Final answer:
The measure of the angle of rotation that will map vertex S onto vertex U in a regular pentagon is 72 degrees.
Explanation:
The student is asking about an angle of rotation in a geometric context, specifically concerning mapping one vertex of a regular pentagon onto another through rotation about the center of the shape. In a regular pentagon, the angles between adjacent vertices are all equal, as it is a symmetrical shape. Since there are five vertices in a pentagon, you can divide the full rotation of 360 degrees by the number of vertices to find the angle of rotation that will map one vertex onto the next.
To map vertex S onto vertex U in a regular pentagon, you will need to rotate the pentagon by 360 degrees divided by 5 vertices, which is 72 degrees. Therefore, a rotation of 72 degrees around the center point X of the pentagon will map S onto U.
What is the volume of a cylinder with a diameter of 12 in. and a height of 7 in.?
Answer
Find out the volume of a cylinder .
To prove
Formula
[tex]Volume\ of\ cylinder = \pi r^{2}h[/tex]
Where r is the radius and h is the height.
As given
Diameter of 12 in. and a height of 7 in.
[tex]Radius = \frac{Diameter}{2}[/tex]
[tex]Radius = \frac{12}{2}[/tex]
Radius = 6 in
[tex]\pi = 3.14[/tex]
put all the values in the formula
[tex]Volume\ of\ cylinder = 3.14\times 6\times 6\times 7[/tex]
= 791.28 in³
Therefore the volume of the cylinder is 791 .28 in³ .
Graphic lesions to solve the system Y equals 1/3 X +6 and why equals 1/3 X +4
Lines b and c are parallel. What is the measure of <6?
m<6 = 45
m<6 = 54
m<6 = 117
m<6 = 126
Answer:
m<6 = 54
St,ep-by-step explanation:
Lines b and c are parallel.
13x +9 and 5x+9 are consecutive exterior angles.
Consecutive exterior angles are supplementary.
[tex]13x+9+5x+9= 180[/tex]
Now we solve for x. combine like terms
[tex]18x+18= 180[/tex]
Subtract 18 from both sides
[tex]18x=162[/tex]
Divide both sides by 18
x=9
So the value of x=9
angle 6 and 5x+9 are vertical opposite angles . they are equal
m<6= 5x+9
Plug in 9 for x
m<6= 5(9)+9=54
m<6 = 54
Answer:
m<6 = 54
Step-by-step explanation:
Rewrite the radicand as two factors, one of which is a perfect cube.
3/250
solve the equation 2 cos x + 1 = 0 , 0 <= x <= 2pi PLEASE HELP! WILL AWARD!
The solution of the given trigonometric expression is x = 2π/3.
Use the concept of trigonometric ratio defined as:
Trigonometric ratios depend on the value of the ratio of sides of a triangle which is right-angled and contains the values of all trigonometric functions.
The ratios of a right-angled triangle's sides with regard to a certain acute angle are known as it's trigonometric ratios.
The given expression is:
2 cos x + 1 = 0
Where,
0 ≤ x ≤ 2π
To solve it,
Subtract both sides,
2 cos x = - 1
Divide by 2 on both sides,
cos x = -1/2
Take cos inverse on both sides,
[tex]x = cos^{-1} (\frac{1}{2})[/tex]
Since cos(2π/3) = -1
x = 2π/3
Now since 2π/3 lies between 0 ≤ x ≤ 2π
Hence,
The solution of the given expression is x = 2π/3
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PROBABILITY PROBLEM! NEED HELP AND EXPLAIN/SHOW WORK
I think its B
A researcher finds a negative correlation between the total number of people driving for pleasure and the sales of electric cars.
Which variable is most likely the lurking variable that explains the correlation?
population
gas prices
amount of rainfall
water prices
The correct answer is:
gas prices
Explanation:
As the number of people driving for pleasure goes down, the sales of electric cars go up. This is likely due to gas prices. As gas prices go up, fewer people drive for pleasure and more people purchase electric cars. Both are ways to reduce the amount of money spent on gasoline.
The option 'gas prices' variable is most likely the lurking variable that explains the correlation.
Given that a researcher finds a negative correlation between the total number of people driving for pleasure and the sales of electric cars.
It is required to find which variable is most likely the lurking variable that explains the correlation.
What is correlation?It is defined as the relation between two variables which is a quantitative type and gives an idea about the direction of these two variables.
We have a negative correlation between:
The total number of people driving for pleasure and the sales of electric cars.
We know that the negative correlation means one variable decreases and as the other increases and vice versa.
If the sales of electric cars increase the total number of people driving for pleasure goes down.
This can happen if the gas prices go up fewer people drive for pleasure and more people buy an electric car.
Thus, the option 'gas prices' is correct.
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A man weighs 180 lb. He jogs a mile in 8 minutes. How many calories has he used up?
A man weighing 180 lb has burned approximately 100 calories by jogging one mile, based on the average estimate that jogging one mile burns almost 100 calories.
The question relates to the calculation of calories burned during exercise, specifically jogging. Based on the information provided that running or jogging one mile burns almost 100 calories, we can calculate the energy expenditure for a man weighing 180 lb who jogs a mile in 8 minutes.
Since the provided calories burned per mile is an average, the actual number might vary slightly based on individual metabolism and effort level, but it serves as a useful approximation.
To determine how many calories the man has used up, we can use the given information:
Running or jogging one mile burns almost 100 calories.The man jogs a mile, which means he has burned approximately 100 calories for that activity.Therefore, the man has burned approximately 100 calories during his 8-minute mile jog.
Rewrite in simplest radical form x56x16
What is the value of z in the equation 3z − 7 = 14? (4 points)
Answer:
7
Step-by-step explanation:
Amy owns a graphic design store. She purchases a new printer to use in her store.
The printer depreciates by a fixed rate of 14% per year. The function
V = 2,400(1 – 0.14)t can be used to model the value of the printer in dollars after
t years.
Question:
Part A: Explain what the parameter 2,400 represents in the equation of the function.
Part B: What is the factor by which the printer depreciates each year?
Part C: Amy also considered purchasing a printer that costs $4,000 and depreciates by 25% each year. Which printer will have more value in 5 years? Justify your answer by showing/explaining your work.
i really need help :( im working hard to get all my school work done and this one thing is making my head hurt :(
The parameter 2,400 in the depreciation function represents the initial value of Amy's printer. The printer depreciates by a factor of 0.86 each year. After calculations, the first printer has more value ($1,004.40) after 5 years compared to the second printer ($949.24).
Part A: The parameter 2,400 represents the initial purchase price or the original value of the printer that Amy owns in her graphic design store.
Part B: The factor by which the printer depreciates each year is 0.86 (which is calculated as 1 - 0.14, meaning the value retains 86% of its worth each subsequent year).
Part C: To compare which printer will have more value in 5 years, we need to calculate the future value of both printers using their respective depreciation rates:
First printer: V = 2,400(1 - 0.14)^5Second printer: V = 4,000(1 - 0.25)^5After calculating:
Value of the first printer after 5 years: V \\approx 2,400(0.86)^5 \\approx 2,400(0.4185) \\approx $1,004.40Value of the second printer after 5 years: V \\approx 4,000(0.75)^5 \\approx 4,000(0.2373) \\approx $949.24Therefore, the first printer will have more value after 5 years.
When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a constant amount each year for the next 6 years. at the end of the 6th year, the tree was \frac{1}{5} taller than it was at the end of the 4th year. by how many feet did the height of the tree increase each year?
use the distance formula and the pythagorean theorem to find the distance, to the nearest tenth, from T (4,-2) to (-2,3).
Difference between ellipse circle parabola and hyperbola equations
The solution is: these have a subtraction operation, the exact opposite ellipse.
What is parabola?The parabola is a plane curve which is mirror symmetrical and is approximately U-shaped. It fits several superficial different mathematical descriptions.
here, we have,
The equation of a circle is:
(x - h)² + (y - k)² = r²
The equation of a parabola is:
(x - h)² = 4p(y - k)
The equation of an ellipse is:
(x - h)²/ a² + (y - k)²/ b² = 1
where variables a and b and the two different measurements of the vertices
The equation of a hyperbola is:
(x - h)²/ a² - (y - k)²/ b² = 1 if it is with a horizontal transverse axis
(y - k)²/ b² - (x - h)²/ a² = 1 if it is with a vertical transverse axis
Notice these have a subtraction operation, the exact opposite ellipse.
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The area of a parallelogram is 3.36 square feet. the base is 2.8 feet. if the measures of the base and height are each doubled, find the area of the resulting parallelogram
A metal washer is made by cutting out a circle 13.2 mm in diameter from a larger circle. To the nearest tenth, what is the area of the washer?
The dollar amount (d) that erin earns varies directly as the number of hours (t) that she works. if she earns $206.25 in 25 hours, how many hours did she work if she earned $264?
Find the product. 4(−12)(−3) A) −144 B) −96 C) 144 D) 72
An airplane is sighted at the same time by two ground observers who are 5 miles apart and both directly west of the airplane. they report the angles of elevation as 14° and how high is the airplane? round to the nearest hundredth of a mile.
.48 divided by 9.23 rounded by nearest tenth
Johnny flips a coin three times. what is the probability he lands on heads every time
[tex] |\Omega|=2^3=8\\
|A|=1\\\\
P(A)=\dfrac{1}{8}=12.5\% [/tex]
The probability of picking two black marbles from a box at random without replacement is 1091 . The probability of drawing a black marble first is 514 . What is the probability of picking a second black marble, given that the first marble picked was black?
Final answer:
The probability of picking a second black marble, given that the first marble picked was black, is 1.
Explanation:
To find the probability of picking a second black marble, given that the first marble picked was black, we can use the formula for conditional probability: P(A|B) = P(A and B)/P(B).
In this case, A represents the event of picking a black marble on the second draw, and B represents the event of picking a black marble on the first draw.
We are given that P(B) = 514, and the probability of picking two black marbles without replacement is 1091. Therefore, P(A and B) = P(A|B) * P(B) = (1091/514) * (514/1091) = 1.
So, the probability of picking a second black marble, given that the first marble picked was black, is 1.
the rational roots of a polynomial function F(x) can be written in the form p/q,
where p is a factor of the constant term of the polynomial, and q is a factor of the leading coefficient
TRUE OR FALSE??
ANSWER
True
EXPLANATION
According to the Rational Roots Theorem,the rational roots of a polynomial function F(x) can be written in the form
[tex] \frac{p}{q} [/tex]
,
where p is a factor of the constant term of the polynomial, and q is a factor of the leading coefficient.
The polynomial must be written in standard form.
This means the polynomial must be written in descending powers of x.
The leading term is the first term of a polynomial written in standard form.
The constant term is the term independent of x.
The temperature has been going down at a constant rate. In 3 hours it went down 15 degrees. Which expression best shows the temperature change each hour? A.−15⋅−3 B. 15⋅3 C. −15÷3 D.15÷3
Write the sum in sigma notation. 5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 + 45 + 50
Please mark brainliest
The sum in sigma notation for the sequence as follows:
From
5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 + 45 + 50
first term=5
common difference=5
number of terms=10
n=nth term
therefore the total will be:
(i=2 to 10)∑(5(n-1)+5
Which of the following sets shows all the numbers from the set {2, 3, 4, 5} that are part of the solution to the inequality 4n + 6 > 22?
Answer:
the answer is
{2, 3, 4}
Step-by-step explanation:
if 5 is the only one that works and it has to be inequality so
{2, 3, 4} can be the only answer
helpppp! pls! 10 points
four-barrel of colored marbles you randomly select three blue to Yellow 7 red eight green and two purple marbles. find the experimental probability of randomly selecting either green or purple marble
Standard number cube is rolled 180 times. Predict how many times 3 or 5 will be the result
The movie open the other day. So far 500,000 people have seen it. the producers of the movie needed to know if the people liked it. a random sample of 8000 people were asked as they were leaving the theater if they like the movie. of those interviewed 4,200 enjoyed the movie. predict the total number of people who have enjoyed the movie.
Jamestown Builders has a development of new homes. there are 6 different floor plans 7 exterior color than an option of either one car or two car garage . How many choices are there for one home?
if no digit may be used more than once how many 5 digits can be formed using only three digits. 8 1 2 5 and7?
The answer provides the experimental probability of selecting green or purple marbles, predicts the occurrences of rolling 3 or 5 on a number cube, and estimates the total number of people who enjoyed the movie.
Experimental Probability Calculation: In the given scenario, there are 8 green marbles and 2 purple marbles, making a total of 10 marbles. The probability of selecting a green or purple marble is the sum of the individual probabilities, which is (8/10) + (2/10) = 0.8.
Expected Outcome of Rolling a Number Cube: Since a standard number cube has numbers 1 to 6, each number has an equal probability of 1/6. Predicting how many times 3 or 5 will be rolled out of 180 rolls can be calculated by (1/6 + 1/6) x 180 = 60 times each for 3 and 5.
Total Number of People Who Enjoyed the Movie: Based on the sample data, 4,200 out of 8,000 people enjoyed the movie. Extrapolating this to the total viewers, the predicted number of people who enjoyed the movie would be: (4,200/8,000) x 500,000 = 262,500 people.
Write an inequality for the given statement: The sum of –18 and a number is more than 22. A. 18 – n < 22 B. 18 – n > 22 C. –18 + n < 22 D. –18 + n > 22
Ernesto tried to determine the solution for the system of equations using substitution. His work is shown below. x – y = 7 3x – 2y = 8 Step 1: x = y + 7 Step 2: 3(y + 7) – 2y = 8 Step 3: 3y + 7 – 2y = 8 Step 4: y + 7 = 8 Step 5: y = 1