180
= 4 × 180
= 720°
The measure of each interior angle of the hexagonal pond = 720/6 = 120°.
Therefore, it implies that, you made 120 degrees turn at each corner, and altogether, you made 720°.
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Let n be the largest integer for which 14n has exactly 100 digits. Counting from right to left, find the 68th digit of n
Counting from right to left, find the 68th digit of n is 10.
An integer, is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers that are not integers are some examples.
The largest integer with exactly 100 digits is the integer that consists of 100 copies of the digit 9.
This integer is equal to 10100 = 10
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