Determine the surface area of the cylinder. (Use π = 3. 14)
net of a cylinder where radius of base is labeled 5 inches and a rectangle with a height labeled 4 inches
157 in2
219. 8 in2
282. 6 in2
314 in2
The surface area of the cylinder with radius 5 inches and rectangle with height 4 inches is equal to 282.6 square inches.
Radius of the base = 5 inches
Height of the rectangle = 4 inches
Surface area of a cylinder
= area of the top and bottom circular faces + the area of the curved surface.
Here,
Rectangle represents the curved surface of the cylinder, with a height of 4 inches and a length equal to the circumference of the base.
Circumference of the base is equal to,
Circumference
= 2πr
= 2 x 3.14 x 5
= 31.4 inches (approx.)
Area of the curved surface of the cylinder is ,
Curved surface area
= Length x Height
= 31.4 inches x 4 inches
= 125.6 square inches
Area of each circular face of the cylinder is ,
Circular face area
= πr²
= 3.14 x 5²
= 78.5 square inches
Substitute the value to get total surface area of the cylinder we have,
Total surface area of the cylinder
= 2 x Circular face area + Curved surface area
= 2 x 78.5 square inches + 125.6 square inches
= 282.6 square inches (approx.)
Therefore, the surface area of the cylinder is approximately equal to 282.6 square inches.
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the slant height of a cone measures 26 centimeters. The height of the cone measures 24 centimeters.
What is the exact surface area of the cone?
help!!
Enter your answer in the box.
The value of the exact surface area of the cone is 360π
What is the exact surface area of the cone?To find the surface area of a cone, we need to calculate the area of the circular base and the curved lateral surface.
The radius of the circular base can be found using the Pythagorean theorem:
r = √(s^2 - h^2)
where s is the slant height and h is the height.
In this case, we have:
r = √(26^2 - 24^2)
r = 10
So, the surface area is
S = πr² + πrl
This gives
S = π * 10² + π * 10 * 26
S = 360π
Hence, the exact surface area of the cone is 360π
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describe in words how to calculate the probability of two mece events from their odds using the ratio method.
To calculate the probability of two separate events using the ratio method, we must first understand the odds associated with each event. The odds are expressed as a ratio, with the first number representing the chances of success and the second number representing the chances of failure. For example, the odds of an event happening might be 3:2, which indicates that there is a 3/5 chance of success.
Once the odds for each event are known, we can calculate the probability of both events occurring by multiplying the odds of each event together. So, for example, if the odds of Event A are 3:2 and the odds of Event B are 4:5, the probability of both events occurring is 3/2 * 4/5 = 6/10. This means that there is a 6 in 10 chance of both events occurring.
To sum up, calculating the probability of two separate events using the ratio method is fairly simple. Just look at the odds associated with each event and multiply them together to get the probability of both events occurring.
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A scientist measures the amount of water collected in a tub at different times during the day. The table shows the time the water had been running and the amount of water in the tub.
Based on the information in the table, write an equation that can be used to find t, the number of minutes it took to collect w liters of water in the tub.
As a result, the following equation can be used to determine t, or how many minutes it took to fill the tub with w liters of water: t = (w - 0.2) / 0.4
what is slope ?Slope is a unit used to describe how steep or slope a line is. The ratio of the vertical change (rise) to the horizontal change (run) between any two locations on the line is what is referred to as the slope. In other words, the slope of the line going through the two points (x1, y1) and (x2, y2), which are on a line, is given by: Slope is equal to y2 - y1 / x2 - x1. Positive, negative, zero, or undefinable slopes are all possible.
given
With the slope and y-intercept in hand, we can now write the line's equation:
y = 0.4x + 0.2
Given a value for y, we wish to find a solution to this equation for x. In this instance, we're looking for t, or how many minutes it took to fill the tub with w liters of water. We can solve for x by substituting w for y:
w = 0.4t + 0.2
0.4t = w - 0.2
t = (w - 0.2) / 0.4
As a result, the following equation can be used to determine t, or how many minutes it took to fill the tub with w liters of water: t = (w - 0.2) / 0.4.
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the attendance for a basketball team declined at a rate of 5% per game throughout a losing season. 15 games were played in the season and 23,500 people were at the first game. how many people were at game 7?
At Game 7, the attendance for the basketball team had declined by 5% x 6 games = 30% and This means that the attendance at Game 7 was 23,500 x (1 - 0.3) = 16,450 people.
The attendance for a basketball team declined at a rate of 5% per game throughout a losing season. This means that for every game, the attendance dropped by 5% in comparison to the attendance of the game before it.
15 games were played in the season and 23,500 people were at the first game. To calculate the attendance at Game 7, we first need to calculate the total amount that the attendance had declined by by the 7th game.
This can be done by multiplying the rate of decline (5%) by the number of games that had passed (6 games). This gives us a total decline of 30%. We then need to calculate the attendance at Game 7 by subtracting the total decline from the initial attendance.
This can be done by multiplying the initial attendance (23,500) by (1 - 0.3), which gives us 16,450 people. Therefore, the attendance at Game 7 was 16,450 people.
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How do you solve this
The value of side x in the box is 8cm.
Definition of a cuboidA cuboid defined as a solid or figure in three dimensions with six rectangular sides known as faces. A cuboid contains six faces, each of which is a rectangle with all four corners at 90 degrees. It has 12 edges and 8 vertices. A cuboid's opposing faces are always equal. It indicates that the cuboid's opposing surfaces are in the same dimension.
Surface area of box=152cm²
Given:
l=6cm
b=2cm
h=x cm
Surface area of box=2(lb+bh+lh)
152=2(6×2+2×x+x×6)
152=2(12+8x)
12+8x=76
8x=64
x=8
Hence, The value of side x of the box is8cm.
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Which function has an inverse that is also a function? • g(x)=2x-3 •k(x) = -9x² • f(x) = |x + 2| •w(x) = -20
The function has an inverse that is also a function is g(x)=2x-3
What is Inverse function?A function that can turn into another function is known as an inverse function or anti function. In other terms, the inverse of a function "f" will take y to x if any function "f" takes x to y. The inverse function is designated by f⁻¹ or F⁻¹ if the function is written by f or F. Here, (-1) should not be confused with an exponent or an inverse.
A function takes in values, applies specific procedures to them, and produces an output. The inverse function works, agrees with the outcome, and returns to the initial function.
The solution in which x and y have been reversed is known as an inverse function.
The vertical line test determines whether a function succeeds or fails when you solve for y once more.
1. Here g(x) = 2x - 3 has inverse x = 2y - 3 which simplifies to;
[tex]y=\frac{x-3}{2}[/tex]
This is a line and is a function;
[tex]y=\frac{x}{2} +\frac{1}{2}[/tex]
2. k(x) = -9x² has the inverse x = -9y² which simplifies to;
[tex]y=\sqrt{x/(-9)}[/tex]
This is a function but only for certain values of x.
3. f(x) = |x+2| is an absolute value function.
Not all absolute value functions have function-based inverses.
4. A function's inverse does not exist for the equation w(x) = -20.
The function therefore has a negative that is also a function, which is
g(x)= 2x – 3.
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For the following indefinite integral, find the full power series centered at
x=0 and then give the first 5 nonzero terms of the power series. [infinity]
Σ∫(e^9x - 1) / 6x dx
n=0
From the given information provided, the first 5 nonzero terms of the power series are 1.5 + 13.5x + 60.75x² + 183.375x³ + 1018.1595x⁴.
To find the power series for the given indefinite integral, we can first find the antiderivative of the integrand using substitution. Let u = 9x, du = 9dx, then:
∫(e⁹ˣ - 1) / 6x dx = (1/6) ∫([tex]e^u[/tex] - 1) / u du
We can then expand the integrand into a power series using the Maclaurin series for [tex]e^u[/tex] and ln(1+u):
(1/6) ∫([tex]e^u[/tex] - 1) / u du = (1/6) ∫[Σ(uⁿ/n!) - Σ(-1)ⁿ(u⁽ⁿ⁺¹⁾/(n+1))] du
= (1/6) [Σ(uⁿ/n! × du) + Σ(-1)ⁿ(u⁽ⁿ⁺¹⁾/(n+1) × du)]
= (1/6) [Σ(uⁿ/n! × 9dx) + Σ(-1)ⁿ(u⁽ⁿ⁺¹⁾/(n+1) × 9dx)]
= (3/2) Σ(9ⁿ x⁽ⁿ⁻¹⁾ / n!) - (1/6) Σ(-1)ⁿ (9⁽ⁿ⁺⁾ xⁿ / (n+1))
We can now simplify and group terms to obtain the power series centered at x=0:
(3/2) Σ(9ⁿ x⁽ⁿ⁻¹⁾ / n!) - (1/6) Σ(-1)ⁿ (9⁽ⁿ⁺¹⁾ xⁿ / (n+1))
= (3/2) Σ(9ⁿ x⁽ⁿ⁻¹⁾ / n!) + (1/6) Σ((-1)ⁿ × (-9)⁽ⁿ⁺¹⁾ × xⁿ / (n+1))
To find the first 5 nonzero terms, we can plug in n=0 through n=4 and evaluate each term:
n=0: (3/2) × 1 = 1.5
n=1: (3/2) × 9x = 13.5x
n=2: (3/2) × 81x² / 2 - (1/6) × 81x² / 3 = 60.75x²
n=3: (3/2) × 729x³ / 6 + (1/6) × 729x³ / 4 = 183.375x³
n=4: (3/2) * 6561x⁴ / 24 - (1/6) * 6561x⁴ / 5 = 1018.1595x⁴
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what is the probability of observing the expected value for the distribution of binomial(100, 0.20)?
The probability of observing the expected value for the distribution of a binomial (100, 0.20) is 0.20 (or 20%).
The probability of observing the expected value for a binomial distribution can be calculated using the following formula:
Probability = (n C r) p^r (1-p)^(n-r)
where n = number of trials,
r = expected value,
p = probability of success
For the given distribution, binomial (100, 0.20), we know that n = 100 and p = 0.20.
The expected value is given by:E(X) = np = 100 * 0.20 = 20
So, to find the probability of observing the expected value of 20, we need to plug in the values of n, r, and p into the formula:
Probability = (n C r) p^r (1-p)^(n-r)=
(100 C 20) (0.20)^20 (0.80)^80≈
0.1875 ≈ 0.20 (rounded to two decimal places)
Therefore, the probability of observing the expected value for the distribution of binomial (100, 0.20) is approximately 0.20 (or 20%).
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researchers are studying a population of small plants on an island. before and after a major drought, they dug up a random sample of plants and measured their root length. during the drought, no plant reproduction took place. what can be concluded from the plot below?
The correct conclusion that can be drawn from the plot is that the plant population had a significantly lower mean root length after the major drought occurred.
Explanation:
A frequency polygon is a graphical representation of a frequency distribution using line segments connected to points that indicate the midpoint of each class interval.
The horizontal axis shows the measurement variable, while the vertical axis shows the number of occurrences of the variable for each bin. The midpoint of each bin is used to represent the distribution of data that falls within that bin's range.
Since the values of adjacent bins overlap, the lines are connected. The points are connected by straight lines in a frequency polygon.
In this case, the conclusion that can be drawn from the plot is that the plant population had a significantly lower mean root length after the major drought occurred.
The peak of the frequency polygon has shifted to the left, indicating that the majority of plants have a shorter root length. The decrease in the mean root length of the plant population is due to the impact of the major drought on the island.
As a result, no plant reproduction took place, indicating a decrease in the plant population.
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What are the values of x and y? *
The values of sides x and y of the triangle are 6.75 and 11.25 units respectively.
The Pythagorean TheoremThe square of the hypotenuse side of the right-angled triangle equals the sum of the squares of the other two sides, according to Pythagoras' Theorem. The three sides of this triangle are referred to as the perpendicular, base, and hypotenuse.
by using the Pythagorean theorem:
Equation1: y ² =x ² + 9²
Equation2: (12 + x) ² =1 5 ² + y ²
Putting values of equation1 in 2 we get
(12 + x) ² =1 5 ² +x ² + 9²
144 + x²+ 2×12x = 225 + x²+ 81
x=6.75
Putting value of x in equation1
y ² =6.75 ² + 9²
y=11.25
Hence, the values of x and y are
x = 6.75 unit
y =11.25 unit
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-7 + ◾ = 0 x 11
- 11+=-11
6+(-4+)=(6+(-4)+(-7)
The domain of the function using the attached diagram is given by option A. { x / x = -5, -3, 1, 2, 6 }.
As per the attach diagram,
The mapping in the diagram represents the relation between input values and the output values.
Let us consider all input values are represented by variable 'x'.
And all output values are represented by variable 'y'.
All input values represents the domain of the function.
-5 relates to 4
-3 relates to -9
1 relates to 2
2 relates to -6
6 relates to 0
Here,
Domain of the function is ,
{ x / x = -5, -3, 1, 2, 6 }
Range of the function is ,
{ y / y = 4, -9, 2, -6,0 }
Therefore, the domain of the function is equal to option A. { x / x = -5, -3, 1, 2, 6 }.
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The given question is incomplete, I answer the question in general according to my knowledge:
A mapping diagram shows a relation, using arrows, between inputs and outputs for the following ordered pairs: (negative 6, 0), (2, 1), (negative 7, negative 4), (11, 2), (3, 2).
What is the domain of the relation?
Diagram is attached.
Please help with these two questions if you are good at vertical angles! thank you!!
Step-by-step explanation:
Blank 1 = 82
Blank 2 = 82
Blank 3 = 98
How much fencing is required to enclose a circular garden whose radius is 26 m? Use 3. 14 for PI
to enclose the circular garden, we need 163.64 meters of fencing. This means that if we were to wrap a measuring tape or any other material around the perimeter of the garden, it would need to be 163.64 meters long to cover the entire circumference of the circle.
To determine the amount of fencing required to enclose a circular garden with a radius of 26 meters, we need to calculate the circumference of the circle. The circumference is the distance around the perimeter of the circle, which can be calculated using the formula:
Circumference = 2 x π x radius
where π is the mathematical constant approximately equal to 3.14, and the radius is the distance from the center of the circle to any point on its perimeter.
So, in this case, the circumference of the circular garden can be calculated as follows:
Circumference = 2 x 3.14 x 26 m
= 163.64 m
Therefore, to enclose the circular garden, we need 163.64 meters of fencing. This means that if we were to wrap a measuring tape or any other material around the perimeter of the garden, it would need to be 163.64 meters long to cover the entire circumference of the circle.
It's worth noting that the formula for calculating the circumference of a circle can be used to find the amount of fencing required for any circular enclosure, such as a circular pond or a circular pool.
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when is welch's t-test used to compare two population means, and what distributional assumptions are needed?
Welch's t-test is a modified version of the t-test for independent means. Welch's t-test is an important statistical test that compares the mean of two groups that have different variances and is utilized when the assumptions of the t-test for independent means are violated.
However, unlike the standard t-test for independent means, Welch's t-test does not rely on the assumption that the variances of the two groups are equal. Instead, Welch's t-test relies on a more flexible assumption, that is, the assumption of unequal variances.
Welch's t-test's basic assumptions include the following:Independent samples: The sample sizes should be equal or almost equal in size. Normality: The two groups must have normally distributed populations. Even though Welch's t-test is more flexible than the standard t-test for independent means, the test is most accurate when the distributional assumptions are met.
It should be remembered that it is more conservative when the distributional assumptions are violated.
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5x+2y=10
Find the Y intercept and gradient
Math Homework Due Tomorrow,PLEASE HELP.
The cards below have various rational numbers on them. Which of the following diagrams shows the numbers in correct sets?
Answer:
Looks like J is right.
Step-by-step explanation:
Because the others are not right, and J was what my calculator said the numbers belonged to as in groups.
(Brainliest please?)
Brooke played her flute for 3/4 hour each day for 5 days and for 1/2 hour each day for 2 days how many hours did she play it in all
⇒To be able to answer this question to find how many hours Brooke played his flute for 5 days we ought to first convert the 5 days to hours.
⇒There are 24 hours in a day this means that in 5 days we have =24×5
=120 hours.
⇒We have 120 hours in 5 days , it is said that Brooke played her flute [tex]\frac{3}{4}[/tex],
Meaning she played the flute [tex]\frac{3}{4}[/tex] hours of 120 hours which is equal
[tex]\frac{3}{4} *\frac{120}{1}\\=90[/tex]
For 5 days Brooke played her flute 90 hours
⇒The next step is to convert the 2 days to hours which is equivalent to 24×2
=48 hours are in 2 days, it is said Brooke played the flute [tex]\frac{1}{2}[/tex] hours of 2 days. This simply is equivalent to
[tex]\frac{1}{2} *\frac{48}{1} \\=24[/tex]
⇒For 2 days Brooke played the flute 24 hours,
The total number of hours she played it all is =Number of hours she played it in 5 days+ Number of hours she played it in 2 days.
=90+24
=114
⇒In total of these 7 days she played the flute for 114 hours
math is too hard for me help
Answer:
Step-by-step explanation:
1/5(-25) + 16/8
-5 + 2 = -3
Option A
Define The Fundamental Counting Principle: Unit 2: Probability Lesson 2: Counting Our Way to Probabilities Describe what it means to count with replacement and without replacement: You need a new password for an email account. The requirements are that the password needs to be 8 characters long considering of 5 lowercase letters followed by 3 numbers. If you are allowed to use characters more than once (with replacement), how many different possibilities are there for a password? (Use an image to help you understand). Let's use the same example as above, only this time you may only use each letter or number one time. That is without replacement or repetition.
Similarly, there are 10 choices for the first number, 9 choices for the second number, and 8 choices for the third number. Therefore, the total number of possibilities is[tex]26 × 25 × 24 × 23 × 22 × 10 × 9 × 8 = 14,776,320[/tex] possibilities.
Fundamental Counting Principle and how to count with and without replacement.The Fundamental Counting Principle (FCP) states that if there are m ways to perform an event and n ways to perform a second event, then there are m × n ways to perform both events. For example, suppose there are 2 shirts, 3 pants, and 4 pairs of shoes in your closet. Using the FCP, you can calculate the number of outfit combinations: 2 × 3 × 4 = 24.If you are allowed to use characters more than once (with replacement), the number of different possibilities for a password can be calculated by multiplying the number of choices for each character type. There are 26 lowercase letters, so there are 26 choices for the first letter, 26 choices for the second letter, and so on. Similarly, there are 10 digits, so there are 10 choices for each number.
Therefore, the total number of possibilities is [tex]26 × 26 × 26 × 26 × 26 × 10 × 10 × 10 = 26^5 × 10^3 = 11,881,376,000[/tex] possibilities.If you may only use each letter or number one time, then you cannot repeat any choices. Therefore, the number of possibilities is reduced. There are 26 choices for the first letter, 25 choices for the second letter (since one has already been used), and so on.
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Harold walks once round a circle with diameter 100 metres.
There are 6 points equally spaced
on the circumference of the circle.
a) Find the distance Harold walks between
b) What is the mean distance covered by Harold
when walking from one point to the next?
m (1)
Harold therefore walks an average distance of 10 metres when moving from one location to another.
what is circle ?All the points in a plane that are equally spaced from a fixed point known as the centre make up a circle, which is a geometric form. The radius of a circle is the separation between any two points on the circle and its centre. A circle's diameter is defined as a line segment whose endpoints are on the circle and which goes through the centre of the circle. Circles are helpful in many areas of mathematics and science due to a number of significant characteristics.
given
A circle with a dimension of 100 metres has a circumference of d, where d is the diameter. As a result, this circle's diameter is:
C = d = (100) = 100 m
Harold will walk from one spot to the next after completing 1/6
of the circle's circumference because the circle's circumference has six points that are all equally spaced apart. As a result, Harold travels the following distance between each location:
Distance equals 1/6 * C * 1/6 * 100 * (50/3) metres.
b) The average of the distances between each location, which we just discovered to be (50/3) metres, represents the average distance that Harold covers when moving from one place to another. The circle has six evenly distributed points, so the average distance travelled by Harold is:
(Total distance travelled) / Mean distance (Number of segments)
Total distance travelled equals the distance between two adjacent locations on the circle, which is C/2, or (1/2) 100 metres, or 50 metres.
Segment count equals number of marks - 1 (i.e., 6 - 1 = 5).
The average distance Harold travels while strolling is as follows:
Typical distance is calculated as (Total distance travelled) / (Number of segments), which equals (50) / 5 = 10 metres.
Harold therefore walks an average distance of 10 metres when moving from one location to another.
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How can it be proven that a Rubik's cube will return to its original state if you repeat any algorithm for a number of times?
It can be proven that a Rubik's cube will return to its original state if you repeat any algorithm for a number of times
To prove that a Rubik's cube will return to its original state if you repeat any algorithm for a number of times, follow these steps,
1. Choose an algorithm, Select any algorithm that can be applied to the Rubik's cube. For example, the R U R' U' algorithm.
2. Apply the algorithm repeatedly, Perform the chosen algorithm on the Rubik's cube multiple times. Keep track of the number of times the algorithm is applied.
3. Observe the cube's state, After each iteration, observe the state of the Rubik's cube to see if it returns to its original state.
4. Identify the cycle length, Eventually, the Rubik's cube will return to its original state after a certain number of repetitions of the algorithm. This number is the cycle length of the algorithm.
5. Generalize the proof, The proof holds true for any algorithm on the Rubik's cube, as every algorithm has a finite cycle length due to the finite number of possible configurations of the cube.
In conclusion, it can be proven that a Rubik's cube will return to its original state if you repeat any algorithm for a number of times, because every algorithm has a finite cycle length due to the finite number of possible configurations of the cube.
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PLEASE HELP, GIVING BRAINLIST!
This prism has a right triangle for a base. What is the volume of the prism?
Answer:
volume v = base area * height
= 1/2*9*4 * 8
Which of the following is the fourth vertex needed to create a rectangle with vertices located at (5, 6), (9, 6), and (5, 3)? (5, –6) (5, –3) (9, –6) (9, 3)
PLSSS ANYONEEEE
A strain of Mycobacterium tuberculosis that is deficient in nonhomologous end joining repair should be more sensitive to damage by
X raysUV radiationGlycosylaseDepurination
Explanation:
A strain of Mycobacterium tuberculosis that is deficient in nonhomologous end joining repair should be more sensitive to damage by X-rays.
Nonhomologous end joining is a DNA repair mechanism that can join two DNA fragments with little or no homology between them. X-rays, which are high-energy electromagnetic waves, can cause damage to DNA by breaking the strands of the double helix.
This damage can be repaired by mechanisms like nonhomologous end joining, so a strain of Mycobacterium tuberculosis that is deficient in this repair mechanism would be more sensitive to damage by X-rays.
UV radiation, glycosylase, and depurination are not directly related to nonhomologous end joining repair and would not have the same effect.
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If the dartboard has a diameter of 14 inches and each number occupies 1/20 of the board, how much space does a single number occupy in square inches?
Each number occupies 7.7 inches² of the dartboard.
What is area?In geοmetry, area is the amοunt οf space a flat shape, like a pοlygοn, circle οr ellipse, takes up οn a plane. The area οf a shape is always measured in square units. Tο find the area οf simple shapes like a square οr the area οf a rectangle, yοu οnly need its width, w, and length, l (οr base, b). The area is length times width:
First we need the area of the dartboard
Area = πr²
here r = d/2 = 14/2 = 7
Area of dartboard = πr²
[tex]$ \rm = \frac{22}{7 } \times 7 \times 7[/tex]
= 22 × 7
= 154 inches²
Now, its is said that each number occupies 1/20 of the board,
Then area of each number = 154 × 1/20
= 7.7 inches²
Thus, Each number occupies 7.7 inches² of the dartboard.
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you are making cookies and missing a key ingredient eggs. you have most of the other ingredients, except you only have 1.33 cups of butter. the recipe calls for two cups of butter and three eggs to make six dozen cookies. how many eggs do you need use all of the butter?
By using equation in two variable we need to use 2 eggs to make all the cookies with 1.33 cups of butter.
To make six dozen cookies, the recipe calls for two cups of butter and three eggs. We can use proportionality to solve this question: If 2 cups of butter require 3 eggs to make 6 dozen cookies, then 1.33 cups of butter require x eggs to make all of the cookies.
x eggs = (1.33 cups of butter x 3 eggs)/(2 cups of butter). x = 1.99 eggs. Since we cannot use .99 eggs to make cookies, we would need to round up to the nearest whole number of eggs.
Therefore, we need to use 2 eggs to make all the cookies with 1.33 cups of butter.
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i am stuck on this question and need help.
1. 53
2. can you explain more it would really help more
Two ships are near a buoy in the open ocean. One ship is 20 km due north of the buoy, and the other ship is 13.5 km due east of the buoy.
Enter a number in the box to correctly complete the statement. Round the answer to the nearest tenth.
In this instance, the buoy forms the right corner of a triangle made up of the two ships and the buoy. To the closest tenth, the distance between the two ships is roughly [tex]24.1[/tex] km.
What is the distance between two object?To find the distance between the two ships, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the legs
(the sides that form the right angle) is equal to the square of the length of the hypotenuse (the side opposite the right angle).
In this case, the two ships and the buoy form a right triangle, with the buoy at the right angle.
Let d be the distance between the two ships, x be the distance of the northern ship to the buoy and y be the distance of the eastern ship to the buoy. Then we have:
[tex]d^2 = x^2 + y^2[/tex]
Substituting the given values, we get:
[tex]d^2 = (20 km)^2 + (13.5 km)^2[/tex]
[tex]d^2 = 400 km^2 + 182.25 km^2[/tex]
[tex]d^2 = 582.25 km^2[/tex]
[tex]d ≈ 24.1 km[/tex]
Therefore, the distance between the two ships is approximately 24.1 km, rounded to the nearest tenth.
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a bag contains 13 balls numbered 1 through 13. what is the probability of selecting a ball that has an even number?
The probability of selecting a ball that has an even number from a bag containing 13 balls numbered 1 through 13 is 6/13 or approximately 0.4615. This is because out of the 13 balls, 6 of them have even numbers.
To calculate the probability, we use the formula:
Probability = Number of Favorable Outcomes / Total Number of Outcomes
In this case, the favorable outcomes would be the number of even numbers, which is 6. The total number of outcomes would be 13 (the total number of balls in the bag). Therefore, the probability of selecting a ball that has an even number is 6/13.
Another way to look at this is to think of the probability as the ratio of favorable outcomes to total possible outcomes. In this case, the ratio is 6:13, which can be simplified to 3:6 or 1:2. Since one out of every two outcomes is favorable, the probability is 0.5, which is the same as 6/13.
To further understand the concept of probability, consider the example of a fair coin. If a fair coin is flipped, the probability of getting either heads or tails is 50%. This is because the ratio of favorable outcomes (one head and one tail) to total possible outcomes (two heads and two tails) is 1:2.
In conclusion, the probability of selecting a ball that has an even number from a bag containing 13 balls numbered 1 through 13 is 6/13 or approximately 0.4615.
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