The probability of drawing a 5 from a randomly chosen card from the set of cards with numbers 2, 3, 4, 5, and 6 is 20%.
This is because there is only one card with a 5 out of a total of five cards, so the probability of selecting the 5 card is 1/5, or 0.2, which is equivalent to 20%.
The formula for calculating probability is the number of favorable outcomes divided by the total number of possible outcomes. In this case, the favorable outcome is drawing the 5 card, and the total number of possible outcomes is the number of cards in the set, which is 5. Therefore, the probability of drawing a 5 is 1/5 or 0.2 or 20%.
The probability of drawing a 5 is independent of any previous draws or future draws, assuming the cards are being drawn randomly and with replacement.
Learn more about probability here:
https://brainly.com/question/30034780
#SPJ4
I need help on all of these problems
Answer:
1.143
0.6691
Step-by-step explanation:
8/7=1.143
cos48=0.6691306=0.6691
dwight schrute is the top salesman at dunder mifflin paper company. assume that the number of new clients that dwight signs is a poisson distributed random variable. on average, he signs 3.7 new clients a week. what is the probability that on a randomly selected week, dwight signs 6 new clients? round your answer to four decimal places (include a zero if necessary). what is the probability that on a randomly selected week, dwight signs at least 3 new clients? round your answer to four decimal places (include a zero if necessary).
a) The probability that Dwight signs 6 new clients in a randomly selected week is approximately 0.1047
b) The probability that Dwight signs at least 3 new clients in a randomly selected week is approximately 0.7227.
Let X be the number of new clients that Dwight signs in a randomly selected week. Since X follows a Poisson distribution with an average rate of 3.7 new clients per week, we can write:
P(X = x) = [tex](e^{-\lambda} \times \lambda ^x)[/tex] / x!, x = 0, 1, 2, ...
where λ is the average rate and e is the mathematical constant e ≈ 2.71828.
a) Probability that Dwight signs 6 new clients:
To calculate this probability, we need to substitute x = 6 and λ = 3.7 into the above formula:
P(X = 6) = ([tex]e^{-3.7}[/tex] x 3.7⁶) / 6! ≈ 0.1047
b) Probability that Dwight signs at least 3 new clients:
To calculate this probability, we need to sum the probabilities of signing 3, 4, 5, 6, and so on, new clients. Since the Poisson distribution is a discrete probability distribution, we can use the cumulative distribution function (CDF) to compute this probability:
P(X ≥ 3) = 1 - P(X < 3) = 1 - P(X = 0) - P(X = 1) - P(X = 2)
Substituting λ = 3.7 into the Poisson probability formula, we get:
P(X = 0) = [tex]e^{-3.7}[/tex] x 3.7⁰ / 0! ≈ 0.0240
P(X = 1) = [tex]e^{-3.7}[/tex] x 3.7¹ / 1! ≈ 0.0890
P(X = 2) = [tex]e^{-3.7}[/tex] x 3.7² / 2! ≈ 0.1643
Therefore,
P(X ≥ 3) = 1 - 0.0240 - 0.0890 - 0.1643 ≈ 0.7227
To know more about probability here
https://brainly.com/question/11234923
#SPJ4
Find the value of p for which the graph of f has exactly one point with a gradient of zero.
The value p = 1/2 + √(3)/2 does give us exactly one point with a gradient of zero.
What is quadratic equation?A quadratic equation, or sometimes just quadratics, is a polynomial equation with a maximum degree of two. It takes the following form:
ax² + bx + c = 0
To find the value of p for which the graph of f has exactly one point with a gradient of zero, we need to find the derivative of f(x) and set it equal to zero.
First, we can simplify f(x) by factoring out 4x:
f(x) = 4x(x + p/(4x+4))
Now, we can find the derivative of f(x):
f'(x) = 4(x + p/(4x+4)) + 4x(1 - p/(4x+4)²)
To find the point(s) where f'(x) = 0, we set it equal to zero and solve for x:
4(x + p/(4x+4)) + 4x(1 - p/(4x+4)²) = 0
Simplifying and multiplying through by (4x+4)²:
16x³ + 32px² + 16px - 16p = 0
Dividing through by 16x:
x² + 2px + p - 1 = 0
Now, we can use the discriminant of this quadratic equation to determine the value of p that gives exactly one point with a gradient of zero. The discriminant is:
b² - 4ac = (2p)² - 4(1)(p-1) = 4p² - 4p + 4 = 4(p² - p + 1)
For the graph of f to have exactly one point with a gradient of zero, the discriminant must be equal to zero, because that means there is only one value of x that satisfies f'(x) = 0. So, we set the discriminant equal to zero and solve for p:
4(p² - p + 1) = 0
p² - p + 1 = 0
Using the quadratic formula:
p = (1 ± √(1 - 4))/2 = 1/2 ± √(3)/2
So, the two possible values of p for which the graph of f has exactly one point with a gradient of zero are:
p = 1/2 + √3)/2
p = 1/2 - √(3)/2
Note that we should check that these values of p actually give us a point with a gradient of zero. If we substitute each value of p back into the derivative f'(x), we get:
When p = 1/2 + √(3)/2:
f'(x) = 4(x + (1/2 + √(3)/2)/(4x+4)) + 4x(1 - (1/2 + √(3)/2)/(4x+4)²)
Simplifying, we get:
f'(x) = (16x³ - 8x² + (4√(3) - 4)x + 4√(3) - 4)/(4(x+1)²(x+1+√(3)))
We can see that the denominator is always positive, so the gradient of f can only be zero when the numerator is zero. To find the value of x that satisfies this, we need to solve the cubic equation:
16x³ - 8x² + (4√(3) - 4)x + 4√(3) - 4 = 0
Using numerical methods, we find that there is only one real root, which is approximately x = 0.265. Therefore, the value p = 1/2 + √(3)/2 does give us exactly one point with a gradient of zero.
Learn more about quadratic equation on:
https://brainly.com/question/1214333
#SPJ1
Traffic planning the lincoln memorial in washington dc is surrounded by a circular drive
The polynomial equation for the area A of the space between the two concentric circles is [tex]A = 20π(r - 5)[/tex].
To find the equation for the area between two concentric circles, we need to subtract the area of the smaller circle from the area of the larger circle. Let the radius of the outside circle be r and the radius of the inside circle be r-10. Then, the area A between the two circles is given by:
[tex]A = πr^2 - π(r-10)^2[/tex]
Expanding and simplifying, we get:
[tex]A = πr^2 - π(r^2 - 20r + 100)[/tex]
[tex]A = πr^2 - πr^2 + 20πr - 100π[/tex]
[tex]A = 20πr - 100π[/tex]
[tex]A = 20π(r - 5)[/tex]
The National Park Service may want to change the layout of Lincoln Circle to accommodate increased traffic flow or to improve pedestrian safety. The new design with two concentric circles can help to organize traffic better by separating different types of vehicles or controlling speeds. It may also provide additional space for parking or public events. The impact of any changes on the surrounding community and environment, as well as the cost and feasibility of implementation. Proper planning and consultation with stakeholders can help to ensure that the new design meets the needs of all parties involved.
The complete question is: TRAFFIC PLANNING The Lincoln Memorial in Washington, D.C., is surrounded by a circular drive called Lincoln Circle. Suppose the National Park Service wants to change the layout of Lincoln Circle so that there are two concentric circular roads. Write a polynomial equation for the area A of the space between the roads if the radius of the inside road is 10 meters less than the radius of the outside road.
Learn more about polynomial here:
https://brainly.com/question/11536910
#SPJ4
In scientific notation, a number is written as the base number times ten raised to a power. This base number is known as the significand, and sometimes also by what other term, which is also used for the fractional part of a common logarithm?
In scientific notation, a number is written as the base number times ten raised to a power. The base number, known as the significand, is also referred to as the mantissa.
The term mantissa is used for the fractional part of a common logarithm as well.
The mantissa is the fractional part of a logarithm. In the context of scientific notation, the mantissa refers to the base number, which is multiplied by 10 raised to a certain power to represent a number.
In other words, the mantissa is the significant digits of a number, excluding the leading and trailing zeros, expressed as a decimal fraction between 1 and 10. For example, in the number 3.24 x 10^5, the mantissa is 3.24.
Learn more about mantissa,
https://brainly.com/question/30708908
#SPJ11
he American Housing Survey is done every year by the Bureau of the Census. Data from the 2003 survey can be used to find the distribu- tion of occupied housing units (this includes apartments) by number of rooms. Results for the whole U.S. are shown below, separately for "owner- occupied" and "renter-occupied" units. Draw a histogram for each of the two distributions. (You may assume "10 or more" means 10 or 11; very few units have more than 11 rooms.) (a) The owner-occupied percents add up to 100.2% while the renter- occupied percents add up to 100.0%. Why? (b) The percentage of one-room units is much smaller for owner-occupied housing. Is that because there are so many more owner-occupied units in total? Answer yes or no, and explain briefly c) Which are larger, on the whole: the owner-occupied units or the renter-occupied units?
The American Housing Survey is conducted annually by the Bureau of the Census to gather data on the distribution of occupied housing units in the United States.
Using data from the 2003 survey, the distribution of occupied housing units by the number of rooms can be found. To visualize this data, histograms can be drawn separately for owner-occupied and renter-occupied units.
It is important to note that "10 or more" mean 10 or 11, as very few units have more than 11 rooms.
(a) The This could be due to rounding errors or differences in sample sizes between the two groups.
(b) The percentage of one-room units is much smaller for owner-occupied housing. This is not necessarily because there are more owner-occupied units in total, but could be due to differences in the length preferences and financial means of renters versus owners.
(c) It is unclear which group, on the whole, has larger units without additional information about the distribution of rooms.
To know more about length click here
brainly.com/question/30625256
#SPJ11
1.)
A jet took off from a runway and flew a constant 35° upward. What is the height of the jet after traveling due east 15,000ft from the point of liftoff?
2.)
Use Pythagorean theorem and find the distance the jet has traveled. (the hypotenuse)
a^2 + b^2 = c^2
Please show work in Desmos
tan(35) = 0.70020753821 = Perpendicular(BC)/Base(AB)
0.70020753821 = BC/15000
BC = 10503 ft.
B)AC² = AB² + BC²
AC = √15000² + 10503²
AC = √225000000 + 110313009
AC = √335313009
AC = 18311.5 ft
10503 ft is the height of the jet after traveling due east 15,000ft from the point of liftoff and 18311.5 ft is the distance the jet has traveled.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Given that a jet took off from a runway and flew a constant 35° upward
We have to find the height of the jet after traveling due east 15,000ft from the point of liftoff
We know that tan is the ratio of opposite side and adjacent side
tan(35) = BC/15000
0.70020753821 = BC/15000
BC = 10503 ft.
B) By pythagoras theorem we find the distance the jet has traveled.
AC² = AB² + BC²
AC = √15000² + 10503²
AC = √225000000 + 110313009
AC = √335313009
AC = 18311.5 ft
Hence, 10503 ft is the height of the jet after traveling due east 15,000ft from the point of liftoff and 18311.5 ft is the distance the jet has traveled.
To learn more on trigonometry click:
https://brainly.com/question/25122835
#SPJ2
don conducted a survey of two groups (n subscript 1 equals 50 comma space n subscript 2 space end subscript equals 50 )of students that recently graduated from private and public colleges. he found that the mean debt for the students who attended private college was $26,600, while those who attended public colleges had a mean debt of $24,400. don wants to see if the difference in mean debt is statistically significant. what should don state for the null hypothesis?
Don's null hypothesis is that there is no statistically significant difference between the mean debt of students who attended private college and the mean debt of students who attended public colleges, represented as H₀: μ₁ - μ₂ = 0
The null hypothesis (H0) is a statement of "no difference" or "no effect" and is typically represented as "there is no statistically significant difference between the mean debt of students who attended private college and the mean debt of students who attended public colleges." Therefore, in this case, Don's null hypothesis can be stated as
H₀: μ₁ - μ₂ = 0
where μ₁ represents the population mean debt for students who attended private college, and μ₂ represents the population mean debt for students who attended public colleges.
Learn more about null hypothesis here
brainly.com/question/19263925
#SPJ4
the following estimated regression equation is based on observations. the values of sst and ssr are and , respectively. a. compute (to 3 decimals). b. compute (to 3 decimals). c. comment on the goodness of fit. the estimated regression equation - select your answer - .
The coefficient of determination (R²) for the given regression model is 0.974
The coefficient of determination, R², is a measure of how well the regression line fits the data. It represents the proportion of the total variation in the dependent variable that is explained by the independent variables in the regression model.
To compute R², we first need to calculate the sum of squares total (SST), which is the total variation in the dependent variable
SST = ∑(yi - y)²
where yi is the ith observed value of the dependent variable, and y is the mean of the dependent variable.
In this case, SST = 1805, as given.
Next, we need to calculate the sum of squares regression (SSR), which represents the variation in the dependent variable that is explained by the independent variables
SSR = ∑(yi - y)²
where yi is the ith observed value of the dependent variable, and y is the predicted value of the dependent variable based on the regression model.
In this case, SSR = 1760, as given.
Finally, we can compute R² as
R² = SSR/SST
Substituting the values given, we get:
R² = 1760/1805
R² = 0.974
Learn more about coefficient of determination here
brainly.com/question/28975079
#SPJ4
The given question is incomplete, the complete question is:
The following estimated regression equation based on 30 observations was presented. y = 17.6 + 3.8x₁ – 2.3x₂ + 7.6x₃ + 2.7x₄ The values of SST and SSR are 1805 and 1760, respectively.
Compute R²
A rectangular piece of metal has an area of 56 square centimeters. Its perimeter is 30 centimeters. What are the dimensions of the piece?
The dimensions of the rectangle are L = 7 cm and W = 8 cm.
The perimeter of a two-dimensional shape is the space surrounding its outer edge. It is the sum of the lengths of the shape's sides.
The perimeter of a rectangle, for instance, is equal to the total length of its four sides. The circumference of a circle, also known as the perimeter, is the distance around the circle's edge.
Let's assume that the length and width of the rectangular piece of metal are L and W, respectively. Then we know that:
The area of the rectangle is 56 cm², so we have:
L x W = 56 (Equation 1)
The perimeter of the rectangle is 30 cm, so we have:
2L + 2W = 30 (Equation 2)
We can solve this system of equations by using substitution or elimination. Here, we'll use substitution:
From Equation 2, we can isolate one of the variables. For example, we can isolate L:
2L + 2W = 30
2L = 30 - 2W
L = 15 - W (Equation 3)
Now we can substitute this expression for L into Equation 1:
L x W = 56
(15 - W) * W = 56
Expanding this equation, we get:
15W - W² = 56
Rearranging terms:
W² - 15W + 56 = 0
We can factor this quadratic equation as:
(W - 7)(W - 8) = 0
This gives us two solutions for W: W = 7 or W = 8. We can check each solution to see which one is valid.
If W = 7, then from Equation 3, we have:
L = 15 - W = 15 - 7 = 8
So the dimensions of the rectangle are L = 8 cm and W = 7 cm.
If W = 8, then from Equation 3, we have:
L = 15 - W = 15 - 8 = 7
So the dimensions of the rectangle are L = 7 cm and W = 8 cm.
To know more about perimeter follow
https://brainly.com/question/29274201
#SPJ1
Emily generated 10,000 ramdom digits between 0 and 10. Here are results:
Answer:
ok
Step-by-step explanation:
You took the picture and then wrote a sentence
raise 5 to the 4th power, then find the difference of the result and y
Answer: 625
Step-by-step explanation:
I'm not sure what you mean by the result of y, however...
5^4 = 625
I'm not sure if this is helpful, sorry
Find x° y° z° ( p + 10 ° ) ,p° ( p + 20 °)
Answer:
x° = 50°
y° = 70°
z° = 60°
p° = 50°
(p + 10)° = 60°
(p + 20)° =70°
Step-by-step explanation:
Angles with measurements (p + 20), p and (p + 10) degrees are all on the same line. Therefore these three angles are supplementary angles. In other words the sum of these angles = 180°
Plugging in the expressions for these angles we get
(p + 20 ) + p + (p + 10) = 180°
3p + 30 = 180
Subtracting 150 from both sides,
3p = 180 - 30 = 150
p = 150/3 = 50
x is a vertically opposite angle to p.
Therefor x = p = 50°
y is vertically opposite and equal to p + 20
y = p + 20 = 50 + 20 = 70°
z is vertically opposite and equal to p + 10
z = p + 10 = 50 + 10 = 60°
What is the difference between 33ft^2 and 33ft^3
Explanation:
[tex]33ft^2[/tex] is the area of a 2D figure.
[tex]33ft^3[/tex] is the volume of a 3D object.
ft^2 = area
ft^3 = volume
Evaluate -2.1 x 5
A -2.9 B 2.9 C -10.5 D 10.5
Answer:
bro c. is the corrent ans of this que
I need the answer and explanation for this geometry problem. (this is not a live quiz, test, or exam question, just to clarify)
If we select two cards from "M,A,T,H,I,S,F,U,N' with replacement, then the probability of picking a T and N is (a) 1/81.
The cards are to be selected from {M,A,T,H,I,S,F,U,N},
So, there are total of 9 cards to choose from, and we are selecting two cards with replacement which means that we pick one card, replace it, and then pick another card.
The probability of picking a T on the first draw is : P(T) = 1/9, and
The probability of picking an N on the second draw (after replacing the first card) is also : P(N) = 1/9.
So, the probability of selection of both T and N is written as :
P(T and N) = P(T) × P(N) = (1/9) × (1/9) = 1/81,
Therefore, The correct option is (a).
Learn more about Probability here
https://brainly.com/question/14679000
#SPJ1
HELP NEEDED!!!
Using the following table, what is the term that best describes the entry of 0.31?
Do you prefer dancing or playing sports?
Students | Playing sports | Dancing | Row totals
Male students | 0.25 | 0.27 | 0.52
Female students | 0.17 | 0.31 | 0.48
Column totals | 0.42 | 0.58 | 1
A.Joint frequency
B.Joint relative frequency
C.Marginal frequency
D.Marginal relative frequency
bekah has exactly three brass house number digits: $2$, $3$ and $5$. how many distinct numbers can she form using one or more of the digits?
There are seven elements in the set S, which represents the total number of distinct numbers we can form using one or more of the digits.
To find out how many distinct numbers we can form using these digits, we need to consider all possible combinations of digits. We can use one, two, or all three digits to form a number.
If we use only one digit, we can form three distinct numbers: 2, 3, and 5.
If we use two digits, we can form three distinct two-digit numbers: 23, 25, and 35. We cannot form the number 32 because we do not have the digit 2 available twice.
If we use all three digits, we can form only one three-digit number: 235.
Therefore, in total, we can form 7 distinct numbers using one or more of the digits 2, 3, and 5.
Mathematically, we can represent the solution as follows:
Let S be the set of all distinct numbers we can form using one or more of the digits 2, 3, and 5.
Then, S = {2, 3, 5, 23, 25, 35, 235} = 7
To know more about digit here
https://brainly.com/question/30142622
#SPJ4
you have a coupon good for $3 off the price of a large pizza. you also get a 10% discount if you show your student ID. how much more will you pay for a $25 large pizza if the cashier applies the coupon first?
Answer:
Step-by-step explanation:
Coupon gives $3 off
$25 - $3 = $22
After first coupon, the pizza price will be $22
10% dicscount
90% of 25 = 22.5
22.50 - 3 = 19.50
After first coupon and discount, the pizza price will be $19.50
a regression analysis involved 8 independent variables and 99 observations. the critical value of t for testing the significance of each of the independent variable's coefficients will have
Critical value of t for testing the significance of each of the independent variable's coefficients will have 90 degree of freedom.
We are given the following parameters or data or information
"A regression analysis involved 8 independent variables", " 99 observations. "
Number of observations = 99
Number of independent variables = 8
In regression, the critical value t for testing the significance of variable's coefficients has the number of degrees of freedom formula which is (number of observations) - (number of independent variables + 1).
To determine the critical value of t for testing the significance of each of the independent variable's coefficient.
Hence, the formula below will used in Calculating or in the determination of the degree of freedom;
Degree of freedom = (number of observations) - (number of independent variables + 1).
Thus, slotting bin the values into the formula above, we have;
The degree of freedom = 99 - (8 +1) = 90.
Learn more about degree of freedom here :-
https://brainly.com/question/31424137
#SPJ4
21.12 divided by 1.2
The requried 21.12 divided by 1.2 is 17.6.
To divide 21.12 by 1.2, we can use long division.
The first step is to place 1.2 outside of the division bracket and 21.12 inside. We divide 1.2 into 2, which gives 1.
We write this above the 2 and subtract, which gives us 0.8. We then bring down the next digit, 1, to get 8.
We divide 1.2 into 8, which gives 6 with a remainder of 2. We bring down the next digit, 1, and get 21.
We divide 1.2 into 21, which gives 17 with a remainder of 6. So the final answer is 17.6.
Thus, the requried 21.12 divided by 1.2 is 17.6.
Learn more about divide here:
https://brainly.com/question/15381501
#SPJ1
Zena used a probability simulator to roll a 12-sided number cube 100 times. Her results are shown in the table below:
Answer:
18/100
Step-by-step explanation:
she has rolled the number 1 eighteen times out of the 100 tries
a farmer wants to test the effectiveness of a pest control method in allowing strawberry blooms to yield marketable strawberries. out of a random sample of 100 blooms, 77 yield marketable strawberries. specifically, he wants to test know if there is sufficient evidence that more than two-thirds of all blooms grown with this pest control method end up as marketable strawberries. what is the null hypothesis for a test to answer this question? question 8 options:
The null hypothesis for testing the effectiveness of a pest control method in allowing strawberry blooms to yield marketable strawberries is that the proportion of all blooms grown (i.e., 0.67).
The null hypothesis is a statistical hypothesis that assumes there is no significant difference or relationship between two or more variables or populations being studied.
The null hypothesis is a statement of no effect or no difference. In this case, the null hypothesis is that the proportion of all blooms grown with the pest control method that yield marketable strawberries is equal to or less than two-thirds (i.e., 0.67).
Therefore, the null hypothesis can be stated as follows:
H0: p ≤ 0.67
Where p represents the population proportion of blooms that yield marketable strawberries.
Learn more about null hypothesis here
brainly.com/question/19263925
#SPJ4
What is the additive identity matrix for A= 127349568
Answer: B
Step-by-step explanation:
For matrix addition to happen,
1) the 'number of rows' of all matricies have to be same.
2) the 'number of columns' of all matricies have to be same.
So the answer should be <B>.
simplifly 63 divided by 9 multiplied by 7 + 2
Answer:
63
Step-by-step explanation:
(63/9) x (7 + 2)
= (63/9) x 9
= (63 x 9/9)
= 63 x 1
= 63
a square has one dimension increased by 4 feet and another dimension decreased by 2 feet. If the resulting rectangle has an area of 72 square feet, which of the following equations could be used to solve for the squares original side length, x?
[tex]x^{2}[/tex] + 2x - 80 = 0 will be the equation that could be used to solve for the square's original side length, x.
Let's assume that the original side length of the square is x feet.
According to the problem, one dimension of the rectangle (let's call it length) is x + 4 feet, and the other dimension (let's call it width) is x - 2 feet. The area of the rectangle is given as 72 square feet.
We can write an equation to represent this information as:
(x + 4)(x - 2) = 72
Simplifying the left side of the equation, we get:
[tex]x^{2}[/tex] + 2x - 8 = 72
Bringing all the terms to one side of the equation, we get:
[tex]x^{2}[/tex] + 2x - 80 = 0
This is a quadratic equation that we can solve using the quadratic formula:
x = (-2 ± [tex]\sqrt{2^{2}-4(1)(-80)}[/tex] ) / 2(1)
x = (-2 ± [tex]\sqrt{324}[/tex]) / 2
x = (-2 ± 18) / 2
The two possible values of x are:
x = 8 or x = -10
Since the side length of a square cannot be negative, we can disregard the solution x = -10. Therefore, the original side length of the square was x = 8 feet.
Answer: (x + 4)(x - 2) = 72 or [tex]x^{2}[/tex] + 2x - 80 = 0, with a solution of x = 8 feet.
To learn more about side length here:
https://brainly.com/question/24584437
#SPJ1
Jacque is using a soup can for a school project and wants to paint it. If the can is 11 cm tall and has a diameter of 9 cm, at least how many square centimeters of paint is needed? Approximate using π = 3.14.
The amount of paint needed to paint a soup can = 438.03 cm²
The correct answer is an option (D)
We know that the formula for the surface area of the cylinder is :
A = 2πrh + 2πr²
Here, the diameter of the can is 9 sm
So, the radius of the can would be,
⇒ r = d/2
⇒ r = 9/2
⇒ r = 4.5 cm
And the height of the can is h = 11 cm
Since the can is cylindrical, we use above formula of surface area of the cylinder to find the amount of paint needed.
Using above formula,
⇒ A = 2πrh + 2πr²
⇒ A = (2 × π × 4.5 × 11) + (2 × π × (4.5)²)
⇒ A = 311.02 + 127.01
⇒ A = 438.03 cm²
This is the required amount of paint needed to paint a soup can.
Therefore, the correct answer is an option (D)
Learn more about the surface area of the cylinder here:
brainly.com/question/31178158
#SPJ1
Please help!! I'm super confused about this question..
CB² + AC² = AB (BD + AD) ---------> segment addition postulate
BD + AD = AB -----------> substitution
CB² + AC² = AB(AB) -----------> Factor
CB² + AC² = AB² -----------> multiply
What is the correct statement that matches the proof?
The statement that matches the steps of the proof is determined as follows;
The given options are;
factorsegment addition postulatesubstitutionmultiplyThe first proof and its correct statement is determined as;
CB² + AC² = AB (BD + AD) ---------> segment addition postulate
The second proof and its correct statement is determined as;
BD + AD = AB -----------> substitution
The third proof and its correct statement is determined as;
CB² + AC² = AB(AB) -----------> Factor
The fourth proof and its correct statement is determined as;
CB² + AC² = AB² -----------> multiply
Learn more about segment addition postulate here: https://brainly.com/question/2134445
#SPJ1
Devin says if a triangle has the side lengths of 6, 6√3, and 12, then the triangle is a 30- 60-90 triangle. Glenn says if a triangle has the side lengths of 7, 7√3, and 49, then the triangle is a 30- 60-90 triangle.
Who is correct and why?
A. Both because the middle side length is the square root of 3 times the smallest side.
B.Neither because the middle side length is the square root of 3 times the largest side, not the smallest side.
C. Devin because the second side length is the square root of 3 times the measure of the smallest side length and the largest side is twice the smallest side.
D.Glenn because the second side length is the square root of 3 times the measure of the smallest side length and the largest side is the square of the smallest side.
Answer:
Step-by-step explanation:
30-60-90 triangles
30-60-90 triangles are right triangles whose acute angles are
3
0
∘
30
∘
30, degrees and
6
0
∘
60
∘
60, degrees. The sides in such triangles have special proportions:
A thirty-sixty-ninety triangle. The length of the shorter leg of the triangle is one half h units. The length of the longer leg of the triangle is square root three over two times h. The length of the hypotenuse of the triangle is h units.
A thirty-sixty-ninety triangle. The length of the shorter leg of the triangle is one half h units. The length of the longer leg of the triangle is square root three over two times h. The length of the hypotenuse of the triangle is h units.
[How can we find these ratios using the Pythagorean theorem?]
Want to learn more about 30-60-90 triangles? Check out this video.
45-45-90 triangles
45-45-90 triangles are right triangles whose acute angles are both
4
5
∘
45
∘
45, degrees. This makes them isosceles triangles, and their sides have special proportions:
A forty-five-forty-five-ninety triangle. The length of both legs are k units. The length of the hypotenuse of the triangle is square root of two times k units.
A forty-five-forty-five-ninety triangle. The length of both legs are k units. The length of the hypotenuse of the triangle is square root of two times k units.
[How can we find these ratios using the Pythagorean theorem?]
The special properties of both of these special right triangles are a result of the Pythagorean theorem.
so A is right. i hope
Devin because the second side length is the square root of 3 times the measure of the smallest side length, and the largest side is twice the smallest side. Glenn's claim is incorrect because his triangle's side lengths do not match the 30-60-90 ratio, unlike Devin's triangle, which satisfies the conditions of a 30-60-90 triangle.
A 30-60-90 triangle has specific side length ratios: the sides opposite the angles measuring 30 degrees, 60 degrees, and 90 degrees are in the ratio 1:√3:2. Let's analyze the claims made by Devin and Glenn:
Devin's claim:
Devin states that a triangle with side lengths of 6, 6√3, and 12 is a 30-60-90 triangle. To verify this, we need to check if the side lengths satisfy the 30-60-90 ratio. If we divide the longest side by 2, we get 12/2 = 6, which matches the length of the shortest side. Also, the middle side (6√3) is indeed √3 times the length of the shortest side (6). Thus, Devin's claim is correct, and the triangle with side lengths 6, 6√3, and 12 is a 30-60-90 triangle.
Glenn's claim:
Glenn states that a triangle with side lengths 7, 7√3, and 49 is a 30-60-90 triangle. Again, we need to check if the side lengths satisfy the 30-60-90 ratio. However, upon examination, we find that dividing the longest side by 2 (49/2) does not result in the length of the shortest side (7). Also, the middle side (7√3) is not √3 times the length of the shortest side (7). Therefore, Glenn's claim is incorrect, and the triangle with side lengths 7, 7√3, and 49 is not a 30-60-90 triangle.
Hence the correct option is (c).
To know more about triangle here
https://brainly.com/question/8587906
#SPJ2
how many total pounds of tnt are required to create an abatis that has 72 trees with an average diameter of 30 inches?
It would take approximately 176,369 pounds of TNT to destroy an abatis made of 72 trees with an average diameter of 30 inches, assuming an average height of 20 feet.
The formula for the volume of a cylinder is V = πr^2h. In this case, we can use the average radius of 15 inches and the average height of 240 inches to estimate the total volume of all 72 trees:
Total volume of all 72 trees = 72 x V
Total volume of all 72 trees = 72 x 169,646
Total volume of all 72 trees ≈ 12,214,832 cubic inches
In this equation, we need to know the density of wood and the REF of TNT. The density of wood can vary depending on the species, but we can use an average value of 0.5 grams per cubic centimeter (g/cm^3). The REF of TNT is 1, by definition. The factor of 0.8 in the equation accounts for losses due to fragmentation and other factors.
Converting the units of volume and density to match, we get:
Total volume of all 72 trees ≈ 200,000,000 cubic centimeters
Density of wood = 0.5 g/cm³
Plugging these values into the equation, we get:
Amount of TNT required = (Total volume of all 72 trees x Density of wood x 0.8) / REF
Amount of TNT required = (200,000,000 x 0.5 x 0.8) / 1
Amount of TNT required = 80,000,000 grams
To convert grams to pounds, we divide by 453.592, which is the number of grams in a pound:
Amount of TNT required = 80,000,000 / 453.592
Amount of TNT required ≈ 176,369 pounds
To know more about average here
https://brainly.com/question/16956746
#SPJ4
