The percentage of scores greater than 34 is 0.5398 or 53.98%.
Given that the mean of scores (μ) = 35 and the standard deviation (σ) = 10. We need to find the percentage of scores greater than 34. Since the scores are normally distributed, we can standardize the variable by using the z-score formula.
z = (x - μ) / σ
Here, x = 34, μ = 35 and σ = 10z = (34 - 35) / 10z = -0.1
We need to find the area to the right of the z-score line on the standard normal distribution table. The standard normal distribution table provides the probabilities corresponding to the z-scores, i.e. the area under the curve to the right or left of the z-score line on the distribution table. The area to the right of the z-score line represents the percentage of scores that are greater than the given value. Using the standard normal distribution table, the area to the right of the z-score line -0.1 is 0.5398.
The percentage of scores greater than 34 is 0.5398 or 53.98%.
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jennifer needs to estimate the average age of vets in houston. the standard deviation of ages is 22 years. she wants the standard error of her mean to be 3.42 years. how many vets is she going to need to sample to get at least that kind of accuracy? (be sure to round up; you can't survey part of a person)
Jennifer needs to sample at least 151 vets to achieve a standard error of the mean of 3.42 years or less.
The variability or uncertainty of a sample statistic, like the mean or proportion, is measured by standard error. It represents the sample distribution's standard deviation for that statistic. In other words, it calculates the amount by which chance is likely to cause the sample statistic to deviate from the actual population parameter.
The calculation of the standard error is based on the particular statistic being produced as well as the characteristics of the sampled population. For instance, the population's standard deviation is divided by the square root of the sample size to determine the standard error of the mean. If p is the estimated proportion based on the sample, then the standard error of a proportion is determined as (p * (1 - p)) divided by the square root of the sample size.
A population parameter estimate that has a lower standard error is more accurate. Inferential statistics frequently employ the standard error to compute confidence intervals and test population parameter-related hypotheses.
The formula for the standard error of the mean can be used to get the approximate number of veterans Jennifer needs to sample:
[tex]SE = / \sqrt{n}[/tex]
where n: sample size, delta: age standard deviation, and SE: standard error of the mean.
In this instance, we are aware that = 22 years and SE = 3.42 years. As we solve for n, we obtain:
[tex]n = (delta / SE)^2 n = (22 / 3.42)^2 \sn = 150.39[/tex]
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pleaseee help super confused, and if you can please explain it i don’t understand
Answer:
China's top ten famous flowers are: the queen of flowers - plum blossom, the king of flowers - peony, frost blooming - chrysanthemum, gentleman's flower - orchid, the queen of flowers - rose, blooming flowers - Rhododendron, delicate flowers - camellia, water hibiscus - lotus, ten miles of fragrance - osmanthus, Lingbo fairy - daffodil 10 kinds of precious and beautiful local flowers.
Plum blossom is known as the "top ten famous flowers in China". These ten kinds of flowers respectively contain different levels of Chinese spiritual and cultural deposits, with profound and strong historical connotation. They are unique in the flower industry, marking the extraordinary significance of Chinese traditional culture. However, among China's top 10 traditional famous flowers, only the plum blossom, osmanthus and lotus have international registration rights.
Helppp.. also show work pls
Answer:
Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
Please help this is my last question on my unit test and I do not know it
Find and explain the error in the student’s work below.
Solve 2x² - 5x -12 = 0 using the Quadratic Formula.
The roots of the given quadratic equation are x= 4, [tex]\frac{-3}{2}[/tex]
The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the following generic form:
ax² + bx + c = 0The roots of a quadratic equation are found using the quadratic formula. In place of the factorization method, this formula aids in evaluating the quadratic equations' solutions. The quadratic formula aids in identifying the problem's fictitious roots when a quadratic equation lacks actual roots. Shreedhara Acharya's formula is another name for the quadratic formula.
2x² - 5x -12 = 0
The Shridharacharya formula or quadratic formula -
[tex]x=\frac{-b\ +-\sqrt{b^2-4ac}}{2a}[/tex]
we have a=2, b=-5 and c=-12
[tex]x=\frac{5+-\sqrt{5^2-4*2*12}}{2*2}\\\\x=\frac{5+-\sqrt{25+96}}{4}\\\\x=\frac{5+\sqrt{121}}{4}\\\\x=\frac{5+-11}{4}\\now, \\x=\frac{5+11}{4}=\frac{16}{4}\\x=4\\x=\frac{5-11}{4}\\x=-6/4\\x=-3/2[/tex]
The mistake in your solution is we have the value of b=-5 so , when we put the value of b in a formula then -5 will be 5.
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samantha recently hired a mechanic to do some necessary work. on the final bill, samantha was charged a total of $568. $475 was listed for parts and the rest for labor. if the hourly rate for labor was $31, how many hours of labor was needed to complete the job? (a) first write an equation you can use to answer this question. use x as your variable
Total of 3 hours are needed to complete the job.
The required equation that can be used to answer this question is: 31x = 568 − 475, where x is the number of hours of labor that was needed to complete the job.
Here's how you can solve it:Samantha recently hired a mechanic to do some necessary work. On the final bill, Samantha was charged a total of $568. $475 was listed for parts and the rest for labor.
If the hourly rate for labor was $31, how many hours of labor were needed to complete the job?Solution:Let x be the number of hours of labor needed to complete the job.
Labor cost = $31/hourTotal labor cost = 31x dollars. Total cost of the job = $568.
Cost of parts = $475.
Labor cost = Total cost − Cost of parts.
31x = 568 − 47531x = 93x = 3
Therefore, 3 hours of labor was needed to complete the job.
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Two landing points, A and B, lie on the straight bank of a river and are separated by 50 meters. Find the distance from each landing point to a boat pulled ashore on the opposite bank at a point C if
The distance from point A to the boat is approximately 23.3 meters, and the distance from point B to the boat is approximately 26.7 meters, rounded to the nearest foot.
Describe Distance?Distance can be calculated using a variety of methods, depending on the context. For example, the distance between two points in a straight line can be calculated using the Pythagorean theorem in two dimensions or the distance formula in three dimensions. In more complex situations, such as when the two points are not in a straight line, distance may be calculated using other mathematical methods or by estimating the distance based on contextual information.
Distance is often used in everyday life to describe how far apart objects or locations are from each other, such as the distance between two cities, the distance from home to work, or the distance between two landmarks. It is also used in many scientific fields to describe the separation between celestial objects, the distances traveled by particles in a chemical reaction, or the distances between neurons in the brain.
We can solve this problem using the Law of Sines, which states that for any triangle with sides a, b, and c and opposite angles A, B, and C:
a/sin A = b/sin B = c/sin C
Let's label the distance from point A to the boat as a, the distance from point B to the boat as b, and the distance from point C to the opposite bank as c. We are given that AB = 50 meters, angle ABC = 68 degrees, and angle BCA = 73 degrees. We want to find a and b.
First, we can find the measure of angle ACB by using the fact that the sum of angles in a triangle is 180 degrees:
angle ACB = 180 - angle ABC - angle BCA
angle ACB = 180 - 68 - 73
angle ACB = 39 degrees
Next, we can use the Law of Sines to find a and b:
a/sin 68 = c/sin 39
b/sin 73 = c/sin 39
Solving for c in both equations gives:
c = a sin 39 / sin 68
c = b sin 39 / sin 73
We can set these two equations equal to each other and solve for b:
a sin 39 / sin 68 = b sin 39 / sin 73
b = a (sin 39 / sin 73) * (sin 68 / sin 39)
b = a (sin 68 / sin 73)
We know that a + b = 50, so we can substitute the expression for b into this equation:
a + a (sin 68 / sin 73) = 50
Solving for a gives:
a = 50 / (1 + sin 68 / sin 73)
a ≈ 23.3 meters
Substituting this value of a into the expression for b gives:
b ≈ 26.7 meters
So the distance from point A to the boat is approximately 23.3 meters, and the distance from point B to the boat is approximately 26.7 meters, rounded to the nearest foot.
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The complete question is
Two landing points, A and B, lie on the straight bank of a river and are separated by 50 meters. Find the distance from each landing point to a boat pulled ashore on the opposite bank at a point C if angle ABC=68 degree and angle BCA=73 degree. Round to the nearest foot.
the fact that the overall frequency of an event can be determined by multiplying together the frequencies of the independently occurring factors related to that event is called what?
The fact that the overall frequency of an event can be determined by multiplying together the frequencies of the independently occurring factors related to that event is called a frequency multiplier. Also called as multiplication rule.
What is the multiplication rule?
The multiplication rule states that the overall probability of a sequence of events happening jointly is the product of the probabilities of the individual events.
In probability, the multiplication rule is used to calculate the joint probability of two independent events that occur together.
What are the factors in a probability scenario?In probability scenarios, the factors are the set of conditions that influence the probability of a certain occurrence, event, or outcome.
These factors are used to calculate the probability of an event. The likelihood of the occurrence of an event is based on these factors.
The multiplication rule can be used to calculate the overall frequency of an event by multiplying the frequency of each factor independently related to the event.
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the probability that a dessert sold at a certain cafe contains chocolate is 86%. the probability that a dessert containing chocolate also contains nuts is 30%. find the probability that a dessert chosen at random contains nuts given that it contains chocolate. round to the nearest tenth of a percent.
The probability that a dessert chosen at random contains nuts given that it contains chocolate is 34.9%.
The likelihood of any event A happening when another event B related to A has already happened is known as conditional probability. This implies that the likelihood of event A relies on event B.
The conditional probability symbol is P(A|B). Conditional probability P(A|B) is crucial for any exam that is part of a competition. The concept of conditional probability P(A|B), formula, and examples with solutions are all covered in this article. The Bayes theorem predicts the likelihood that an event connected to any condition would occur. For the situation of conditional probability, this theorem is taken into account.
Let A : a certain cafe contains chocolates
B: a dessert contains Nuts
P(A) = 86% = 0.86
P(AB) = 30% = 0.3
[tex]P(B|A) =\frac{P(AB)}{P(A)}[/tex]
= 0.3/0.86
= 34.9 %
So the answer is 34.9%
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11. if 3 men can dig a 3 x 2 x 4 meter hole in 20 minutes, how long will it take 6 men to dig a 4 x 4 x 3 meter hole?
it would take 6 men 20 minutes to dig a hole that is 4 x 4 x 3 meters
To solve this problem, we can use the formula that relates the time taken to do a job to the number of workers available, assuming that all workers have the same productivity. This formula is given by the equation:Work Done = Productivity x Time Taken x Number of Workers available. If we let the work done be W, the productivity be P, and the time taken be T, then the equation becomes:W = P x T x N. We are given that 3 men can dig a hole that is 3 x 2 x 4 meters in 20 minutes. We can find the volume of this hole by multiplying its dimensions:V = 3 x 2 x 4 = 24 cubic metersThis means that 3 men can dig a volume of 24 cubic meters in 20 minutes.
To find their productivity, we can use the formula: Productivity = Work Done / (Time Taken x Number of Workers)P = W / (T x N) = 24 / (20 x 3) = 0.4 cubic meters per minute per worker. Now we can use this productivity to find the time taken for 6 men to dig a hole that is 4 x 4 x 3 meters. We can find the volume of this hole by multiplying its dimensions:V = 4 x 4 x 3 = 48 cubic meters.
To dig this hole, the amount of work done would be 48 cubic meters. The productivity per worker is still 0.4 cubic meters per minute, but the number of workers is now 6. Therefore, the time taken would be:T = W / (P x N) = 48 / (0.4 x 6) = 20 minutes.Therefore, it would take 6 men 20 minutes to dig a hole that is 4 x 4 x 3 meters, given that 3 men can dig a hole that is 3 x 2 x 4 meters in 20 minutes.
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explain what the p-value means in the given context. a state university wants to increase its retention rate of 4% for graduating students from the previous year. after implementing several new programs during the last two years, the university reevaluates its retention rate and comes up with a p-value of 0.075. using , what can we conclude?
In this context, the p-value represents the probability of observing the data or a more extreme result, assuming that the null hypothesis (the retention rate is still 4%) is true.
In other words, it measures the strength of evidence against the null hypothesis. A small p-value indicates that the observed result is unlikely to have occurred by chance alone, while a large p-value suggests that the null hypothesis cannot be rejected.
In this case, the calculated p-value of 0.075 suggests that there is some evidence to reject the null hypothesis that the retention rate is still 4%.
However, since the p-value is above the conventional threshold of 0.05, we cannot conclude with certainty that the new programs have significantly increased the retention rate. Instead, we can say that there is some indication that the programs may have been effective, but further investigation is needed to determine if this is true.
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Solve for x. Round to the nearest tenth, if necessary.
D
59⁰
7.7
E
Xx
F
Click her
The value of x in the right triangle when calculated is approximately 13.8 units
Calculating the value of x in the triangleGiven the right-angled triangle
The side length x can be calculated using the following sine ratio
So, we have
sin(39) = x/22
To find x, we can use the fact that sin(39 degrees) = x/22 and solve for x.
First, we can use a calculator to find the value of sin(39 degrees), which is approximately 0.6293.
Then, we can set up the equation:
0.6293 = x/22
To solve for x, we can multiply both sides by 22:
0.6293 * 22 = x
13.8446 = x
Rewrite as
x = 13.8446
Approximate the value of x
x = 13.8
Therefore, x is approximately 13.8 in the triangle
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Which of the following equations could be the function pictured in the graph?
A. y= (x-1)(x+3)
B. y= (x+1)(x-3)
C. y= (x+1)(x+3)
D. y= (x+1)(x-1)
Answer:
B. y = (x+1)(x-3)
Step-by-step explanation:
Bbecause when y intersect the x axis, y = 0
so (x+1)(x-3) = 0, which we get x = -1 and x = 3
As shown in the graph this is true, because the function does indeed also intersect with the x axis at x = -1 and x = 3 as well.
What is the value of x given the following image?
The numerical value of x in the expression (x+5) and 2(x-4) is 61.
What is the numerical value of x?The sum of angles on a straight line equals 180 degrees.
From the figure in the image:
Angle GDC = x + 5Supplemetary angle to GDC = 2( x - 4 )We know that the sum of angles on a straight line equals 180 degrees.
Since angle GDC and its supplement are on a straight line.
Hence;
Angle GDC + Supplemetary angle to GDC = 180
Plug in the given values and solve for x.
( x + 5 ) + 2( x - 4 ) = 180
Apply distributive property.
x + 5 + 2x - 8 = 180
Collect like terms
x + 2x - 8 + 5 = 180
3x - 3 = 180
3x = 180 + 3
3x = 183
x = 183/3
x = 61
Therefore, the value of x is 61.
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. In which step does a mistake first occur?
(24+3 + 10)-14 + 2
Step 1: (8 + 10) -14 + 2
Step 2: 18 -14+2
Step 3: 4 +2
Step 4: 2
NEED HELP ASAP !!
TY
Answer:
The first one...............
Como resolver ecuaciones que tienen diferentes incógnitas
Ej: -x-4z=-15
To solve an equation with multiple unknowns, you need to have as many equations as there are unknowns.the solution to the system of equations is [tex]x = 13/11 and z = 37/11.[/tex]
What is the system of equations?For the equation you provided, [tex]-x - 4z = -15[/tex] , there are two unknowns: x and z. To solve for both, you need another equation that involves x and z.
If you have another equation that involves x and z, you can use a method like substitution or elimination to solve for both variables simultaneously.
For example, let's say you have the equation [tex]2x + 3z = 7.[/tex] You can use substitution to solve for one variable in terms of the other and substitute the result into the other equation.
To solve for x, rearrange the first equation to get x in terms of z:
[tex]-x - 4z = -15[/tex]
[tex]x = -15 + 4z[/tex]
Substitute the expression for x into the second equation:
[tex]2x + 3z = 7[/tex]
[tex]2(-15 + 4z) + 3z = 7[/tex]
Distribute the 2:
[tex]-30 + 8z + 3z = 7[/tex]
Simplify:
[tex]11z = 37[/tex]
Solve for z:
[tex]z = 37/11[/tex]
Substitute the value of z back into the equation for x:
[tex]x = -15 + 4z[/tex]
[tex]x = -15 + 4(37/11)[/tex]
[tex]x = -15 + 148/11[/tex]
Simplify:
[tex]x = 13/11[/tex]
Therefore, the solution to the system of equations is x = 13/11 and z = 37/11.
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assume that the relationship between test scores and the student-teacher ratio can be modeled as a linear function with an intercept of 698.9 and a slope of (-2.28). a decrease in the student-teacher ratio by 2 will:
the relationship between test scores and the student-teacher ratio can be modeled as a linear function: The right choice is D) lessen test scores by 4.56 for each school locale.
In view of the data in the inquiry, the relationship between test scores and the understudy educator proportion can be numerically composed as follows:
x = 698.9 - 2.28y .................... (1)
Where,
x = test scores
y = understudy educator proportion
The slant of (- 2.28) shows the sum by which x will change at whatever point there is an adjustment of y.
Hence, when there is a reduction in the understudy educator proportion by 2 (for example y = 2), we will have:
Change in x = - 2.28 * 2 = - 4.56
The negative sign thusly shows that the test scores will decrease by 4.56 for each school area. Accordingly, the right choice is D) lessen test scores by 4.56 for each school locale.
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the complete question is:
Assume that the relationship between test scores and the student-teacher ratio can be modeled as a linear function with an intercept of 698.9 and a slope of (-2.28). A decrease in the student teacher ratio by 2 will: A) reduce test scores by 2.28 on average) result in a test score of 698.9C) reduce test scores by 2.56 on average) reduce test scores by 4.56 for every school district.
in california, people use 63 btu of energy per home. this is 30% less than the national average. how many btu does an average american household use?
The national average for energy usage per home in BTU is approximately 90 BTU.
BTU stands for British Thermal Unit, which is the amount of energy required to raise the temperature of one pound of water by one degree Fahrenheit. It is used to quantify the amount of energy consumed by heating or cooling equipment.In California, people use 63 BTU of energy per home, which is 30% less than the national average. Therefore, to calculate the average BTU consumption for American households, we will use the following formula: National average BTU = California BTU / (1 - 30%)
Let's solve for the national average BTU: National average BTU = 63 BTU / (1 - 0.30)
National average BTU = 63 BTU / 0.70National average BTU = 90 BTU
Therefore, the average American household uses 90 BTU of energy per home.
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Find the exact value of X.
In the given right angled triangle, using Pythagorean theorem, the value of x is 12.73 units.
What is Pythagorean theorem?The Pythagorean theorem, also known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this rule, the length of the squares on the other two sides add up to the length of the square whose side is the hypotenuse, or the side across from the right angle. This theory can be expressed as the Pythagorean equation, which is an equation relating the lengths of the sides a, b, and the hypotenuse c:
a² + b² =c²
What is Hypotenuse?The longest side of a right-angled triangle, or the side across from the right angle, is called the hypotenuse.
In the given right angled triangle, using Pythagorean theorem,
x² = (9[tex]\sqrt{2}[/tex] )²+ (9[tex]\sqrt{2}[/tex] )²
x² = 81×2
x = [tex]\sqrt{162}[/tex]
x = 12.73 units
Therefore, the value of x will be 12.73 units.
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Which!??! HELPP meee
Answer:
Step-by-step explanation:
Replacing it
conditional formulas where the logic would state that if the conditions are met then the tool should exclude the data from analysis. t/f
True, conditional formulas can be used to exclude data from analysis if certain conditions are met. These formulas, often found in spreadsheet software and programming languages, allow you to set specific criteria that must be met in order for the data to be included or excluded from your analysis.
This can be useful in situations where you need to focus on specific subsets of data, or to remove outliers or irrelevant information from your dataset.
By incorporating conditional logic in your formulas, you can ensure that only relevant and useful data is included in your analysis, making it more accurate and efficient. Overall, the use of conditional formulas can greatly enhance your data analysis by providing a flexible and powerful tool to filter and process your data based on specific requirements.
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Oliver spots an airplane on radar that is currently approaching in a straight line, and
that will fly directly overhead. The plane maintains a constant altitude of 6900 feet.
Oliver initially measures an angle of elevation of 16° to the plane at point A. At some
later time, he measures an angle of elevation of 27° to the plane at point B. Find the
distance the plane traveled from point A to point B. Round your answer to the
nearest tenth of a foot if necessary.
Thus, the distance travelled by the airplane from point A to point B is found as: 1159.93 ft.
Explain about the angle of elevation?The angle from of the horizontal upward to an item is referred to as the angle of elevation. The line of sight of an observer will rise above the horizontal.The angle from horizontal downward to an item is referred to as the "angle of depression." The line of sight of an observer would fall short of the horizontal.Let the distance travelled between A and B be 'x'.
Height h = 6900 feet.
The figure is attached.
Using the tan function:
tan Ф = opposite side/ hypotenuse
In right triangle BCE.
tan 27 = 6900 / y
y = 6900 / tan 27
y = 15281.80
In right triangle ACD
tan 16 = 6900 /(x + y)
x + y = 6900/tan 16
x = 26873.72 - 15281.80
x = 1159.93
Thus, the distance travelled by the airplane from point A to point B is found as: 1159.93 ft.
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Solve (x – 3)2 = 49. Select the values of x. –46, -4, 10, 52.
Answer:
x = 10, -4
Step-by-step explanation:
(x – 3)² = 49
x - 3 = √49
x - 3 = ± 7
x = 10, -4
Looking at options, 10 and -4 is the answer.
19% of 43
Help please!!!
Answer:
8.17
Step-by-step explanation:
43x19/100 equals 8.17
There is a system of two linear equations. The first equation is y=7x+8. The system has infinite solutions. What other equation would complete the system?
If the system has infinite solutions, it means that the two equations are not independent, but rather one equation is a multiple of the other. In other words, the second equation must be a multiple of y = 7x + 8.
One possible equation that completes the system is:
14y = 98x + 112
To check that this equation works, we can substitute y = 7x + 8 into the equation:
14(7x + 8) = 98x + 112
98x + 112 = 98x + 112
As we can see, the equation is true for any value of x, which means that it is satisfied for any value of y that corresponds to y = 7x + 8.
Therefore, the system of equations that has y = 7x + 8 as one of its equations and has infinite solutions is:
y = 7x + 8
14y = 98x + 112
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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An airship flies 150 km with the wind and then turns around and flies back, taking 6 hr and 15 min for the round trip. Find the speed of the wind if the speed of the airship in calm weather is 50 km/hr.
Answer:
10km/hr
Step-by-step explanation:
The speed of the wind is approximately 6.93 km/hr.
We have,
Let's call the speed of the wind "w" (in km/hr).
When the airship is flying with the wind, its speed relative to the ground is the sum of its speed in calm weather (50 km/hr) and the speed of the wind (w km/hr). So the airship's speed with the wind is 50 + w km/hr.
When the airship is flying against the wind, its speed relative to the ground is the difference between its speed in calm weather (50 km/hr) and the speed of the wind (w km/hr).
So the airship's speed against the wind is 50 - w km/hr.
The distance flown by airship in each direction is the same (150 km).
Let's use the formula for distance, rate, and time:
distance = rate x time
For the first leg of the trip (flying with the wind), we have:
distance = (50 + w) x time
distance = (50 + w) x t(1)
where t(1) is the time taken for the first leg of the trip.
For the second leg of the trip (flying against the wind), we have:
distance = (50 - w) x time
distance = (50 - w) x t(2)
where t(2) is the time taken for the second leg of the trip.
The total time for the round trip is given as 6 hours and 15 minutes, or 6.25 hours.
So we have:
t(1) + t(2) = 6.25
We also know that the distance flown in each direction is 150 km. So we have:
(50 + w) x t(10 = 150
(50 - w) x t(2) = 150
Now we can solve this system of equations for w:
t(1) = 150 / (50 + w)
t(2) = 150 / (50 - w)
t(1) + t(2) = 6.25
Substituting the first two equations into the third equation, we get:
150 / (50 + w) + 150 / (50 - w) = 6.25
Multiplying both sides by (50 + w)(50 - w), we get:
150(50 - w) + 150(50 + w) = 6.25(50 + w)(50 - w)
Expanding and simplifying, we get:
7500 - 150w + 7500 + 150w = 15625 - 312.5w²
Simplifying further, we get:
15000 = 312.5w²
Dividing both sides by 312.5, we get:
w² = 48
Taking the square root of both sides, we get:
w = ±√(48)
Since the speed of the wind cannot be negative, we take the positive square root:
w = √(48) ≈ 6.93 km/hr
Therefore,
The speed of the wind is approximately 6.93 km/hr.
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12. STEM An engineer is designing solar
panels for a rover that will explore
Mars. The solar panel unfolds to an
isosceles trapezoid. The length of
one leg is 0.1.x -0.5 meters, and the
length of the other leg is 0.3.x-2.1
meters. What is the length of each of
the legs of the solar panel?
Answer:
Step-by-step explanation:
Let's call the length of the shorter leg of the isosceles trapezoid "a" and the length of the longer leg "b".
From the problem, we know that:
a = 0.1x - 0.5 (length of one leg is 0.1.x - 0.5 meters)
b = 0.3x - 2.1 (length of the other leg is 0.3.x-2.1 meters)
Since we know that the trapezoid is isosceles, we know that a = b. So we can set the two expressions equal to each other:
0.1x - 0.5 = 0.3x - 2.1
Now we can solve for x:
0.2x = 1.6
x = 8
Now that we know x, we can substitute it back into the expressions for a and b to find their lengths:
a = 0.1(8) - 0.5 = 0.3 meters
b = 0.3(8) - 2.1 = 0.3 meters
Therefore, each of the legs of the solar panel are 0.3 meters long.
Compare the amount of sand in the top cone of the hourglass to the amount there will be when the height of the sand in the top cone is only 1 inch.
HINT: The cones are similar
the amount of sand in the top cone when the height of the sand is only 1 inch is (h-1)/h times the amount of sand in the top cone originally.
the cones are similar, their volumes are proportional to the cube of their heights. Let's denote the height of the top cone as h, and the radius of the top and bottom bases as r. Then, the volume of the top cone can be expressed as:
V₁ = (1/3)π[tex]r^2[/tex]h
If the height of the sand in the top cone is reduced to 1 inch, then the height of the remaining sand in the top cone is (h-1) inches. The volume of the remaining sand in the top cone can be expressed as:
V₂ = (1/3)π[tex]r^2[/tex](h-1)
To compare the amount of sand in the top cone in these two scenarios, we can take the ratio of their volumes:
V₂/V₁ = [(1/3)π[tex]r^2[/tex](h-1)] / [(1/3)π[tex]r^2[/tex]h] = (h-1)/h
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solve the following polynomial inequality: x^2-5x-36>0
include all steps and place the answer in interval notation form.
please explain the steps and how you got the answer
Answer:
To solve the inequality x^2-5x-36>0, we need to find the values of x for which the expression is greater than zero.
One way to do this is by factoring the quadratic expression:
x^2-5x-36 = (x-9)(x+4)
The expression is positive when either both factors are positive or both factors are negative.
When both factors are positive: x-9 > 0 and x+4 > 0
Solving for x, we get x > 9 and x > -4. Therefore, x > 9.
When both factors are negative: x-9 < 0 and x+4 < 0
Solving for x, we get x < 9 and x < -4. Therefore, x < -4.
Now, we have two intervals: x < -4 and x > 9. To check whether the expression is positive within these intervals, we can pick a value within each interval and plug it into the expression.
Let's choose x = -5 (within x < -4) and x = 10 (within x > 9).
For x = -5:
x^2-5x-36 = (-5)^2-5(-5)-36
= 25+25-36
= 14
Since 14 is greater than zero, the expression is positive when x = -5.
For x = 10:
x^2-5x-36 = 10^2-5(10)-36
= 100-50-36
= 14
Since 14 is greater than zero, the expression is also positive when x = 10.
Therefore, the solution to the inequality x^2-5x-36>0 is x < -4 or x > 9, which can be written in interval notation as (-∞,-4) ∪ (9,∞).
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Answer:
first box (pies): 3, 6, 9, 12, 15, 18, 33
-> increments of 3
2nd box [cost ($)]: 11, 22, 33, 44, 55, 66, 121
-> increment of 11
Step-by-step explanation:
$44 ÷ 12 pies = $3.67 per 1 pie
3 × $3.67 = $11.01
same process: (number of pies) × $3.67 ≈ COST
Answer:
Step-by-step explanation:
So start off with 66 x 33. That will equal 2,178. Divide 2,178 by 18, like this: 2,178/18. That will equal 121. that will mean that 33 = 121. So 9 = 33 because 9 x 44 = 396 so you will divide that by 12 meaning that 9 equals 33. So now you will multiply 9 and 22 and then divide that answer by 33 making 6 = 22. now divide 22 by 6. That will equal 3.67. So 3.67 is the cost of one pie.
For the boxes above 12 and 44 it will be 16 = 59.
I hope it helped