The number of laps per minute is equal to 1.25 laps.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, time is 4 minutes and the number of laps is 5.
We can calculate as Number of laps per minute = Total number of laps/Number of minutes
= 5/4
= 1.25 laps
Hence, the number of laps per minute is 1.25 laps.
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A 2015 Gallup survey asked respondents to consider several different foods and beverages and to indicate whether these were things that they actively tried to include in their diet, actively tried to avoid in their diet, or did not think about at all. Of the 1009 adults surveyed, 616 indicated that they actively tried to avoid drinking regular soda or pop. Assume that the sample was an SRS.
Suppose we computed a large sample 99% confidence interval for the proportion of all American adults who actively try to avoid drinking regular soda or pop.
This 99% confidence interval:
would have a larger margin of error than a 90% confidence interval.
would have a smaller margin of error than a 90% confidence interval.
could have either a smaller or a larger margin of error than a 90% confidence interval. This varies from sample to sample.
would have the exact same margin of error as a 90% confidence interval.
Answer:
would have a larger margin of error than a 90% confidence interval.
Step-by-step explanation:
Margin of error in statistics can be defined as a small amount that is allowed for in case of miscalculation or change of circumstances.
For a statistical data margin of error can be expressed as;
M.E = zr/√n
Where;
Given that;
r = Standard deviation
z = z score at a particular confidence interval
n = sample size
z at 99% = 2.58
z at 90% = 1.645
Since z at 99% is higher than z at 90% Confidence interval, the Margin of error M.E at 99% confidence interval will be higher than that of 90% confidence interval.
What is the result of adding these two equations? 6 x + 2 y = − 2 3 x − 2 y = − 5 6x+2y 3x−2y =−2 =−5
Answer:
The result gives the equation: 9x = -7
solution: (-7/9, 4/3)
Step-by-step explanation:
6 x + 2y = − 2
and
3 x − 2y = − 5
add together
6x + 3x + 2y - 2y = -2 + -5
9x + 0 = -7
9x = -7
then x = -7/9
and y = -3x - 1:
y = -3*(-7/9) - 1
y = 7/3 - 1 = 4/3
solution: (-7/9, 4/3)
-----------------------------------------
6x+2y= -2 and 3x−2y =−5
6x + 3x + 2y - 2y = -2 + -5
Write inequalities to represent the situations below
The distance to the nearest exit door is no more than 150 feet.
Use d to represent the distance (in feet) to the nearest exit door.
To ride a roller coaster, a visitor must be taller than 60 inches.
Use h to represent the height (in inches) of a visitor able to ride.
Answer:
The distance to the nearest exit door is no more than 150 feet.
Use d to represent the distance (in feet) to the nearest exit door.
For this case we can create the following inequality based in the notation and condition given, when they says no more means that the possible value nees to be equal or lower than the specified value.
[tex] d \leq 150[/tex]
To ride a roller coaster, a visitor must be taller than 60 inches.
Use h to represent the height (in inches) of a visitor able to ride.
For this case we can create the following inequality based in the notation and condition given, when they says must be taller means that the possible value nees to be higher than the specified value.
[tex] h > 60[/tex]
Step-by-step explanation:
The distance to the nearest exit door is no more than 150 feet.
Use d to represent the distance (in feet) to the nearest exit door.
For this case we can create the following inequality based in the notation and condition given, when they says no more means that the possible value nees to be equal or lower than the specified value.
[tex] d \leq 150[/tex]
To ride a roller coaster, a visitor must be taller than 60 inches.
Use h to represent the height (in inches) of a visitor able to ride.
For this case we can create the following inequality based in the notation and condition given, when they says must be taller means that the possible value nees to be higher than the specified value.
[tex] h > 60[/tex]
A cone with height 12 centimeters and volume 16 pi centimeters cubed. What is the radius of the cone? 1 cm 2 cm 4 cm 8 cm
Answer:
2
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
Took the assignment
A multiple choice exam has ten questions. Each question has five possible answers, of which one is correct. Suppose that a student did not study for the exam and, as a result, they guess on every question so that the probability of answering any question correctly is 0.20. 19. What is the probability that the student answers exactly 4 questions correctly
Answer:
8.81% probability that the student answers exactly 4 questions correctly
Step-by-step explanation:
For each question, there are only two possible outcomes. Either he answers it correctly, or he does not. The probability of answering a question correctly is independent of other questions. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
A multiple choice exam has ten questions.
This means that [tex]n = 10[/tex]
The probability of answering any question correctly is 0.20.
This means that [tex]p = 0.2[/tex]
What is the probability that the student answers exactly 4 questions correctly
This is P(X = 4).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{10,4}.(0.2)^{4}.(0.8)^{6} = 0.0881[/tex]
8.81% probability that the student answers exactly 4 questions correctly
Kelsey's car can go 120 miles on 4.8 gallons of gas.If her tank holds 18 gallons,how far can she travel on a full tank of fuel.
Answer: She can travel 450 miles with 18 gallons.
Step-by-step explanation:
[tex]\frac{4.8}{120}[/tex] = [tex]\frac{18}{x}[/tex] solve by cross product
4.8x = 2160
x= 450
Kelsey's car gets 25 miles per gallon, and with an 18-gallon tank, she can travel a total of 450 miles on a full tank.
Explanation:To calculate how far Kelsey can travel on a full tank of fuel, first we need to determine her car's fuel efficiency and then apply it to the full tank capacity. We are given that her car can travel 120 miles on 4.8 gallons of gas. This gives us a fuel efficiency rate we can use to find out the total distance she can travel on 18 gallons.
Step-by-step CalculationCalculate the miles per gallon (mpg) her car gets by dividing the total miles traveled by the gallons of gas used: 120 miles ÷ 4.8 gallons = 25 mpg.Calculate the total distance that can be traveled on a full 18-gallon tank by multiplying the fuel efficiency rate by the tank size: 25 mpg × 18 gallons = 450 miles.Therefore, Kelsey can travel 450 miles on a full tank of fuel.
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how many gallons of paint are needed to paint one coat, if a gallon of paint covers 400ft squared?
Answer:
6.28 gallons
Step-by-step explanation:
first we need to find the area of a half sphere, and then find how much paint will be needed for that area.
The area of a sphere:
[tex]a=4 \pi r^2[/tex]
thus, the area of half a sphere is:
[tex]a=2 \pi r^2[/tex]
we know that the radius is:
[tex]r=20ft[/tex]
we substitute this to find the area of the half sphere (the area they need to paint):
[tex]a=2\pi (20ft)^2\\a=2(3.1416) (400ft^2)\\a=2,513.27ft^2[/tex]
now the question is how many gallons of paint are needed to paint 2,513.27 square feet.
We are told that 1 gallon covers 400 square feet
thus, we must divide 2,513.27 by 400:
[tex]\frac{2,513.27ft^2}{400ft^2} =6.28[/tex]
6.28 gallons of paint are needed.
y = -7x -1
4x - 7y = 7
Answer:
(x, y) = (0, -1)
Step-by-step explanation:
Since we have an expression for y, it is convenient to substitute that into the second equation:
4x -7(-7x -1) = 7
4x +49x +7 = 7
53x = 0
x = 0
Substituting into the first equation gives ...
y = -7·0 -1
y = -1
The solution is (x, y) = (0, -1).
Meeko Insurance offers an annuity with a minimum interest rate of 3% for the
next 5 years. You decide to invest $5000 into this account. What type of
annuity is this?
Answer:
Single-payment variable annuity
Step-by-step explanation:
The type of Annuity is single-payment variable annuity.
What is annuity?An annuity is a contract between you and an insurance company in which the insurer agrees to pay you either immediately or in the future. An Annuity plan guarantees you a predetermined sum of money for the remainder of your life in exchange for a lump sum payment or a series of instalments.
Annuities are a type of insurance in which a portion of the money is paid each year to ensure the future.
There are two kinds of annuities:
Single payment variable annuity - This annuity pays out at the end of each period for a set amount of time. Payments are made monthly, quarterly, semi-annually, or annually in this annuity.
Annuity due is the inverse of a single payment variable annuity in that payments are made at the start of each period.
In the given situation the annuity is single payment variable annuity because the investment is done each year for 5 years.
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You are interested in estimating the the mean age of the citizens living in your community. In order to do this, you plan on constructing a confidence interval; however, you are not sure how many citizens should be included in the sample. If you want your sample estimate to be within 4 years of the actual mean with a confidence level of 95%, how many citizens should be included in your sample? Assume that the standard deviation of the ages of all the citizens in this community is 25 years.
To estimate the mean age of the citizens in your community with a confidence interval of 95% and a margin of error of 4 years, you need a sample size of at least 25 citizens.
Explanation:To estimate the mean age of the citizens in your community with a confidence interval of 95% and a margin of error of 4 years, you need to determine the required sample size. The formula for sample size calculation in this case is:
n = (Z * σ / E)²
where:
n = required sample sizeZ = z-score for the desired confidence level (in this case, 1.96 for 95% confidence)σ = standard deviation of the population (given as 25 years)E = desired margin of error (in this case, 4 years)Substituting the values into the formula, we get:
n = (1.96 * 25 / 4)² = 3.8416 * 6.25 = 24.0101 ≈ 25
Therefore, you would need a sample size of at least 25 citizens to estimate the mean age of your community with a 95% confidence level and a margin of error of 4 years.
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150 citizens should be included in the sample to achieve the desired precision and confidence level.
The sample size required to estimate the mean age of the citizens within 4 years of the actual mean with a 95% confidence level, we can use the formula for the sample size in the context of a confidence interval for a population mean when the population standard deviation is known: [tex]\[ n = \left(\frac{z \sigma}{E}\right)^2 \][/tex]
where:
[tex]- \( n \)[/tex] is the sample size,
[tex]- \( z \)[/tex] is the z-score corresponding to the desired confidence level,
[tex]- \( \sigma \)[/tex] is the population standard deviation, and
[tex]- \( E \)[/tex] is the margin of error (half the width of the confidence interval).
Given:
[tex]- \( \sigma = 25 \)[/tex] years (population standard deviation),
[tex]- \( E = 4 \)[/tex] years (margin of error),
- Confidence level = 95% (corresponding to a z-score of 1.96 for a two-tailed test).
Plugging in the values:
[tex]\[ n = \left(\frac{1.96 \times 25}{4}\right)^2 \] \[ n = \left(\frac{49}{4}\right)^2 \] \[ n = (12.25)^2 \] \[ n \approx 149.0625 \][/tex]
Since we cannot have a fraction of a citizen in our sample, we round up to the nearest whole number:
[tex]\[ n = 150 \][/tex]
The sample size required is 150 citizens.
Determine the graph that represents a function
The circle graph and parabola graph do not represent the function because they both fail the vertical line test option (A) and (C) are correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
Since a circle fails the vertical line test, it cannot be a function. In other words, we can create a vertical line that crosses a circle's graph more than once.
Not every parabola is a function. Only parabolas with upward or downward openings are regarded as functions.
Thus, the circle graph and parabola graph do not represent the function because they both fail the vertical line test option (A) and (C) are correct.
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The only graph that represents a function is the: Third Graph
What graph depicts a function?
To check whether the graph represents a function or not, we perform vertical line test.
Vertical Line test:
The Vertical Line Test is a method used to determine whether a given graph represents a function or not. To apply the test, draw a vertical line through the graph and observe the points of intersection. If the vertical line intersects the graph at exactly one point for each value of x, then the graph represents a function. If the vertical line intersects the graph more than once for any value of x, then the graph does not represent a function
Looking into the graphs, the vertical line intersects the graph C at only one point.
Hence, graph C represents a function.
Write the equation of the line that is parallel to y = -2x - 9 and passes through the point (-2,-4).
Answer: y=-2x-8
Step-by-step explanation:
Parallel lines need to have the same slopes but different y-intercept.
y=-2x -9 is parallel to y=-2x - 8
With Claudia’s loan does loan length or interest rate have a greater effect on the cost of the interest for the loan explain
Loan length affects total interest by spreading payments; interest rate directly impacts borrowing cost. Relative effect depends on borrower's goals.
The cost of interest for a loan is influenced by both the loan length (term) and the interest rate, but the degree of impact each has depends on several factors, including the specific terms of the loan and the borrower's financial situation. Let's break down their effects:
1. Loan Length (Term):
- Longer loan terms typically result in lower monthly payments since they spread the principal amount over more payments.
- However, longer terms also mean more time for interest to accrue, resulting in higher overall interest costs over the life of the loan.
- For example, if Claudia takes out a loan with a longer term, she may pay less each month but end up paying more in total interest over the entire term compared to a shorter-term loan with the same interest rate.
2. Interest Rate:
- The interest rate directly impacts the cost of borrowing. Higher interest rates mean higher monthly payments and more interest paid over the life of the loan.
- Lower interest rates, on the other hand, result in lower monthly payments and less interest paid overall.
- Even a small difference in interest rates can significantly affect the total interest paid over the life of the loan, especially for large loan amounts or longer terms.
Now, to determine which factor has a greater effect on the cost of interest for Claudia's loan, we need to consider her specific situation:
- If Claudia prioritizes minimizing her monthly payments, she might opt for a longer loan term despite potentially paying more interest in the long run.
- If Claudia is focused on minimizing the total interest paid over the life of the loan, she might prioritize securing a lower interest rate, even if it means higher monthly payments.
Ultimately, the relative importance of loan length and interest rate in determining the cost of interest depends on Claudia's financial goals, her ability to make monthly payments, and her overall financial situation. It's essential for her to carefully consider both factors and choose the loan terms that best align with her needs and financial objectives.
if h is positive how does the parabola's move?
Answer:
it would move upwards.
Step-by-step explanation:
there is no such thing as a negative exponent because, if you were suppose to graph that you have the parabola go up and down, and that is not how it works.
ASAP! GIVING BRAINLIEST! Please read the question THEN answer correctly! No guessing. Show your work or give an explaination.
Answer:
D
Step-by-step explanation:
Look at the graph. You want to see how much distance he is at 9 minutes. Go all the way to 9 minutes, then go up. What coordinate does it fall in? (9,80). He travelled 80 meters in 9 minutes. (D)
Which inequality is equivalent to this one?
Y-8≤-2
Answer:
y-8+8
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Can anyone help me, thanks
Answer:
When x=0 y=6
When x=3 y=0
Step-by-step explanation:
-6x-3y ≤-18
Let x = 0
-6x-3y =-18
-3y =-18
Divide each side by -3
-3y/-3 = -18/-3
y = 6
Let y = 0
-6x-3y =-18
-6x =-18
Divide each side by -6
-6x/-6 = -18/-6
x = 3
Question 3
State the value of the discriminant of 5x2 + 9x = 3.
a) 21
b) 12
c) 141
d) 5
Answer:
D = 141
Step-by-step explanation:
The given quadratic equation is
[tex]5x^2+9x=3\\\\5x^2+9x-3=0[/tex].
It is required to find the value of the discriminant. The value of discriminant of any quadratic equation is given by :
[tex]D=b^2-4ac[/tex]
Here, a = 5, b = 9 and c = -3
On plugging all the values, we get :
[tex]D=(9)^2-4\times 5\times (-3)\\\\D=141[/tex]
So, the value of discriminant for y is 141.
A triangle has sides that measure 2 units, 5 units, and 5.39 units. What is the area?
Answer:
12 units squared
Step-by-step explanation:
12.39 = 2 (3.14)r
12.39 / 6.28 = 6.28r / 6.28
1.97= r
A= (3.14) (1.97)^2
A= 12.18
The triangle's side lengths of 2, 5, and 5.39 units. So the area is 4.1506 square units.
To compute the area of a triangle, we employ formula, which utilizes the semi-perimeter [tex]\(s\)[/tex] (half of the perimeter):
[tex]\[ s = \frac{a + b + c}{2} \][/tex]
The area [tex]\(A\)[/tex] is:
[tex]\[ A = \sqrt{s(s - a)(s - b)(s - c)} \][/tex]
Triangle's sides as 2 units, 5 units, and 5.39 units:
[tex]\[ a = 2 \][/tex]
[tex]\[ b = 5 \][/tex]
[tex]\[ c = 5.39 \][/tex]
The semi-perimeter [tex]\(s\)[/tex]:
[tex]\[ s = \frac{2 + 5 + 5.39}{2} = \frac{12.39}{2} = 6.195 \][/tex]
Apply formula:
[tex]\[ A = \sqrt{s(s-a)(s-b)(s-c)} \\A= \sqrt{6.195(6.195-2)(6.195-5)(6.195-5.39)} \][/tex]
[tex]\[ A = \sqrt{6.195 \times 4.195 \times 1.195 \times 0.805} \][/tex]
Square root:
[tex]=\[ 6.195 \times 4.195 \times 1.195 \times 0.805\\= 25.201572[/tex]
The square root:
[tex]\[ A = \sqrt{25.201572} =5.02 \text{ square units} \][/tex]
Complete question:
A triangle has sides that measure 2 units, 5 units, and 5.39 units. What is the area?
If the relationships below are given in the form (input, output) which pairing always describes a function?
Answer:
B, the second one
Step-by-step explanation:
The Wall Street Journal reported that approximately 25% of the people who are told a product is improved will believe that it is in fact improved. The remaining 75% believe that this is just hype. Suppose a marketing study consists of a random sample of eight people who are given a sales talk about a new, improved product. What is the standard deviation of the number of people who believe that the product is in fact improved
Answer:
The standard deviation of the number of people who believe that the product is in fact improved is 1.50.
Step-by-step explanation:
The random variable X can be defined as the number of people who believe that a product is improved when they are told so.
The probability of a person believing that a product is improved is, p = 0.25.
A random sample of n = 8 people who are given a sales talk about a new, improved product are selected.
The event of a person believing that the product is improved is independent of others.
The random variable X follows a Binomial distribution with parameters n = 8 and p = 0.25.
The success is defined as a person believing that a product is improved.
The mean and standard deviation of a Binomial distribution is given by:
μ = n × p
σ = √[n × p × (1 - p)]
Compute the standard deviation as follows:
σ = √[n × p × (1 - p)]
= √[8 × 0.25 × (1 - 0.25)]
= √(2.25)
= 1.50
Thus, the standard deviation of the number of people who believe that the product is in fact improved is 1.50.
simplify: 2{10-5+x[1+3(6-2)]}
Answer:
10+26x
Step-by-step explanation:
To solve this, work your way from the inner most parentheses to the outer most:
The inner most parentheses is around 6-2, meaning you solve this first. When you solve this, you get 4.The second most inner parentheses is around (1+3 times 4) using PEMDAS, you first solve the multiplication, and then add. Once you solve this, you get 13.Next, the outer most parentheses is around (10-5+13x). When you simplify this, you get 5+13xFinally, you multiply 2(5+13x). Using distributive property, you get 10+26x as your final simplified answer.The graph of y=h(x) is shown below. The function f(x) is defined by f(x) =-1/2h(x)+3. (a) What three transformations have occurred to the graph of h to produce the graph of f? Specify the transformations and the order they occurred in.
Answer:
Reflection over x, Stretch by 1/2, translate up 3 units
Step-by-step explanation:
:)
The graph of the function h(x) has undergone three transformations to produce the function f(x) = -1/2h(x) + 3: a reflection in the x-axis, a vertical scaling by 1/2, and a vertical shift upward by 3 units.
Explanation:The function f(x) = -1/2h(x) + 3 has gone through three transformations to become the graph of h(x), which are determined by applying different values of x and the corresponding values of y. Firstly, the graph h(x) is reflected in the x-axis due to the negative sign in front of the h(x), which reverses the direction of the graph. Secondly, the graph is scaled vertically by a factor of 1/2 due to the multiplication of h(x) by 1/2, which compresses the graph towards the x-axis. Lastly, the graph is translated vertically upwards by 3 units as a result of the +3 in the equation, shifting the entire graph upwards.
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An instructor reports that as the number of student interruptions during class decreases, student scores on in-class quizzes increase. Is this an example of a positive correlation or a negative correlation?
Answer:
Negative correlation
Step-by-step explanation:
In a negative correlation, as one variable increases, the other variable decreases, and as one variable decreases, the other variable increases. In positive correlation, as one variable increases, so does the other and as one variable decreases, so does the other.
In the given question, as the number of student interruptions during class decreases, student scores on in-class quizzes increase. So, this an example of a negative correlation.
A clown is shot out of cannon with a velocity of 200 feet per second at an angle of 24°
with the horizontal. Find the vertical and horizontal components of the velocity of this clown.
Answer:
Vertical component of velocity is [tex]81.35 ft/sec.[/tex]
Horizontal component of velocity is [tex]182.6 ft/sec[/tex].
Step-by-step explanation:
Horizontal component of velocity is defined as:
[tex]v_{x} = v\times cos\theta[/tex]
Vertical component of velocity is defined as:
[tex]v_{y} = v\times sin\theta[/tex]
Where [tex]v_{x} , v_{y}[/tex] are the horizontal and vertical components of velocity.
[tex]v[/tex] is the actual velocity and
[tex]\theta[/tex] is the angle with horizontal axis at which the object was thrown.
Here, we are provided with the following:
[tex]v = 200 ft/sec[/tex]
[tex]\theta = 24^\circ[/tex]
[tex]v_{x} = 200 \times cos24^\circ\\\Rightarrow 200 \times 0.913\\\Rightarrow v_{x} = 182.6 ft/sec[/tex]
[tex]v_{y} = 200 \times sin24^\circ\\\Rightarrow 200 \times 0.407\\\Rightarrow v_{y} = 81.35 ft/sec[/tex]
So, Vertical component of velocity is [tex]81.35 ft/sec.[/tex]
Horizontal component of velocity is [tex]182.6 ft/sec[/tex].
Twelve synchronized swimmers are forming a circle. The locations of three of those swimmers are (13,-2),(-1,-2),and (6,-9). A 4th swimmer will appear in the middle of the circle. Where would the center swimmer need to be located?
Answer:(6,-2)
Step-by-step explanation:
The center swimmer need to be located at the point (6, -2).
What is the Standard form of a Circle?Standard form of a circle is given by the equation,
(x - h)² + (y - k)² = r²
where, (h, k) is the center of the circle and r is the radius of the circle.
Given are three points on a circle.
(13, -2), (-1, -2) and (6, -9).
Substituting each of the point in the standard form,
(13 - h)² + (-2 - k)² = r²
(-1 - h)² + (-2 - k)² = r²
(6 - h)² + (-9 - k)² = r²
Since the radius are equal,
(13 - h)² + (-2 - k)² = (-1 - h)² + (-2 - k)² = (6 - h)² + (-9 - k)²
Solving the first two equations, we get,
(13 - h)² = (-1 - h)²
28h = 168
h = 6
From the last two equations,
(-1 - h)² + (-2 - k)² = (6 - h)² + (-9 - k)²
49 + (-2 - k)² = (-9 - k)²
k = -2
Hence the center of the circle is (h, k) = (6, -2).
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Given the equation y = 3x - 4, what is the value of y when x = 4
Answer:
y=8
Step-by-step explanation:
y=3(4)-4
y=12-4
y=8
In a business class, 15% of the students have never taken a statistics class, 40% have taken only one semester of statistics, and the rest have taken two or more semesters of statistics. The professor randomly assigns students to groups of three to work on a project for the course. Assume everyone in the group is independent. What is the probability that neither of your two group mates has studied statistics
Answer:
Pr(neither of two groups) = 0.0225
Step-by-step explanation:
Given:
15% of the students have never taken a statistics class = Pr(none)
Pr(none) = 0.15
40% have taken only one semester of statistics =Pr(one semester)
Pr(one semester) = 0.40
the rest have taken two or more semesters of statistics = Pr(two or more semester)
Pr(two or more semester) = 1 - [Pr(one semester) + Pr(none) ]
Pr(two or more semester) = 1-(0.40+0.15) = 1 - 0.55
Pr(two or more semester) = 0.45
Where Pr = probability
Let probability that neither of your two group mates has studied statistics = Pr(neither of two groups)
=Pr(none in group 1) ×Pr(none in group 2)
= 0.15 × 0.15
Pr(neither of two groups) = 0.0225
Vignesh owns a cottage in the shape of a cube with each edge of length 26 feet. The roof is in the shape of a square pyramid and it extends two feet over the edge of the cottage on each side. The lateral sides of the roof are 17 feet long. What is the total surface area of the roof?
Answer:
Step-by-step explanation:
The shape of the cottage is cube
The edge of the cube is of length is 26ft
L_1 = 26ft.
The roof is in form of a square with with length 17ft.
L_2 = 17ft.
The roof is made up of 4 congruent isosceles triangles. Since the roof extends 2 ft over the edge of the cottage on each side, then the base of each triangle is 26 + 2 = 28 ft.
L_2 = 28 ft
Then, area of the roof is
A = 28²
A = 784 ft²
The triangular pyramid.
The triangular has four sides
Then,
Each of the area can be calculated using
A = ½ × b × h
Then, the four area of the triangular pyramid
A_total = 4 × ½ × b × h
A_total = 2 × b × h
The base of the triangle is 28ft.
The calculate the height of the triangle
Let's calculate the area of one of the triangles and then just multiply by 4. See attachment. Drop a perpendicular from the vertex of a triangle to its base. We now have the triangle broken up into two right triangles. The hypotenuse is 17 ft and one of the legs of the right triangle is 28 / 2 = 14 ft. Then the height is using Pythagoras theorem
a² = b² + c²
17² = 14² + h²
17² - 14² = h²
h² = 93
h = √93
Then, the area of the triangular pyramid is
A = 2 × b × h
A = 2 × 28 × √93
A = 540.04 ft²
Then, the area of the pyramid is approximately 540 ft², since the base of the pyramid cannot be seen.
But if we include the base, then, the total surface area is
A_t = A_triangular + A_base
A_t = 540 + 784
A_t = 1324 ft²
A personal pizza is $7.00 plus $0.50 per topping. Is this proportional?