Number of ways , two contaminated and 8 non- contaminated farms be choosen is 3,304,845,180.
Permutation and Combination
Combination is a mathematical way to arranging the set of values randomly.
ⁿCᵣ = n! / r! (n-r)!
we have given that ,
total number of farms for lead contamination = 50
Number of farms have dangerously high level of lead = 8
so, number of non- containmated farms ( no high level of lead ) = 50-8 = 42
We have to find the number of ways to choose two contaminated farms and eight non- contaminated farms. Two containmated farms are selected from 8 containated farms and 8 non- contaminated farms are selected from 42 farms .
Number of ways for selecting two containmated farms = ⁸C₂ = 8!/2!×6! = 8×7/2 = 28
Number of ways for selecting eight non-containmated farms from 42 farms = ⁴²C₈
= 42! / 8! 34! = 42×41×---×35/8×7×----×1
= 118013185
The total number of ways to obtain 2 containmated farms and 8 non- contaminated farms in 10 farms selected is then product of number of ways to select the 2 containmated farms and number of ways to select 8 non-containmated farms .
= 118030185× 28 = 3,304,845,180
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easy analyzing (due in 20 minutes)
Answer: f = 12m
Step-by-step explanation:
Starting at mile 5 we notice it's 60. But now at mile 7, we notice its 84. This means that we increase by 12 for each mile. Ergo, the answer should be f = 12m.
can you please help me find the measure of an exterior angle of a regular hexagon?
thanks
The measure of each exterior angles of a regular hexagon is 60 degrees
The interior angle of the regular polygon is
d = 180(n - 2) / n
Where d is the measure of interior angle
n is the number of sides
The number of sides in a regular hexagon
d = 180(6 - 2) / 6
= 180×4 / 6
= 720 / 6
=120 degrees
The each interior angle of the regular hexagon is 120 degrees
The measure of exterior angle = 180 - The measure of interior angle
= 180 - 120
= 60 degrees
Hence, the measure of each exterior angles of a regular hexagon is 60 degrees
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if our circadian clocks are not reset each morning by exposure to light, they: a. tend to run a cycle that is a little longer than 24 hours b. tend to run a cycle that is a little shorter than 24 hours c. tend to run on a 12-hour cycle d. still run exactly on a 24-hour cycle
If our circadian clocks are not reset each morning by exposure to light, they a. tend to run a cycle that is a little longer than 24 hours.
Chronobiology, the study of the body's circadian rhythms, contends that our daily routine, including when we eat, exercise, go to bed, and are exposed to light, may have a significant impact on how our bodies function on a day-to-day basis.
According to the National Institute of General Medical Sciences, circadian rhythms are the normal physical, mental, and behavioral changes that take place in the body on a 24-hour cycle, typically in reaction to light and darkness. One illustration is resting at night and remaining awake during the day.
You might not be able to avoid daytime sleep and evening work if you work an overnight shift or other irregular hours. According to Wright, those people should pay extra close attention to making other healthy decisions a priority, such as getting enough exercise and quitting smoking.
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Please help!!! photo is attached.
find the value of x
x = √ [?]
The required value of x is x = [tex]\sqrt{79}[/tex]
Given : A right angled triangle
This right angles triangle is again divided in two parts
the first part has measures 3 , z and the other side can be calculated by using The Pythagoras Theorem
According to this theorem
3² + z² = y²
thus 9 + z² = y² ------------------equation 1
Also 7 + 3 = 10
thus 10² = z² + x²-----------------equation 2
And 7² + y² = x² --------------- equation 3
from equation 1 we know
9 + z² + 49 = x²
58 + z² = x²
Thus on substituting this in equation 2 we get
100 = 58 + z² + z²
42 = 2z²
21 = z²
z = [tex]\sqrt{21}[/tex]
thus x² = 58 + 21 = 79
x = [tex]\sqrt{79}[/tex]
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What are the correct set of factors for the given equation?
1. 4x² - 11x - 3=0 18
A (2x + 1)(2x − 3)
B (4x + 1)(x − 3)
C (4x − 3)(x + 1)
Suzette ran and biked for a total of 50 mi in 4 h. Her average running speed was 5mph and her average biking speed was 15 mph.
Let x= total hours ran
Let y= total hours biked
How many hours did suzette run?
How many hours did she bike?
In total 4 hours Suzette ran for 1 hour and biked for 3 hours having average speed 5mph and 15mph respectively.
What is Average Speed?
Average speed is defined as total distance covered by the body divided by the time taken.
Average speed = Total distance covered/ total time taken
According to the given question:
Let x = total hours ran and y = total hours biked
Total time she ran and biked = 4h
∴ x + y = 4 ----- 1)
Total distance she biked and ran = 50 miles
Now, average running speed = 5 mph
Distance she ran = 5x
Similarly average biking speed = 15 mph
Distance she biked = 15y
∴ 5x + 15y = 50 ----- 2)
Solving 1) and 2) to get the values of x and y
Substituting x = 4 - y from 1) in 2)
5 (4 - y) + 15y = 50
On solving further we get y = 3
Substituting y = 3 to get x
x = 4 - 3
x = 1
Hence the Suzette ran for 1h and biked for 3h.
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. Kendra has a painting canvas that is 23 inches wide by 33 inches high. She painted a red
rose, which covered 30% of the canvas. What was the area of the canvas which was
covered by the red rose?
Answer:
227.7 in²
Step-by-step explanation:
You want to know the area that is 30% of a canvas that is 23 inches by 33 inches.
AreaThe area of the canvas is the product of its length and width.
A = LW
A = (33 in)(23 in) = 759 in²
RoseThe rose covers 30% of that area, so an area of ...
rose = 0.30 × 759 in² = 227.7 in²
The area of the canvas covered by the rose was 227.7 square inches.
Can anyone write the equation of the graph?
The equation of given graph is y = |x - 3| + 5.
The graph of a absolute or modulus function is a V- shape graph. The function of absolute is f(x) = |x|. The general form of absolute function is f(x)=a |x - h| + k. Where (h,k) is the vertex of graph.
Here, we can see that graph is in the form of V shape, so the function will be absolute function. Now, we have to find the vertex of graph.
As seen from the graph the minimum point on the graph is located at the point (3, 5) and the value of a should be 1.
So, by putting the value of vertex in general equation we get the equation of the graph,
y = |x - 3| + 5
Therefore, the equation of given graph is y = |x - 3| + 5.
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follow the steps to find the area of the Shaded region. use trigonometry to find the height of the triangle. ROUND TO THE FOURTH DECIMAL PLACE!
The height h of the triangle is equal 6.2cm
Trigonometric RatioTrigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle. The basic trigonometric ratios are sin, cos, and tan, namely sine, cosine, and tangent ratios.
In this case, we have some data and we can easily plug in those values and find the height.
Angle = 51 degreesHypothenuse = 8cmopposite = hWe can apply the sine ratio to this problem and solve.
sinθ = opposite / hypothenuse
sin 51 = h /8
h = 8 sin 51
h = 6.2cm
Using trigonometric ratio, the value of h is 6.2cm
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(10x-20)°
(6x + 8)º. help
Answer:
x=12°
Step-by-step explanation:
10x-20+6x+8=180°
16x=180+20-8
16x=192
x=12°
According to the fundamental theorem of algebra, how many zeros does the function f(x) = 5x - 9 have?
The algebraic fundamental theorem states that there are 12 zeros in the function f(x) = 15x12 + 41x9 + 13x2 10.
What is fundamental theorem?Theorem that connects the ideas of differentiating a function (calculating the gradient) and integrating a function is known as the fundamental theorem of calculus (calculating the area under the curve). With the exception of a constant value that depends on where one starts to compute area, the two procedures are inverses of one another.One of the antiderivatives (also known as an indefinite integral), let's say F, of some function f, may be derived as the integral of f with a variable bound of integration, according to the first section of the theorem, which is frequently referred to as the first fundamental theorem of calculus. This indicates that continuous function antiderivatives existacc to our question-
The degree that we need to identify in a polynomial is the largest exponent used in the equation. In this case, 15x¹², has the largest exponent. It is the degree of n used to determine the number of zeros.Thus, n = 12 so number of zero is also 12.hence,there are 12 zeros
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dean halverson recently read that full-time college students study 20 hours each week. she decides to do a study at her university to see if there is evidence that students study an average of more than 20 hours each week. a random sample of 31 students were asked to keep a diary of their activities over a period of several weeks. it was found that the average number of hours that the 31 students studied each week was 22.4 hours. the sample standard deviation of 3.7 hours.find the p -value. the p -value should be rounded to 4-decimal places.
Dean halverson recently read that full-time college students study 20 hours each week. 0.000519 is the p -value.
How to find the p-value ?
Given :
Population mean, μ = 20
Sample mean, xbar = 22.4
Sample standard deviation, s = 3.7
Sample size, n = 31
The hypothesis :
H0 : μ = 20
H0 : μ > 20
The test statistic :
(xbar - μ) ÷ (s/√(n))
T = (22.4 - 20) ÷ (3.7/√(31))
T = 2.4*5.6 ÷ 3.7
Test statistic = 3.632
Using the Pvalue calculator :
df = n - 1 = 31 - 1 = 30
Pvalue(3.632, 30) = .000519.
The p-value is .000519.
The result is significant at p < .05
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a bicycle wheel company packages each wheel in a square box. each wheel has a circumference of about 56.5 inches. what is the approximate length of each side of the box? a. 81 in b. 9 in c. 18 in d. 24 in
The approximate length of each side of the box is 18 inch.
Define circumference.The distance between the center of the sphere and any plane passing through it is known as the circumference. Any large circle that passes through a point known as a pole is called a meridian. The shortest path between any two points on a sphere called a geodesic. The space around a circle is known as its circumference. By calculating the distance required to walk around the globe, we may determine the size of the earth's circumference.
The circumference of a circle or other curved geometric object refers to its length. It is the boundary across any two-dimensional circular surface measured linearly in one dimension.
Given,
Circumference of circle = 56.5
c = π diameter
diameter = 3.14 × 56.5
diameter = 18
The approximate length of each side of the box is 18 inch.
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f(x) = −3 x 2+ 18x − 27
Answer:
18x−33−f(x)=0
Step-by-step explanation:Solve for f by simplifying both sides of the equation, then isolating the variable.
which is a net for this triangular prism
Answer:
this One...............
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The vertex of the graph is (-2, 2), the axis of symmetry of parabola is -2 and the parabola opens downwards.
In the given question we have to find the vertex, axis of symmetry and whether the parabola opens upwards and downwards.
Firstly we find ing the vertex of the graph.
As we know that vertex is the highest and lowest point of the graph.
From the graph the highest point is (-2, 2).
So the vertex of the graph is (-2, 2).
As we know that the axis of symmetry always passes through the vertex of parabola. The x coordinate of the vertex of parabola is the axis of symmetry of parabola.
So the axis of symmetry of parabola is -2.
As we can see that the parabola opens downwards.
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The front elevation of a solid shape is a triangle. The side elevation of the solid shape is a triangle. The plan view of the solid shape is a circle. Write the name of the shape.
Answer:
Cone
Step-by-step explanation:
The Angles are all triangle-shaped, but the bottom is circle-shaped.
What is the value of -2|6x - y| when x = -3 and y = 4?
O-44
O-28
O 28
O 44
Answer:
-44
Step-by-step explanation:
-2|6 * -3 - 4|
-2|-18-4|
-2|-22|
-2 * 22
-44
The geometric mean of a number and nine times the number is 30. What is the number?
victor, a student at um, conducted a similar survey among undergraduate students at the university of michigan using a random sample of the same size from the study conducted at cornell university and obtained the same sample proportion. the undergraduate student body at the university of michigan is almost twice as large as the undergraduate student body at cornell university. victor is concerned that the computation of the margin of error for a confidence interval for the population proportion will be affected by the population size. do you agree with victor's concern?
Yes, Victor needs to have similar portion of the population in the sample.
What is population size?
The number of objects inside a geographical area that has been arbitrary assigned as the population size.
In a fair, unbiased poll
Population proportion plus random error equals sample proportion.
According to the Normal Approximation, the standard deviation of the distribution of these random mistakes across all feasible samples is
[tex]\sqrt{\frac{\text{Population proportion}(1-\text{Population proportion})}{n}}[/tex]
The sample estimate's variance from the actual population value is known as the random error. Numerous alternative summaries, such as sample averages or discrepancies between two sample proportions or averages, are likewise consistent with the observation that random mistakes follow the normal curve.
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Serena just started working at the local salon. She is paid $9.85 per hour and earns, on
average, $58.50 in tips each day. Roseline just started working at a bank. Since she
does not receive tips, she earns $16.35 an hour. The system of equations
{y=9.85x+58.50 y=16.35x can be used to represent the amount of money earned, y,
each day for working x hours.
Determine the number of hours Serena and Roseline have to work to earn the same
amount of money.
The number of hours Serena and Roseline have to work to earn the same amount of money will be 9 hours.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Serena recently began working at the nearby salon. By and large, $58.50 in tips every day. Roseline recently began working at a bank. Since she doesn't get tips, she procures $16.35 60 minutes. The arrangement of conditions {y = 9.85x + 58.50 and y = 16.35x} can be utilized to address how much cash is procured, y, every day for working x hours.
The number of hours Serena and Roseline have to work to earn the same amount of money will be given as,
16.35x = 9.85x + 58.5
6.5x = 58.5
x = 9 hours
The number of hours Serena and Roseline have to work to earn the same amount of money will be 9 hours.
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For a floral arrangement class, Alicia has to create an arrangement of twigs and flowers that has a total of 9 objects.
Alicia wants the arrangement to have twice as many flowers as twigs. Write and solve a system of equations to find the number of twigs and flowers that Alicia will need.
By solving a system of two simultaneous linear equations, it can be calculated that
Alicia will need 3 twigs and 6 flowers
What is simultaneous linear equation?
At first it is important to know about linear equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.
Here, a system of two simultaneous linear equation needs to be solved
Let the number of twigs Alicia needed be x and the number of flowers Alicia needed be y
Alicia has to create an arrangement of twigs and flowers that has a total of 9 objects.
x + y = 9 ..... (1)
Alicia wants the arrangement to have twice as many flowers as twigs
2x = y .... (2)
Putting the value of x in (1)
x + 2x = 9
3x = 9
[tex]x = \frac{9}{3}[/tex]
x = 3
Putiing the value of x in (2),
y = 2 [tex]\times[/tex] 3
y = 6
Alicia will need 3 twigs and 6 flowers
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The handle of a car jack is moved 75cm and the car is lifted 2.5 cm. What is the ideal mechnical advantage of this car
Jack?
The ideal mechanical advantage of this car Jack: 30cm
What is Ideal mechanical advantage?
The length of the effort arm of a lever divided by the length of the resistance arm represents the optimal mechanical advantage. The IMA is typically calculated as the resistance force (Fr) divided by the effort force (Fe). IMA is also equal to the product of the load's travel distance (dr) and the distance over which the effort is applied (de).
The Handle of the car jack = 75cm
The car lifted by the jack = 2.5cm
According to the formula:
Ideal mechanical advantage = The resistance force / The effort force
or, (Fr/Fe)
IMA = 75 / 2.5
IMA = 30cm
Hence, Ideal mechanical advantage of the car jack = 30cm
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i need help with this asap please!!!
Answer:
54°
Step-by-step explanation:
m and the 54° angle are VERTICAL ANGLES. That means they are the same measure.
Answer:
Step-by-step explanation:
54 degree
Graph the line that satisfies each condition.
11. slope = 3, passes through A(0,1)
12. slope = - 3 − 2 , passes through R(-4, 5)
13. passes through Y(3, 0), parallel to DJ
14. passes through T(0, -2), perpendicular with D(-3, 1) and J(3, 3) to CX with C(0, 3) and X(2, -1)
The graph of line 3x-y= -1 will be as follows.
What is a line?
A line is an endlessly long, straight object that, despite being drawn with a minimum width, is considered to have no particular width in mathematics.
Main Body:
slope = m = 3 point = (0,1)
The formula for one point form for a line is -
y-y₁ = m(x-x₁)
y- 1 = 3(x-0)
3x-y =-1
Now the graph for the line will be plotted by using the point given and the slope--
on Graph mark the point (0,1)
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Members of the track team can run 400 meters in an average time of 58.2 sec. The fastest and slowest times varied from the average by 6.4 sec.
Write an absolute value equation to model this equation.
The absolute value equation modelling this situation is presented as follows:
|x - 58.2| = 6.4.
What is the absolute value of a number?The function giving the absolute value of another function is defined by the piece-wise rule presented as follows:
|f(x)| = f(x), f(x) ≥ 0.|f(x)| = -f(x), f(x) < 0.The result is never negative, as the function gives the distance of the function f(x) from the origin, which is the point in which f(x) = 0.
The difference between both the fastest and the slowest time from the average time of 58.2 seconds is of 6.4 seconds, hence the absolute value equation is given as follows:
|x - 58.2| = 6.4.
Which can be solved applying these following rules:
x - 58.2 = -6.4.x - 58.2 = 6.4.To find the fastest and slowest times, respectively.
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NEED HELP FINDING THE EQUATION!!! THXXXX
Answer:
See below
Step-by-step explanation:
Horizontal lines have ZERO slope
Vertical lines have 'undefined' slope
for this example x = 1/2 includes the point and has undiefined slope
the breaking strengths of a random sample of 20 bundles of wool fibers have a sample mean 436.5 and a sample standard deviation 11.9. (a) construct 90%, 95%, and 99% confidence intervals for the average breaking strength of the wool fibers. (b) compare the widths of the three confidence intervals. at which level of confidence do you have the widest interval? (c) do you think it is plausible that the average breaking strength is equal to 450?
With the help of standard deviation we can conclude our answer.
What is standard deviation?The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers.While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean (also known as the anticipated value) of the collection.The lower case Greek letter (sigma), for the population standard deviation, or the Latin symbol s, for the sample standard deviation, are most frequently used in mathematical texts and equations to indicate standard deviation. Standard deviation may be written as SD.acc to our question-
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most social science researchers are willing to declare that a relationship is statistically significant if the chances of observing the relationship in the sample when actually nothing is going on in the population (i.e., random chance) are less than what percent?
Most researcher fix level of significance at 5% i.e. they conclude a significant relationship when nothing is going on in 5% of cases. Hence,
Option A is correct which is 1.5%
Given that,
The majority of social scientists are willing to claim that a link is statistically significant if the likelihood of observing the relationship in the sample when nothing is happening in the population is greater than a certain threshold.
To find:
Less than what percentage of the population truly experiences nothing at all (i.e., random chance)
The majority of researchers set the level of significance at 5%, which means they draw conclusions about a meaningful association even when nothing is happening in 5% of cases.
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Jamal runs at a constant speed of 3.7 meters per second for
1/2
hour. Then he walks at a rate of 1.3 meters per seconds for 1/2 hour far did Jamal Uruk walk in 60 minutes
Answer:
9 km
Step-by-step explanation:
1/2 hr = 1800 seconds
3.7 m/s * 1800s + 1.3 m/s * 1800 s = 9000 m in 1 hr
( he walked AND ran this far)
