Answer:12
Step-by-step explanation:
have a good day
There is a statue that is 12 feet tall. When the sun is really low, it casts a shadow on the ground that is 20 feet long. What is the distance from the top of the statue to the top of the shadow?
Answer
sqrt 544 feet
Step-by-step explanation:
Pythagorean theorem: a^2 + b^2 = c^2
12^2 + 20^2= c^2
144+400=c^2
544=c^2
c= sqrt 544
Each big square below represents one whole.
A big square with 100 of the 100 equal pieces shaded
A big square with 5 of the 100 equal pieces shaded
Express the shaded area as both a fraction and a decimal.
Fraction:
Decimal:
A big square with 100 squares in the whole square. 5 of those squares are shaded. The shaded area as both a fraction and a decimal is expressed as:
Fraction: 5/100
Decimal: 0.05
What are decimals and fractions?In the form of a numerator and a denominator, fractions express a portion of a whole. Decimals are used to express fractions with a denominator of a power of ten, such as 10, 100, or 1000, in numerical form. Arithmetic is the representation of fractions in their decimal form, where the denominator is 10 or a power of 10 more, such as 100, 1000, or 10,000, etc.
Given:
Area of the whole square = 10 by 10
= 10×10 = 100unit²
The shaded area expressed as a fraction = 5unit²/100unit²
= 51/100
Shaded area expressed as a decimal = 5/100
Then take the number 5 and carry the point by two decimal place from the right
= 0.05
Shaded area expressed as a percent of the whole = (5/100) × 100
= (5×100)/100
= 5%
To learn more about square, visit:
https://brainly.com/question/14239024
#SPJ1
what if you were not restricted to using just rectangles to fill up the space between the curve and the x-axis? suggest a different geometric shape that you think might give us a more accurate estimate for this area? justify why you think your new geometric shape would yield a more accurate result.
If you were not restricted to using just rectangles to fill up the space between the curve and the x-axis, a different geometric shape that might give a more accurate estimate for this area is a trapezoid.
Using trapezoids would likely yield a more accurate result because they can better approximate the curve's shape.
Here's a step-by-step explanation of how using trapezoids can provide a more accurate estimate:
Divide the interval on the x-axis into equal subintervals.
In each subinterval, form a trapezoid by connecting the endpoints of the subinterval to the curve and then closing the shape by drawing a horizontal line from the curve to the x-axis
Calculate the area of each trapezoid using the formula: A = (1/2) * (base1 + base2) * height, where base1 and base2 are the lengths of the parallel sides of the trapezoid (the lengths along the x-axis and the curve), and the height is the length of the vertical line connecting the two bases (the width of the subinterval)
Sum the areas of all trapezoids to approximate the total area between the curve and the x-axis.
The reason trapezoids can provide a more accurate estimate is that they can closely follow the shape of the curve, especially when the curve is not a straight line. Since trapezoids have two different base lengths, they can better accommodate the changes in the curve's slope within each subinterval. This results in a closer fit to the curve compared to using rectangles, which can overestimate or underestimate the area depending on the curve's concavity.
Overall, using trapezoids for estimating the area under a curve can provide more accurate results, especially as the number of subintervals increases.
for more questions on trapezoid
https://brainly.com/question/1463152
#SPJ11
Darius is building a table. He cuts 12-foot-long boards into sections that are each ¼ foot long. How many sections of the board will Darius have when he is finished cutting?
Answer: 48
Step-by-step explanation: 1/4 goes into 1 four times: 4x12=48
Triangle
P
Q
R
PQR is a right triangle. The triangle has vertices at
P
(
−
2
,
4
)
,
Q
(
3
,
4
)
P(−2,4), Q(3,4) and
R
(
−
2
,
−
2
)
R(−2,−2). Graph the triangle on the triangle on the coordinate plane. To graph a triangle, plot all the vertices on the coordinate plane.
The graph of the triangle PQR is created by connect the three vertices.
What is triangle?A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry. A triangle is a clοsed, 2-dimensiοnal shape with 3 sides, 3 angles, and 3 vertices. A triangle is alsο a pοlygοn.
To graph the triangle PQR, we first plot the three vertices P(-2,4), Q(3,4), and R(-2,-2) on a coordinate plane:
Now, we connect the three vertices to form the triangle PQR:
Thus, the graph of the triangle ΔPQR is shown in the attachment..
To learn more about triangle from the given link:
https://brainly.com/question/2773823
#SPJ1
show that p/p²- 7 ÷ p²/p²- 49 can be written in the form a + b/p where a and b are integers
We can simplify the expression as follows:
p/(p² - 7) ÷ p²/(p² - 49)
= p/(p² - 7) * (p² - 49)/p² (by flipping the second fraction and multiplying)
= p(p + 7)(p - 7)/(p² - 7)(p²)
= (p + 7)(p - 7)/(p²)
Now, we can write this expression in the form of a + b/p as follows:
(p + 7)(p - 7)/(p²) = (p² - 49 + 2 * 49p)/(p²)
= 1 - 49/p² + 98/p³
Therefore, we can write the expression as:
p/(p² - 7) ÷ p²/(p² - 49) = (p + 7)(p - 7)/(p²) = 1 - 49/p² + 98/p³
So, we have expressed the given expression in the desired form of a + b/p where a = 1 and b = 0 and they are both integers.
A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below:
Spinner Results
Color Frequency
Red 19
Blue 4
Green 11
Yellow 15
Purple 4
Based on these results, express the probability that the next spin will land on red or green or yellow as a percent to the nearest whole number.
The probability of the next spin landing on red or green or yellow is approximately 85%.
what is probability?
Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur.
In the given question,
The total frequency of all colors is:
19 (red) + 4 (blue) + 11 (green) + 15 (yellow) + 4 (purple) = 53
The probability of the next spin landing on red or green or yellow is the sum of the frequencies of these colors divided by the total frequency:
(19 + 11 + 15) / 53 = 45 / 53
To express this as a percent to the nearest whole number, we can multiply by 100 and round to the nearest whole number:
(45 / 53) * 100 ≈ 85%
Therefore, the probability of the next spin landing on red or green or yellow is approximately 85%.
To know more about probability , visit:
https://brainly.com/question/30034780
#SPJ1
Answer:
Step-by-step explanation:
73%
A petri dish contains 4 viruses. Each hour, the number of viruses increases, as shown in the table. The population change can be modeled by a geometric sequence. Write a recursive formula and an explicit formula that can model this sequence. Use the formulas to predict how many viruses will be in the dish by the 7th hour.
We predict that there will be 512 viruses in the dish after 7 hours.
What is the model of the population?To model the population growth of the viruses in the dish, we can use a geometric sequence with a common ratio of 2, because the number of viruses doubles every hour.
Let Vn be the number of viruses in the dish after n hours. Then we have:
Recursive formula: Vn = 2Vn-1, with V0 = 4 (since we start with 4 viruses).
Explicit formula: Vn = 4 × 2n.
To predict how many viruses will be in the dish by the 7th hour, we can plug n = 7 into the explicit formula:
V7 = 4 × 27 = 4 × 128 = 512.
Therefore, we predict that there will be 512 viruses in the dish after 7 hours.
Learn more about model for prediction here: https://brainly.com/question/14602602
#SPJ1
Adrian's recipe for raisin muffins calls for 1 and 3/4 cups raisins for one bunch of muffins. Adrian wants to make two and one half batches of muffins for a bake sale. How many cups of raisins will Adrian use?
Answer: Adrian will need 4 and 1/2 cups of raisins for 2.5 batches of muffins
solve this system of equations by using the elimination method. 2x+6y=10 -3x+1y=5
PLEASE
Answer:
x = -1
y = 2
Step-by-step explanation:
2x + 6y = 10
-3x + 1y = 5
Time the second equation by -6
2x + 6y = 10
18x - 6y = -30
20x = -20
x = -1
Now put in -1 for x and solve for y
2(-1) + 6y = 10
-2 + 6y = 10
6y = 12
y = 2
Let's Check
2(-1) + 6(2) = 10
-2 + 12 = 10
10 = 10
So, x = -1 and y = 2 is the correct answer.
carpetland salespersons average per week in sales. steve contois, the firm's vice president, proposes a compensation plan with new selling incentives. steve hopes that the results of a trial selling period will enable him to conclude that the compensation plan increases the average sales per salesperson. a. develop the appropriate null and alternative hypotheses. : - select your answer - : - select your answer - b. what is the type i error in this situation? in this situation, a type i error would occur if it was concluded that the new compensation plan provides a population mean weekly sales - select your answer - when in fact it does not. what are the consequences of making this error? - select your answer - c. what is the type ii error in this situation? in this situation, a type ii error would occur if it was concluded that the new compensation plan provides a population mean weekly sales - select your answer - when in fact it does not. what are the consequences of making this error?
a. The null hypothesis (H0) states that the average sales per salesperson are not increased by the new remuneration scheme.
The new remuneration scheme raises the average sales per salesperson, contrary hypothesis (H1).
b. a Type I error occurs if it is concluded that the new compensation plan provides a population mean weekly sales increase when, in fact, it does not.
c. a Type II error occurs if it is concluded that the new compensation plan does not provide a population mean weekly sales increase when, in fact, it does.
a. The appropriate null and alternative hypotheses are :
Null hypothesis (H0): The new compensation plan does not increase the average sales per salesperson.
Alternative hypothesis (H1): The new compensation plan increases the average sales per salesperson.
b. In this situation, a Type I error occurs if it is concluded that the new compensation plan provides a population mean weekly sales increase when, in fact, it does not.
The consequences of making this error are that the company may adopt the new compensation plan and invest resources into it, without actually benefiting from increased sales.
c. In this situation, a Type II error occurs if it is concluded that the new compensation plan does not provide a population mean weekly sales increase when, in fact, it does.
The consequences of making this error are that the company may miss out on an opportunity to increase sales by not implementing the new compensation plan, which could lead to lower profits and reduced competitiveness in the market.
For similar question on hypotheses.
https://brainly.com/question/29560502
#SPJ11
I need a answer for this
The graph that represents a function is the absolute value graph
Identifying the graph that represents a functionThe vertical line test is a way to determine whether a graph represents a function or not.
To apply the vertical line test, we draw a vertical line through the graph.
If the vertical line intersects the graph at more than one point, then the graph does not represent a function. If the vertical line intersects the graph at only one point, then the graph represents a function.The graph that represents a function using the above as a guide is the absolute value graph in option a
Read more about vertical line test at
https://brainly.com/question/1821791
#SPJ1
what percentage of the world's land area has been granted some degree of protection in a park or preserve? view available hint(s)for part a what percentage of the world's land area has been granted some degree of protection in a park or preserve? 100% 90% 15% 1%
The answer to the question, "What percentage of the world's land area has been granted some degree of protection in a park or preserve?" is 15%.
What is a protected area?
A protected area is a defined geographical space, recognised, dedicated and regulated, through legal or other effective means, to achieve the long-term conservation of nature with associated ecosystem services and cultural values.
How does a protected area achieve conservation?
A protected area, by definition, is a place dedicated to the protection and maintenance of biodiversity and other natural and cultural resources of the area. Protected areas often encompass critical habitats, ecosystems, and landscapes. They offer essential ecological, economic, social, and cultural benefits to society.Conservation objectives are reached by restricting, regulating or prohibiting human activities in the protected area. Some common ways in which protected areas achieve conservation goals include:Enforcing regulations, including limits on extractive and polluting activities.Monitoring and managing species, ecosystems and landscapes to ensure their continued viability and integrity.Restoring degraded habitats or managing them for their long-term health and function.
What is a National Park?
A national park is a natural or semi-natural space designated to protect natural and cultural resources. National parks are established by governments to preserve a country's heritage, usually with the aim of promoting recreation and tourism.
For more questions on land area
https://brainly.com/question/23388895
#SPJ11
a machine cuts corks intended for use in wine bottles. it produces corks with diameters that are normal with mean 3.01cm and standard deviation 0.08cm. acceptable corks have diameters between 2.95cm and 3.05cm. a) what % of the corks produced by the machine is acceptable? enter numerical answer b) 80% of all corks produced by the machine have diameters less than: enter numerical answer
The 69.15% of the corks produced by the machine are acceptable. 80% of all corks produced by the machine have diameters less than 3.0772cm.
a) To find the percentage of acceptable corks, we have to calculate the area under the normal distribution curve corks have diameters between the limits of 2.95 cm and 3.05 cm.
Let X be the diameter of the corks produced by the machine. Then X follows a
The corks with diameters that have a normal distribution with mean μ = 3.01 cm
Standard deviation σ = 0.08cm.
Using the standard normal distribution, we can standardize X as follows:
Z = (X - μ) / σ
= (X - 3.01) / 0.08
The probability that Z lies between (2.95 - 3.01) / 0.08 = - 0.75
The probability that Z lies between(3.05 - 3.01) / 0.08 = 0.50.
Using a standard normal table that this probability is approximately 0.6915.
Therefore, the percentage of acceptable corks produced by the machine is 69.15%.
b) To find the diameter D such that 80% of the corks produced by the machine have diameters less than D.
Using the standard normal distribution the Z-score that corresponds to the 80th percentile is:
Z = InvNorm(0.8)
= 0.84
We can then solve for D:
D = μ + Zσ
= 3.01 + 0.84(0.08)
= 3.0772
Therefore, 80% of all corks produced by the machine have diameters less than 3.0772cm.
To learn more about Standard normal distribution :
https://brainly.com/question/27068375
#SPJ4
a smartphone was purposefully dropped from a height of 10 meters to test its durability from external physical impact. it will be damaged 100% of the time, but the damage can occur in different parts of the phone. it has been shown that 76% of the damages occur in the glass screen, while the other 24% occur in the battery. a number of smartphones were tested and the tests were independent. find the probability that the first time you observe a battery damage is during the third trial or later.
Answer:
what the quistion?
Step-by-step explanation:
sry i cant spell
The probability that the first time a battery damage is observed is during the third trial or later is 42.74%.
To solve this problem, we can use the geometric distribution, which models the number of trials until the first success in a sequence of independent trials. In this case, the probability of success is 0.24 (the probability of a battery damage) and the probability of failure is 0.76 (the probability of a glass screen damage).
The probability of observing a battery damage for the first time on the third trial or later can be calculated as the complement of the probability of observing a battery damage on the first or second trial.
The probability of observing a battery damage on the first trial is 0.24, and the probability of observing a battery damage on the second trial is (0.76)(0.24) = 0.1824 (the probability of no battery damage on the first trial times the probability of battery damage on the second trial). Therefore, the probability of observing a battery damage for the first time on the third trial or later is 1 - 0.24 - 0.1824 = 0.5776.
However, the question asks for the probability of observing a battery damage for the first time on the third trial or later, which means we need to take into account the fact that we may have observed a battery damage before the third trial. Therefore, we need to adjust our calculation by subtracting the probability of observing a battery damage for the first time on the first or second trial from our previous result.
The probability of observing a battery damage for the first time on the first or second trial is 0.24 + 0.1824 = 0.4224. Therefore, the probability of observing a battery damage for the first time on the third trial or later is 0.5776 - 0.4224 = 0.1552 or 15.52%.
Therefore, the probability that the first time a battery damage is observed is during the third trial or later is 42.74%
To learn more about probability here:
brainly.com/question/30034780#
#SPJ11
7. Michelangelo paints 7/8 of a wall in 1 hour. What part of a wall does Michelangelo paint in 1
minute?
The fraction 7/8 of a wall Michelangelo does paint in 1 minute for the given question.
what is fraction?In mathematics, a fraction is a representation of a part of a whole or a ratio of two quantities. It is typically represented as one number (the numerator) over another number (the denominator), separated by a horizontal line. For example, the fraction 3/4 represents three parts out of a total of four equal parts, or a ratio of three to four.
Fractions can also be represented as decimals or percentages. For instance, the fraction 1/2 is equal to the decimal 0.5 or the percentage 50%. Fractions are used in a variety of mathematical operations, such as addition, subtraction, multiplication, and division. They are also used in everyday life, such as in cooking recipes or in measurements of time or distance.
If Michelangelo paints 7/8 of a wall in 1 hour, then he paints (7/8)/1 = 7/8 of a wall in one hour.
So, the answer is 7/8 of a wall.
To learn more about fractions from the given link
https://brainly.com/question/10354322
#SPJ9
HELPPPPPPPPP PLEASE HURRY !!!!!!!!!!!!!!!!! GIVING 40 POINTS!!!!!!!!!!!!!!!!!!
HELPPPPPPPPPPPPPPPPP
The time to reach the maximum height is 3 seconds and the maximum height is 44.1 meters, and other solutions are below
The height of the cannot at launchTo do this, we find h when t = 0
From the graph, we have
h(0) = 70
So, the height of the cannot at launch is 70 meters
The time to reach the maximum heightFrom the graph, we have the vertex to be
Vertex, (t, h) = (3, 114.1)
So, the time to reach the maximum height is 3 seconds
The maximum heightFrom the graph, we have the vertex to be
Vertex, (t, h) = (3, 114.1)
So, the maximum height is 114.1 meters
How long to land on the groundThis is when h(t) = 0
From the graph, we have
h(7.93) = 0
So, the time spent is 7.93 seconds
The equation if the velocity changesThe given equation is
h(t) = -4.9t^2 + 29.4t + 70
If the initial velocity changes, then the equation becomes
h(t) = -4.9t^2 + 40.5t + 70
The equation if the height of launch is 0The given equation is
h(t) = -4.9t^2 + 29.4t + 70
If the initial height changes, then the equation becomes
h(t) = -4.9t^2 + 29.4t
The time to reach the maximum height and the maximum heightWe have
h(t) = -4.9t^2 + 29.4t
Differentiate and set to 0
-9.8t = -29.4
So, we have
t = 3
Next, we have
h(3) = -4.9 * 3^2 + 29.4 * 3
h(3) = 44.1
So, the time to reach the maximum height is 3 seconds and the maximum height is 44.1 meters
Read more about height functions at
https://brainly.com/question/10837575
#SPJ1
The line plot displays the cost of used books in dollars.
A horizontal line starting at 3 with tick marks every one unit up to 8. The line is labeled Cost in Dollars, and the graph is titled Cost of Used Books. There are two dots above 4, 5, and 7. There are four dots above 6.
Which measure of center is most appropriate to represent the data in the graph, and why?
The median is the best measure of center because there are no outliers present.
The mean is the best measure of center because there are no outliers present.
The median is the best measure of center because there are outliers present.
The mean is the best measure of center because there are outliers present.
What is the appropriate measure of variability for the data shown, and what is its value?
The range is the best measure of variability, and it equals 18.5.
The IQR is the best measure of variability, and it equals 45.
The range is the best measure of variability, and it equals 45.
The IQR is the best measure of variability, and it equals 18.5.
The measure οf the center that is mοst apprοpriate tο represent the data in the line plοt graph is -
Optiοn A: The median is the best measure οf center because there are nο οutliers present.
What is line plοt?A line plοt is a graph that uses symbοls tο represent data abοve a frequency number line tο indicate the frequency οf each value. It is emplοyed tο arrange the data simply and is very simple tο understand.
Since the data is displayed using a line plοt and the plοt shοws the frequency οf data values, it is clear that the data is discrete.
In this case, the apprοpriate measure οf center wοuld be the median, which is the middle value when the data is arranged in οrder.
The fact that there are sοme dοts abοve certain values suggests that these values οccur mοre frequently in the data set.
Hοwever, this dοes nοt necessarily mean that there are οutliers present. Outliers are extreme values that are far away frοm the majοrity οf the data and can skew the results when using the mean as a measure οf center.
Therefοre, the median is the mοst apprοpriate measure οf center in this case because it is nοt affected by the presence οf οutliers and it represents the middle value οf the data set.
To learn more about line plot from the given link
brainly.com/question/29946085
#SPJ1
Which one of the following is not equal reast
A 2 of 15
B 3/2 of 400
C 5 of 60
D 6 of50%
Answer:Option(a)
Step-by-step explanation: A) 2 of 15
please help.
see below
Answer:
A
Step-by-step explanation:
in any right triangle the sine ratio of an angle Θ is
sinΘ = [tex]\frac{opposite}{hypotenuse}[/tex]
is 4/9 half of 8/18 shaw how you know
Answer:
To show this, we can simplify both fractions to a common denominator and compare them.
First, we can simplify 8/18 to 4/9 by dividing both the numerator and denominator by 2.
Then, we can compare 4/9 to 4/9.
Since both fractions are equal, we know that 4/9 is half of 8/18.
Alternatively, we can cross-multiply and simplify to compare the fractions:
4/9 = (1/2) * 8/18
4/9 = 4/9
What is the equation of the line that is parallel to y = 6x - 1 and passes through the point (-3, 4)?
The equation will be in slope-intercept form.
Oy=-6x + 5
Oy=6x14
0y=-1/6x-5
O y = 6x + 22
Oy=-1/6x-7
Answer:
y=6x+22
Explanation:
Parallel lines have the same slope and different y-intercepts.
So, all the lines with different slopes will be eliminated.
Now, we can check which line passes through the point (3,4) by substituting x for the x coordinate and y for the y coordinate.
y=6x+22
4=6(-3)+22
4=-18+22
4=4
So, the correct answer is y=6x+22.
Which square root of 225 has a negative value?
The two square roots of 225 are +15 and -15.
However, since negative values are usually not considered answers for practical purposes, the principal square root of 225 is +15 (i.e., √225 = 15).
State different ways to find the measure of a side of triangles.
Pythagorean theorem, trigonometric ratios, Law of sines and Law of cosines are different ways to find the measure of a side of triangles.
There are different ways to find the measure of a side of a triangle;
1.Pythagorean theorem:The theorem states that the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. Therefore, if a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, we have c²= a² + b².
2.Trigonometric ratios:if we know the measure of one acute angle (other than the right angle) and the length of the adjacent side to that angle, we can use the cosine function to find the length of the hypotenuse, or the sine function to find the length of the opposite side.
3.Law of sines:The law states that the ratio of the length of a side to the sine of the angle opposite that side is the same for all sides and angles of the triangle. Therefore, if a, b, and c are the lengths of the sides of a triangle and A, B, and C are the measures of the angles opposite those sides, we have a/sin(A) = b/sin(B) = c/sin(C).
4. Law of cosines:The law states that the square of a side is equal to the sum of the squares of the other two sides minus twice the product of those sides and the cosine of the included angle. Therefore, if a, b, and c are the lengths of the sides of a triangle and C is the measure of the included angle between sides a and b, we have c² = a² + b² - 2abcos(C).
To know more about hypotenuse, visit:
https://brainly.com/question/29407794
#SPJ1
f(x) = 12x - 4.8x²
find the average rate of change over the interval 0
To find the average rate of change of a function over a given interval, we need to calculate the change in the function over that interval, and divide by the length of the interval.
In this case, we want to find the average rate of change of the function f(x) = 12x - 4.8x^2 over the interval [0,5].
First, we need to find the value of the function at the endpoints of the interval:
f(0) = 12(0) - 4.8(0)^2 = 0
f(5) = 12(5) - 4.8(5)^2 = -72
Next, we calculate the change in the function over the interval:
Change in f(x) = f(5) - f(0) = -72 - 0 = -72
Finally, we divide the change in the function by the length of the interval:
Average rate of change = (Change in f(x)) / (Length of interval) = (-72) / (5-0) = -14.4
Therefore, the average rate of change of the function f(x) = 12x - 4.8x^2 over the interval [0,5] is -14.4.
a cable of density p pounds per foot is used to lift w pounds of coal up a mineshaft that is 632 feet deep. how much work is done in this process?
The work done in the process of lifting coal up a mineshaft that is 632 feet deep is found to be 650,000 ft/lb.
For a cable of density, work = ∫k*y dy from 0 to b.
where k is the linear density of the cable (in lb/ft in this case), y is the distance from the top of the cable, and b is the total distance the weight has to travel to the bottom of the cable.
With this setting, the top of the cable should be labeled y=0 and the bottom of the cable (connected to the coal weight) should be labeled y=b. In this case, k = 2 ft/lb and b = 500 ft.
The 800 lb coal weight is additional information that we have not yet calculated.
Since pounds are a unit of force and the force to lift the coal is constant at 800 pounds, you can add the weight of 800 pounds to the integral and the work done to lift the coal is force * distance . The final integral is:
work = ∫(2y + 800) dy from 0 to 500.
integral:
Work = y2 + 800y | 0 to 500
= (500)2 + 800(500)
So, the work done is 650,000 ft/lb.
To know more about work done, visit,
https://brainly.com/question/8119756
#SPJ4
Complete question - A cable that weighs 2 lb/ft is used to lift 800 lb of coal up a mine shaft 500 ft deep. Find the work done.
assume two coins, one fair and the other is unfair. you pick one at random, flip it five times, and observe that it comes up as tails all five times. what is the probability that you are flipping the unfair coin?
The probability of flipping the unfair coin given that we observed five tails in a row is approximately 0.9048
Let's define
A: the event of picking the unfair coin
B: the event of getting five tails in a row
We want to find the conditional probability of picking the unfair coin given that we observed five tails in a row, or P(A|B).
Using Bayes' theorem, we have
P(A|B) = P(B|A) × P(A) / P(B)
P(B|A) is the probability of getting five tails in a row given that we are flipping the unfair coin. Since the unfair coin is not fair, we don't know its probability of coming up as tails, but let's assume it has a probability of 0.9 of coming up as tails. Thus, P(B|A) = 0.9^5 = 0.59049.
P(A) is the prior probability of picking the unfair coin, which is 0.5 since we picked one of two coins at random.
P(B) is the total probability of getting five tails in a row, which is the sum of the probabilities of getting five tails in a row with the fair coin and the unfair coin.
The probability of getting five tails in a row with the fair coin is 0.5^5 = 0.03125. The probability of picking the unfair coin and getting five tails in a row is P(B|A) × P(A) = 0.59049 × 0.5 = 0.295245. Thus, P(B) = 0.03125 + 0.295245 = 0.326495.
Now we can calculate P(A|B)
P(A|B) = P(B|A) × P(A) / P(B) = 0.59049 × 0.5 / 0.326495 = 0.9048
Learn more about probability here
brainly.com/question/11234923
#SPJ4
a bowl contains 10 red balls and 10 blue balls. a woman selects balls at random without looking at them. what is the minimum number of balls she must select to be sure of having at least three blue balls?
The minimum about of balls she should pick is 13.
So, the woman consider all the balls and picks the balls without looking,
To have a clear chance of picking at least 3 blue balls from the bowl she has to first eliminate the possibility of picking red balls.
Therefore,
She first picks 10 balls from the bowl, which gradually eliminates the possibility of picking a red ball.
now, she picks 3 more balls from the rest of the available balls which increases the changes of the balls being blue.
then,
=> 10 + 3 = 13
The minimum about of balls she should pick is 13.
To learn more about Probability,
https://brainly.com/question/24756209
#SPJ4
A 6 inch by 10 inch rectangle is dilated by a factor of 2. What is the area of the dilated rectangle?
I NEED HELP ON THIS ASAP!!!
The perimeter of triangle XYZ with the vertices, X(2, 5), Y(10 9), and Z(6, 1), is approximately 24.07 units.
How to Find the Perimeter of a Triangle?To find the perimeter of the triangle, we need to add up the lengths of all three sides. To do this, we can use the distance formula, which is:
d = √[(x2 - x1)² + (y2 - y1)²]
Using this formula, we can find the length of each side of triangle XYZ:
Side XY:
d = √[(10 - 2)² + (9 - 5)²] = √64 + 16 = √80
Side YZ:
d = √[(6 - 10)² + (1 - 9)²] = √16 + 64 = √80
Side ZX:
d = √[(6 - 2)² + (1 - 5)²] = √16 + 16 = √32
Therefore, the perimeter of triangle XYZ = XY + YZ + ZX = √80 + √80 + √32
Perimeter ≈ 24.07 (rounded to two decimal places)
Learn more about the perimeter of a triangle on:
https://brainly.com/question/17394545
#SPJ1