Therefore, the odds of rolling an even number, getting a tail, and pulling a red card are 1 in 8 or 1/8.
What is probability?Probability is a branch of mathematics that deals with the study of randomness and uncertainty in events. It involves calculating the likelihood or chance of an event occurring based on the available information and assumptions. Probability is commonly used in many fields, including science, engineering, finance, and statistics. The probability of an event is a number between 0 and 1, where 0 means the event is impossible, and 1 means the event is certain.
Here,
The probability of rolling an even number on a fair six-sided dice is 3/6 or 1/2. The probability of flipping a tail on a fair coin is 1/2. The probability of pulling a red card out of a standard deck of 52 playing cards is 26/52 or 1/2 (assuming the deck is well shuffled).
To find the probability of all three events occurring together, we multiply the probabilities of each individual event:
=P(rolling an even number) x P(getting tail) x P(pulling a red card)
= 1/2 x 1/2 x 1/2
= 1/8
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Find the surface area of a cube with edge lengths of 9 centimeters.
The surface area of the cube is 486 cm².
What is surface area?
Surface area refers to the total area of all the faces or surfaces of a three-dimensional object. It is the sum of the areas of each face of the object.²
The formula for surface area varies depending on the shape of the object. For example, the surface area of a cube can be found by adding up the areas of all six faces, where each face has the same area given by the formula A = s², where s is the length of an edge. Therefore, the surface area of a cube with edge length s is 6s².
Calculation steps:
A cube has 6 square faces, all with the same area.
Since the edge length of the cube is 9 centimeters, each face has an area of:
A = (edge length)² = 9² = 81 cm²
Therefore, the total surface area of the cube is:
6A = 6(81) = 486 cm²
Hence, the surface area of the cube is 486 cm² .
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helppppppppppppppppppppp
Answer:
Side length of equilateral triangle is = 29 units
Step-by-step explanation:-In geometry, an equilateral triangle is a triangle that has all its sides equal in length.
3 given lengths are
3x+8 , 5x - 6 , 2x +15
so,
[tex] \rm \: 3x + 8 = 5x - 6 = 2x + 15[/tex]
consider 2 sides,
[tex] \rm \implies 3x + 8 = 2x + 15[/tex]
[tex] \rm \implies 3x - 2x = 15 - 8[/tex]
[tex] \rm \implies x= 7[/tex]
so,
[tex] \rm \: 3x + 8 = 3 \times 7 + 8 = 29[/tex]
As equilateral triangle
3x+8 = 5x - 6 = 2x +15 = 29
The sides of a triangle are straight lines that are joined by the three vertices of the triangle.
so,
Side,length of equilateral triangle is 29 units
Note :-Number of Sides = 3
Number of angles = 3
Each interior angle = 60
Each exterior angle = 120
Perimeter = 3 times of side-length
Area = √3/ 4 x (side)2
Height = √3 (side)/2
Here,
AC ≅ AB
→ 5x -6 = 3x+8
→ 5x - 3x = 8+6
→ 2x = 14
→ x = 14/2
→ x = 7
Now Putting the value of x
AC = 5x - 6
= 5(7) -6
= 35 -6
= 29
AB = 3x + 8
= 3(7) +8
= 21 + 8
= 29
BC = 2x + 15
=2(7)+15
= 14 + 15
= 29
Thus,
Side length of equilateral triangle is 29.More InformationArea of triangle
[tex] \sf \: \frac{1}{2}bh [/tex]
Area of equilateral triangle
[tex] \sf \: \frac{ \sqrt{3} }{4} {a}^{2} [/tex]
Area of Isosceles Triangle
[tex] \sf \: \frac{b}{4} \sqrt{ {4a}^{2} - {b}^{2} } [/tex]
need help with this can seem to anser it
Answer: Third option
Step-by-step explanation:
[tex](a^{b})^{c}[/tex] = [tex]a^{b\times c}[/tex] = [tex]a^{bc}[/tex]
[tex]\frac{(m^{5}n)^{4}}{(pq^{2})^{4}}[/tex] = [tex]\frac{m^{20}n^{4}}{p^{4}q^{8}}[/tex]
Find the approximate radius of a circle with a circumference of 198 centimeters. Use 3.14 for π. Round to the nearest hundredth.
Answer:
≈ 31,53 cm
Step-by-step explanation:
[tex]2\pi \times r = 198[/tex]
[tex]r = \frac{198}{2\pi} = \frac{198}{2 \times 3.14} = \frac{198}{6. 28} ≈ 31.53[/tex]
Coach Miller is using all the ground beef to grill 17 burgers. What is the cost for each burger?
Answer: We can only determine the cost for each burger if we know the total cost of all the ground beef. Let's assume that the ground beef costs $C in total.
If Coach Miller is using all the ground beef to grill 17 burgers, then the cost of each burger is:
Cost per burger = Total cost of ground beef / Number of burgers
We know that the total cost of ground beef is $C, and we know that there are 17 burgers. Substituting these values into the formula gives:
Cost per burger = C / 17
Therefore, the cost for each burger is C/17. We cannot determine the numerical value of C or the cost per burger without additional information.
Step-by-step explanation:
if the given triangles are similar find the value of x
Answer:
x = 33
Step-by-step explanation:
You can find the greatest common factor of the triangle side lengths on the right. It is 9. Both triangles are scaled versions of 3-4-5 triangles. Divide any side from the left triangle by its respective side length from 3-4-5, in this case 44/4 or 55/5. We can see that the scalar for this triangle is 11. This means the 3- the shortest side length. Is actually 3 x 11 = 33.
Therefore x = 33.
Do #7 pls and also my answer is wrong and also give me an explanation
Step-by-step explanation:
Volume of Pyramid = 1/3 (base area ) * height
21 = 1/3 ( s x s) * 3
21 = s^2
s = side length = sqrt (21 )
Find the unit rates,
then find which has the better value
10 oz, $2.50 or 14 oz, $3.65
The unit rate among these for the better values is: 0.25
What further instances of unit rates can you give?
These are a few illustrations of unit rates :The distance travelled in one hour is measured in miles per hour (mph); the price of an item is measured in pounds; and the price of an electrical kilowatt-hour is measured in kWh.
- Price per gallon - the price of a liquid per gallon.
The quantity of calories in one serving of food is known as the "calories per serving."
Now , divide the price by the weight to obtain the unit rate.
The unit rate for the first choice is:
2.50 / 10 = 0.25
The unit rate for the second choice is:
3.65 / 14 = 0.26
Due to its lower unit rate, the first choice is therefore more advantageous.
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Brianna’s math teacher plots student grades on their weekly quizzes against the number of hours they say they study on the pair of coordinate axes and then draws the line of the best fit
Write and equation for the line of the best fit in slop-intercept form
The equation for the line of the best fit in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept of the line.
What is equation?An equation is a mathematical statement that asserts the equality of two expressions. It consists of two expressions, separated by an equal sign, that have the same value. Equations are used in algebra to solve unknown values and to describe the relationship between different variables. Equations are also used to determine the unknown value of a single variable in a given equation.
To calculate m and b, we first need to calculate the sum of the products of the x and y values (Σxy), the sum of the x values (Σx), the sum of the y values (Σy), and the sum of the squares of the x values (Σx2).
Σxy = x1y1 + x2y2 + x3y3 + ... + xnyn
Σx = x1 + x2 + x3 + ... + xn
Σy = y1 + y2 + y3 + ... + yn
Σx2 = x12 + x22 + x32 + ... + xn2
Then, we can calculate the slope m of the line using the following equation:
m = (nΣxy - ΣxΣy) / (nΣx2 - (Σx)2)
Finally, we can calculate the y-intercept b of the line using the following equation:
b = (Σy - mΣx) / n
Once we have calculated the slope m and the y-intercept b, we can write the equation for the line of the best fit in slope-intercept form: y = mx + b.
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Please Answer Please
Answer: 230
Step-by-step explanation: The first thing you need to do is add 1 inch to the length and width. The starting lenght is 22, and that becomes 23. The starting width is 9, and that becomes 10. The new measurements are 23 by 10. To find area you multiply length by width. 23 times 10 gives you an answer of 230. I hope that helped!
what proportion of crows in the sample had lead levels that are classified by the biologist as unhealthy? the mean lead level of the 23 crows in the sample was 4.90 ppm and the standard deviation was 1.12 ppm. construct and interpret a 95 percent confidence interval for the mean lead level of crows in the region.
The 95 percent confidence interval that the true mean lead level of crows in the region is between 4.4157 and 5.3843.
What is a confidence interval?
An estimated range for an unknown parameter is known as a confidence interval. The 95% confidence level is the most popular, however other levels, such as 90% or 99%, are occasionally used when computing confidence intervals.
Here, we have
Given: the mean lead level of the 23 crows in the sample was 4.90 ppm and the standard deviation was 1.12 ppm.
= x ± t×s/√n
= 4.90 ± (2.074)×1.12/√23
= (4.4157, 5.3843)
Hence, the 95 percent confidence interval that the true mean lead level of crows in the region is between 4.4157 and 5.3843.
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Triangle CDE is similar to triangle FGH. Find the measure of side GH. Round you answer to the nearest tenth if necessary. Figures are not drawn to scale.
After answering the provided question, we can conclude that As a result, triangle the side GH measurement is approximately 16 units.
What precisely is a triangle?A triangle is a closed, double-symmetrical object made up of three line segments called sides that intersect at three points called vertices. Triangles can be distinguished by their sides and angles. Triangles can be equilateral (equal factions), isosceles, or scalene based on their sides. Triangles are classified as acute (all angles less than 90 degrees), okay (one angle equal to 90 degrees), or orbicular (all angles greater than 90 degrees) (all angles greater than 90 degrees). The province of a triangle can be calculated using the formula A = (1/2)bh, where an is the neighbourhood, b is the triangle's base, and h is its height.
Due to the similarity of triangles CDE and FGH, their corresponding sides are proportional. That is to say:
CE/GH = CD/FH = DE/FG
Given that DE = 8 and CD = 10, we can use the third ratio to calculate FH:
10/FH = 10/16
When we multiply by two, we get:
FH = 16/10 * 10 = 16
As a result, the side GH measurement is approximately 16 units.
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Phoebe wants to buy 65 swimming lessons that cost £30 each, but she only has £1400. What percentage (%) of the total cost of the lessons does phoebe have? Round your answer to 1 decimal place,
Phoebe has 71.8 percentage of the total cost of the swimming lessons.
Define percentageA number can be expressed as a fraction of 100 using a percentage. It is often represented by the symbol "%". Percentages are commonly used to express a proportion or rate of change, particularly in business, finance, and science. For example, if a student scores 90 out of 100 on an exam, their percentage score is 90%.
The total cost of 65 swimming lessons at £30 each is:
65 x £30 = £1950
Percentage = (Amount / Total) x 100
where "Amount" is the amount that Phoebe has, and "Total" is the total cost of the swimming lessons.
Plugging in the numbers, we get:
Percentage = (1400 / 1950) x 100
Percentage = 0.7179487 x 100
Percentage = 71.8 (rounded to 1 decimal place)
Therefore, Phoebe has 71.8% of the total cost of the swimming lessons.
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1. if ta is multiplication by a matrix a with three columns, then the kernel of ta is one of four possible geometric objects. what are they? explain how you reached your conclusion.
If Ta is multiplication by a matrix, The four possible geometric objects are 0 the origin, Plane through the origin, a line through the origin and R³.
Row reduction results in a line across the origin if the rank of the augmented matrix is 2, which indicates that there is one free variable and that the values of the other two variables depend on the free variable. Therefore a line across the origin is the kernel of TA.
If TA is multiplication by a matrix with Three columns, Then The kernel. of TA is one of four possible geometric objects.
A has three clumps.
So, A is of size : n x 3
and kernel vectors are of size 3 x 1
So dim kernel [tex]\alpha[/tex] = 3.
case 1: dimension (dim) = 3
A 3 dimensional surface.
Case 2: dim = 2.
A. 2 dimensional surface is a plane.
Case 3 dim = 1
AI dimensional surface is a line.
case u! dim = 0
A point.
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bella is watching a baseball game. so far, 4 out of 22 batters have gotten a hit. what is the experimental probability that the next batter will get a hit?
Answer: 2/11
Step-by-step explanation:
The experimental probability that the next batter will get a hit is 2/11.
What is probability?
Probability is a way of calculating how likely something is to happen. It is difficult to provide a complete prediction for many events. Using it, we can only forecast the probability, or likelihood, of an event occurring. The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.
Based on the given condition, the probability that the next batter will get a hit is
=> 4/22
=> 2/11
Hence the experimental probability that the next batter will get a hit is 2/11.
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Look at the poster below showing the price of pencils in a stationery shop. Riley wants to buy exactly 65 pencils. What is the lowest amount he can pay? Give your answer in pounds (£)
Answer:
13
Step-by-step explanation:
0.3*65
=19.5 pounds
[tex]\frac{2}{10} =0.2\\0.2*65=13[/tex]
Try It! Find Lengths of Segments Tangent to a Circle
3. If TX= 12 and TZ = 20, what are XZ and YZ?
The lengths of the segments tangent to the circle are YZ = XZ = 16.
What is tangent to a circle?A line that precisely crosses a circle at that point—referred to as the point of tangency—is said to be tangent to the circle. At the point of tangency, the tangent line is perpendicular to the circle's radius; as a result, the angle between the tangent line and radius is 90 degrees. Depending on where the tangency point is located, a circle can have an unlimited number of tangents. Geometrical uses for tangents to a circle include determining the lengths of line segments that are tangent to the circle.
We know that, triangle TXZ is congruent to triangle TYZ, thus YZ is congruent to XZ using CPCT.
Now, YZ = XZ.
For the right triangle TXZ, TX = 12, and TZ = 20.
Using the Pythagoras Theorem we have:
TX² + XZ² = TZ²
Substituting the values:
12² + XZ² = 20²
XZ² = 400 - 144
XZ = 16
Now, YZ = XZ thus, YZ = 16.
Hence, the lengths of the segments tangent to the circle are YZ = XZ = 16.
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The complete question is:
Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answe f(x) = 2x3 + x2 + 4x x =
There are no critical numbers for the function f(x) = 2x³ + x² + 4x. This is because the discriminant (b² - 4ac) is negative.
1. Calculate the derivative of the function with respect to x (f'(x)). This will help us identify where the function has a critical point (maximum, minimum, or inflection point).
f'(x) = [tex]\frac{d}{dx} (2x^{3} + x^{2} + 4x)[/tex]
2. Use the power rule for differentiation to find the derivative of each term.
f'(x) = (3 * 2)x² + (2 * 1)x + 4
3. Simplify the derivative.
f'(x) = 6x² + 2x + 4
4. To find the critical numbers, set the derivative equal to zero and solve for x.
6x² + 2x + 4 = 0
5. To solve for x, we can use the quadratic formula:
x = [tex]\frac{-b\sqrt{(b^{2} - 4ac) } }{2a}[/tex]
where a = 6, b = 2, and c = 4.
6. Plug the values of a, b, and c into the quadratic formula:
x = [tex]\frac{-2 +\sqrt{(2^{2} - 4(6)(4)) } }{2 * 6}[/tex]
7. Simplify the expression:
x =[tex]\frac{-2 +\sqrt{(92) } }{12}[/tex]
8. Since the discriminant (b² - 4ac) is negative, there are no real solutions for x, meaning there are no critical numbers for the given function.
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The number of students in tumbling classes this week is represented in the list. 5, 8, 11, 13, 5, 9, 2, 4, 6 What is the value of the mode for this data set? 13 6 5 2
in this particular data set, there is only one value that appears most frequently, which is 5.
What are statistics?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It provides a set of methods and tools for extracting meaningful insights and making decisions based on data.
In statistics, the mοde is the value that is repeatedly οccurring in a given set. We can alsο say that the value οr number in a data set, which has a high frequency οr appears mοre frequently, is called mοde οr mοdal value. It is οne οf the three measures οf central tendency, apart frοm mean and median. Fοr example, the mοde οf the set {3, 7, 8, 8, 9}, is 8.
Therefοre, fοr a finite number οf οbservatiοns, we can easily find the mοde. A set οf values may have οne mοde οr mοre than οne mοde οr nο mοde at all.
In the given data 5 has the maximum frequency so 5 is style mode of the given data
Mode=5
Therefore, in this particular data set, there is only one value that appears most frequently, which is 5.
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A beverage company manufactures and fills juice cans. They spend $0.04 on materials for each can, and fill each can with $0.27 worth of juice.
The marketing team wants to make a jumbo version of the can that's a dilated version of the original. They can spend at most $0.16 on materials for the new can. There's no restriction on how much they can spend on the juice to fill each can. The team wants to make the new can as large as possible given their budget.
1. By what factor will the height of the can increase? Explain your reasoning.
2. By what factor will the radius of the can increase? Explain your reasoning.
3. Create drawings of the original and jumbo cans.
4. What geometric solid do the cans resemble? What are some possible differences between the geometric solid in the actual can?
5. What will be the total cost for materials and juice fill for the jumbo can? Explain your reasoning.
6. Describe any other factors that might cause the total cost to be different from your answer.
Volume is a measure of the amount of space occupied by a three-dimensional object. It is typically expressed in cubic units, such as cubic meters, cubic feet, or cubic centimeters. The volume of an object can be calculated by measuring its dimensions and applying the appropriate formula.
In the given questions,
1.The height of the can will increase by a factor of 2. The marketing team wants to make the new can as large as possible given their budget, and since the cost of materials for the new can is limited to $0.16, they need to use the least amount of material possible. The volume of a cylinder is given by V = πr²h, so to maximize the volume of the can while using a limited amount of material, they should increase the height of the can while keeping the radius the same. Since the volume of a cylinder is proportional to the height, doubling the height will double the volume.
2.The radius of the can will remain the same. Since the marketing team wants to make the new can as large as possible given their budget, they need to use the least amount of material possible. Increasing the radius of the can will increase the amount of material needed to make the can, which will increase the cost of materials.
3.The cans resemble a cylinder. The actual can may have minor differences in shape due to manufacturing processes or imperfections.
4.The cost for materials for the jumbo can will be $0.16, and the cost to fill the can with juice will be $0.27. Therefore, the total cost for materials and juice fill will be $0.43 per jumbo can.
5.Other factors that might cause the total cost to be different could include the cost of labor to manufacture the cans, the cost of transporting the materials and finished products, and fluctuations in the cost of materials or juice. Additionally, the marketing team may need to consider the price point of the jumbo can and the demand for the product at that price point.
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Find the length of LM.
Write your answer as a whole number or a decimal
Answer:
LM = 5
Step-by-step explanation:
A secant is a straight line that intersects a circle at two points.
A segment is part of a line that connects two points.
Intersecting Secants TheoremThe product of the measures of one secant segment and its external part is equal to the product of the measures of the other secant segment and its external part.
The given diagram shows two secant segments LN and PN that intersect at exterior point N. Their external parts are MN and ON, respectively.
Therefore, according to the Intersecting Secants Theorem:
[tex]\implies \sf LN \cdot MN =PN \cdot ON[/tex]
Given values:
LN = 3 + x - 2 = x + 1MN = 3PN = 4 + x - 5 = x - 1ON = 4Substitute the values into the equation and solve for x:
[tex]\implies \sf LN \cdot MN =PN \cdot ON[/tex]
[tex]\implies (x+1)\cdot 3=(x-1)\cdot 4[/tex]
[tex]\implies 3x+3=4x-4[/tex]
[tex]\implies 4x-4=3x+3[/tex]
[tex]\implies 4x-4-3x=3x+3-3x[/tex]
[tex]\implies x-4=3[/tex]
[tex]\implies x-4+4=3+4[/tex]
[tex]\implies x=7[/tex]
To determine the length of LM, substitute the found value of x into the expression for the line segment:
[tex]\implies \overline{LM}=7-2=5[/tex]
Therefore, the length of LM is 5.
PLS HELP AND EXPLAIN UR ANSWER ILL MARK U BRAINLIST
Answer:
Microorganism B is 2500 times wider than microorganism A.
Step-by-step explanation:
Microorganism B is 2500 times wider than microorganism A.
Michelle buys 1.2 pounds of grapes. If grapes cost $0.75 per pound, how much did she pay?
Answer:
$1.60
Step-by-step explanation:
This is a very simple question
First start off with 1.2/0.75
1.2 divided by 0.75 = 1.6
Add a zero on to 1.6 and you have your answer of
$1.60
Monique looked at the clock at the beginning of class and at the end of class. How many degrees did the minute hand turn from the beginning of class until the end?
The measure of the angle through which the minute hand of a standard 12-hour clock rotates from the time Monique looked at the clock at the beginning of class to the time she looked at it again at the end of class is 6t degrees, where t is the time elapsed in minutes.
What is order of rotation ?The number of times the figure rotates around for a central point throughout the course of a full 360-degree rotation is referred to as the order of rotation in mathematics. Since it takes 4 of these revolutions to accomplish a full 360-degree rotation, a figure that swings 90 degrees and then returns to its original location has an order of rotation of 4. The idea of rotational symmetry—the characteristic of an image that remains constant during a rotation of a specific angle—and the order of rotation are closely related. The number of rotations a figure with symmetrical can undergo and yet maintain its original appearance is known as the order of rotation.
In the given question,
A normal 12-hour clock's minute hand completes one full rotation every 60 minutes. This implies it rotates 360 degrees in 60 minutes, or at a rate of 6 degrees per minute.
Now, locate the location of the minute hand at the start of class. When Monique looked at the clock at the start of class, the minute hand would be pointing directly at the number 12. As a result, the minute hand begins at 0 degrees.
Then, at the conclusion of class, find the location of the minute hand. If Monique glanced at the clock again at the conclusion of class, she would notice that the minute hand had moved t minutes from its initial position. As a result, the minute hand would be at:
6 degrees per minute × t minutes = 6t degrees
Now, we can find the angle through which the minute hand rotates by taking the difference between the starting and ending positions of the minute hand:
Ending position - Starting position = 6t degrees - 0 degrees = 6t degrees
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The complete question is: What is the measure of the angle through which the minute hand of a standard 12-hour clock rotates from the time Monique looked at the clock at the beginning of class to the time she looked at it again at the end of class?
on average, a textbook author makes two wordprocessing errors per page on the first draft of her textbook. what is the probability that on the next page she will make
Therefore, the probability that on the next page, the author will make at most two word processing errors is 0.99207367.
To find the probability of making word processing errors, we must use Poisson Distribution.
What is Poisson Distribution?
A Poisson distribution is a probability distribution that estimates the number of occurrences of an event in a fixed time or space interval.
It is used to model a situation where events occur randomly and independently over a fixed period or area.
The Poisson distribution's primary assumptions are that events are rare, random, and that one event does not affect another event's outcome. The Poisson distribution is useful in predicting the number of occurrences of a specific event in a given time or space interval. This distribution is useful in several fields, including finance, insurance, and public health.Now let's solve the given problem,
The probability that there are no word processing errors is given by[tex]:P (X = 0) = e^ -μμ = 200/500 = 0.4[/tex] (average number of errors per page = 2/5)P (X = 0) = e^ -0.4 = 0.67032005Now, the probability that there are 2 or fewer errors is given by:[tex]P (X ≤ 2) = ΣP (X = i) i = 0 to 2P (X ≤ 2) = P (X = 0) + P (X = 1) + P (X = 2)P (X ≤ 2) = 0.67032005 + 0.26812802 + 0.0536256P (X ≤ 2) = 0.99207367[/tex]
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The Colossus Ferris wheel debuted at the 1984 New Orleans World’s Fair. The ride is 180 ft tall, and passengers board the ride at an initial height of 15 ft above the ground. The height above ground, h, of a passenger on the ride is a periodic function of time, t. The graph displays the height above ground of the last passenger to board over the course of the 15 min ride.
*REFERRING TO THE GRAPH*
Sine function model: where h is the height of the passenger above the ground measured in feet and t is the time of operation of the ride in minutes.
2) The duration of the ride is 15 min.
(a) How many times does the last passenger who boarded the ride make a complete loop on the Ferris wheel?
(b) What is the position of that passenger when the ride ends
3. A power outage occurs 6 min after the ride started. Passengers must wait for their cage to be manually cranked into the lowest position in order to exit the ride.
Sine function model: Where h is the height of the last passenger above the ground measured in feet and t is the time of operation of the ride in minutes.
(a) What is the height of the last passenger at the moment of the power outage? Verify your answer by evaluating the sine function model.
(b) Will the last passenger to board the ride need to wait in order to exit the ride? Explain.
The heights of the passenger as they move on the Colossus Ferris wheel described by the specified sine function are;
2. (a) 22 times
(b) 180 feet which is the highest point on the ride
3. (a) 15 feet
(b) The last passenger will not need to weight
What is a sine function?A sine function is a mathematical function that describes a smooth repetitive oscillation. The sine function is a periodic function which repeats itself after certain interval. The sine function is the ratio of the opposite side to the hypotenuse side of a right triangle.
2. (a) The period of the sine function model, for the height, h = -82.5×cos(3·π·t) + 97.5 is 2·π/3. Therefore, the last passenger who boarded the ride makes a completer loop on the Ferris wheel every **2/3 minutes**. Since the duration of the ride is 15 minutes, the number of complete loops the passenger makes = 15/(2/3) = 22.5
The passenger completes the 22 times (The passenger cannot make a partial loop)(b) When the ride ends, the height of the last passenger can be found by evaluating the specified sine function at t = 15 minutes (the ride lasts for 15 minutes).
Therefore; h = -82.5 × cos(3 × π × 15) + 97.5 = 180.
Hence the position of the passenger when the ride ends is 180 feet or the highest point of the ride.3. (a) The time of operation of the ride when the power outage occurs is t = 6 minutes. The height of the last passenger at the time of the power outage is; h = -82.5 × cos(3 × π × 6) + 97.5 = 15
The height of the last passenger at the moment of the power outage therefore is; 15 feet(b) The last passenger to board the ride will not need to weight in order to exit the ride. This is because the height of the last passenger at the moment of the power outage is 15 feet, which is the initial height of the passenger when they board the ride. Therefore, the last passenger will be at the same height as the ground, and can exit the ride without waiting.
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In ΔRST, t = 3.7 inches, s = 1.7 inches and ∠S=155°. Find all possible values of ∠T, to the nearest 10th of a degree.
Answer:
The length of s is 5.3 inches to the nearest tenth of an inch
Step-by-step explanation:
In Δ RST
∵ t is the opposite side to ∠T
∵ r is the opposite side to ∠R
∵ s is the opposite side to ∠S
→ To find s let us use the cosine rule
∴ s² = t² + r² - 2 × t × r × cos∠S
∵ t = 3.7 inches, r = 1.7 inches, and m∠S = 155°
→ Substitute them in the rule above
∴ s² = (3.7)² + (1.7)² - 2 × 3.7 × 1.7 × cos(155°)
∴ s² = 13.69 + 2.89 - −11.40135196
∴ s² = 27.9813520
→ Take √ for both sides
∴ s = 5.28974025
→ Round it to the nearest tenth
∴ s = 5.3 inches
∴ The length of s is 5.3 inches to the nearest tenth of an inch
Strontium 90 is a radioactive material that decays according to the function A(t)= A0e^(−0. 02t) where A0 is the initial amount present and A is the amount present at time t(in years)
Expontial decay function, A(t) = A₀e⁻⁰·⁰²ᵗ
a) The decay rate of strontium 90 is equals to the 0.02.
b) The left strontium 90 after 40 years is equals to the 179.73 grams.
c)After approx 34.66 year, only 200 grams of strontium 90 will be left.
Expontial decay function is used to calculate the population decay, half-life,radioactivity decay, etc. Formula,
y(t) = a × eᵏᵗ --(1)
Where y(t) = value at time "t"
a = value at the startk = rate of decay constant (when k <0)t = timeWe have a Strontium 90, which is a radioactive material. Radioactive decay function of it is
A(t) = A₀e⁻⁰·⁰²ᵗ --(2)
where A₀ --> initial amount
A -> amount present at time t(in years)
Initaial amount, A₀ = 400 grams
(a) Comparing equation (1) and (2), we will results the decay constant, k = 0.02
Hence, decay rate of strontium = - 0.02.
(b) we have to determine strontium 90 is left after 40 years. That is t = 40 years
=> A(40) = 400×e⁻⁽⁰·⁰²⁾⁴⁰
=> A(40) = 400 ×0.377
=> A(40) = 179.73
So there will be around 179.73 grams of strontium 90 after 40 years.
c) For determine time there will be only 200 grams of strontium 90 left,
=> 200 = 400e⁻⁰·⁰²ᵗ
=> 1/2 = e⁻⁰·⁰²ᵗ
take natural logarithm both sides
=> ln(2) = ln( e⁰·⁰²ᵗ)
=> 0.02t = ln(2)
=> t = 34.6573
=> t≈ 34.66
So, there will be 200 grams left after approximately 34.66 years.
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Complete question :
Strontium 90 is a radioactive material that decays according to the function
A(t)=A0e−0.02t, where A0 is the initial amount present and A is the amount present at time t (in years). Assume that a scientist has a sample of 400 grams of strontium 90.
a) what is the decay rate of strontium 90?
b) how much strontium 90 is left after 40 years
c) when will only 200 grams of strontium 90 be left?
8th grade math
Geometry
Answer:
58
Step-by-step explanation:
We see that both sides around x are the same length, 6.2. This tells us our triangle is an isosceles triangle, which means two sides are the same lengths. This also tells us that two angles will be equal to each other.
The angle other than x and 61, will be equivalent to 61.
We also know that a triangle's angles equal 180. So,
180 - 61 = 119
119 - 61 = 58
x = 58
Sorry if my explaination isn't fully clear, it's hard to type it out and explain!
Tiffany can type 43 words per minute.If she maintains her typing speed without a break , how many words can she type in 2 hours and 15 minutes?
Answer:
5805 words
Step-by-step explanation:
2 hours × 60 minutes/hour = 120 minutes
120 minutes + 15 minutes = 135 minutes
2 hours and 15 minutes = 135 minutes
135 minutes × 43 words/minute = 5805 words