a rotating light is located 12 feet from a wall. the light completes one rotation every 2 seconds. find the rate at which the light projected onto the wall is moving along the wall when the light's angle is 20 degrees from perpendicular to the wall.
Answers
The rate at which the light's projection moves along the wall when the light's angle is 20 degrees from perpendicular to the wall is approximately 1.078 feet per second.
Let's let t be the time elapsed since the light started rotating, and θ be the angle that the light makes with the perpendicular to the wall, as shown in the diagram. The rate at which the light's projection moves along the wall is given by the derivative of the horizontal distance between the projection point P and the foot of perpendicular Q, with respect to time t. Let's call this distance x.
From the diagram, we can see that:
tan(θ) = x / 12
Differentiating both sides with respect to time t, we get:
sec²(θ) dθ/dt = (dx/dt) / 12
We are given that the light completes one rotation every 2 seconds, which means that the angular velocity of the light is:
dθ/dt = 2π / (2 seconds) = π radians per second
Substituting this value and θ = 20° (converted to radians), we get:
sec²(20°) (π rad/sec) = (dx/dt) / 12
Simplifying:
(1/cos²(20°)) (π/2) = (dx/dt) / 12
Multiplying both sides by 12 and evaluating the left-hand side, we get:
dx/dt = 1.078 feet per second
As a result, when the light's angle is 20 degrees from perpendicular to the wall, the pace at which the projection advances along the wall is roughly 1.078 feet per second.
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Related Questions
identify a characteristic of change managers that an organization should consider when employing people.
Change managers are nonconformists who take risks.
Having a large number of conformist is effective for an organization.
Change managers are usually regarded as peacemakers who follow rules.
Having a large number of radical innovators is effective for an organization.
Answers
While hiring change managers, businesses should take into account their nonconformist, risk-taking nature.
To successfully implement organizational change efforts, change managers must question the status quo, take measured risks, and foster creativity. Organizational stability and routine tasks may be maintained more successfully with a large number of conformists, but change managers need a distinct skill set. They must be able to think creatively, try out novel concepts, and deal with ambiguity and uncertainty.
Option 3: Being seen as a rule-following peacemaker may be an asset in some situations, but it is not always necessary for a change manager. Similarly, having a lot of radical innovators (option 4) could backfire if there isn't a balance with other qualities and abilities crucial for effective change management.
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The complete question is:
identify a characteristic of change managers that an organization should consider when employing people.
→ Change managers are nonconformists who take risks.
→ Having a large number of conformist is effective for an organization.
→ Change managers are usually regarded as peacemakers who follow rules.
→ Having a large number of radical innovators is effective for an organization.
While hiring change managers, businesses should take into account their nonconformist, risk-taking nature.
To successfully implement organizational change efforts, change managers must question the status quo, take measured risks, and foster creativity. Organizational stability and routine tasks may be maintained more successfully with a large number of conformists, but change managers need a distinct skill set. They must be able to think creatively, try out novel concepts, and deal with ambiguity and uncertainty.
Option 3: Being seen as a rule-following peacemaker may be an asset in some situations, but it is not always necessary for a change manager. Similarly, having a lot of radical innovators (option 4) could backfire if there isn't a balance with other qualities and abilities crucial for effective change management.
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which statement about random sampling is true? responses random sampling helps to increase sample size. random sampling helps to increase sample size. random sampling helps to decrease sample size. random sampling helps to decrease sample size. random sampling helps to increase bias. random sampling helps to increase bias. random sampling helps to reduce bias.
Answers
The statement "random sampling helps to reduce bias" is true. Random sampling is a statistical technique where each member of the population has an equal chance of being included in the sample.
How this statement is true?By randomly selecting participants, the sample is more likely to be representative of the population, which helps to reduce bias.
Random sampling helps to reduce bias because it eliminates systematic bias, which can occur when certain individuals or groups are overrepresented or underrepresented in the sample.
For example, if a researcher only sampled individuals from a certain demographic group, the results of the study may not be generalizable to the larger population.
Random sampling also helps to increase the precision of the estimate of the population parameter, as it reduces the variability in the sample. This allows researchers to draw more accurate conclusions about the population based on the sample data.
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Each letter in the word ORLANDO is written on a card and put into a bag. What is the theoretical probability of choosing an “O”, putting it back and then drawing a “A”.
Answers
Hence, The theoretical probability of selecting a "O", returning it to the bag, and then selecting a "A" from the collection is 2/21.
What is the probability?The probability of an occurrence is a number used in mathematics to describe how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.
What is the event in probability?In probability theory, an event is a set of outcomes of an experiment to which a probability is assigned. A single outcome may be an element of many different events, and different events in an experiment are usually not equally likely, since they may include very different groups of outcomes.
The word "ORLANDO" consists of 7 letters,
in this word "ORLANDO" the O letter is 2 times and A is one times
probability of "O" letters is 2/7 before there are two "O"s in total out of the seven letters because we are putting the first letter back before drawing the second.
After that, there are still 2 "O"s and 1 "A" in the bag for the second draw because we placed the first "O" back. Because there is only one "A" out of a possible three letters, the probability of drawing one on the second draw is one in three.
We multiply the probabilities of each occurrence to determine the probability that both will occur:
P("O" on the first draw)* P("A" on the second draw) = (2/7) * (1/3) = 2/21
The theoretical probability of selecting a "O", returning it to the bag, and then selecting a "A" from the collection is therefore 2/21, or roughly 0.095, or 9.5%.
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What is 219.8 rounded as indicated
Answers
Answer:
8 is closer to 10, so 219.8 rounded is 220.
Coach Sanchez is setting up a court for
a game of four-square. He has a
square space, with an area of 64
square feet. What is the longest side
length Coach Sanchez can make for
one side of the court?
Answers
Thus, coach Sanchez can only create a side length of 8 for one side of the court, which is the longest side length.
Explain about the square root:The factor of a number that, when multiplied by itself, equals the original number is known as the square root of the number. Practically speaking, determining a number's square root is the reverse of doing so to find its square.
Properties
A perfect square root corresponds to a perfect square number.The square root of an even perfect number is even.The square root of an odd perfect number is odd.You only need to find that square root of the area to determine the length of a side because we know that a square already has equal sides so the area is determined by two sides.
√64 = 8
Thus, coach Sanchez can only create a side length of 8 for one side of the court, which is the longest side length.
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In triangle ∆ABC, m<A = 33°, m<C = 58°, and AB = 25 in. What is AC to the nearest tenth of an inch?
1. 16.1 in.
2. 38.9 in
3. 42 in.
4. 12 in.
Answers
The value of AC to the nearest tenth is 29.5
What is sine rule?The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.
Angle B = 180-(33+58)
= 180-91 = 89°
using sine rule
represent AC by x
x/ sin89 = 25/sin 58
xsin58 = 25sin89
0.848x = 0.9998×25
0.848x = 24.995
x = 24.995/0.848
x = 29.5( nearest tenth)
therefore the value of AC is 29.5.
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The volume of Box A is 2/5
the volume of Box B. What is the height of Box A
if it has a base area of 32 square centimeters?
Box A
32 cm
Box B
10 cm
8cm
16 cm
Answers
The volume of the box A is approximately 6.4 centimeters
Determining the volume of a boxLet's denote the height of Box A by h, and its volume by V. We can set up a proportion between the volumes of Box A and Box B as follows:
V(A) = (2/5) V(B)
Since the volume of a box is given by its base area times its height, we can express the volumes of Box A and Box B in terms of their base areas and heights:
32h = (2/5) (10 × 8 × 16) = 512
Simplifying the right-hand side:
32h = 204.8
Dividing both sides by 32:
h = 6.4
Therefore, the height of Box A is 6.4 centimeters.
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WILL MARK AS BRAINLEIST!!!!
I have more questions on my account of anyone can help me out!!
The question is in the picture!
Answers
We need to integrate the function
y = 2x - x² with respect to x, from x = 0 to x = 2.
The graph of the function intersects the x-axis at x = 0 and x = 2.
So,
Area of region R = ∫[0,2] (2x - x²) dx
= [x² - (1/3)x³] from 0 to 2
= [2² - (1/3)(2)³] - [0² - (1/3)(0)³]
= 4/3
Now, let's find the equation of the line y = cx. Since the line passes through the origin (0,0), we have y = cx.
To find the value of c that divides the region R into two equal subregions, we need to find the value of x where the
area under the curve y = 2x - x² is equal to the area under the line y = cx.
∫[0,a] (2x - x²) dx = ∫[0,a] cx dx
[2x²/2 - x³/3] from 0 to a = [c/2 x²] from 0 to a
2a²/2 - a³/3 = c/2 a²
We multiply both sides by 6, we get:
12a² - 2a³ = 3ac
2a² - (1/3)a³ = (1/2)ac
2a - (1/3)a² = (1/2)c
c = (4a - (2/3)a²)/2
We know that the area under the line is equal to the area under the curve up to the point of intersection, we have:
∫[0,a] (2x - x²) dx = ∫[0,a] (cx) dx - ∫[a,2] (2x - x²) dx
2a²/2 - a³/3 = c/2 a² - 2a² + (8/3)a³ - 4a + (4/3)a²
10a³/3 - 7a² + 4a = 0
a = 0, 1.4105, -0.6172
The only value of a that is within the range 0 to 2 is a = 1.4105. Substituting this value into the equation for c, we get:
c = (4a - (2/3)a²)/2 = 1.636
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the axis of symmetry for a quadratic equation can be found using the formula , where a and b are coefficients in the quadratic equation and x represents the values along a vertical line on the coordinate plane. what is the equation when solved for a?
Answers
The value of a is a = -b/2x
What Is Quadratic Equation?Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax^2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient and 'c' is called the absolute term of f (x).
Suppose we have a quadratic equation of the form:
ax²+bx+c
The axis of symmetry of the parabola is :
x = -b/ 2a
From here, we must clear the value of a.
1) Pass 2a multiplying to the other side of the equation:
2ax=-b
2) Clear the value of a by passing 2x to divide:
a = -b/2x
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g suppose that the company releases a statement that the mean time for all patients is 2 hours. is this possible? is it likely?
Answers
Answer:
Whether it is possible or likely that the mean time for all patients is 2 hours depends on the context of the situation and the characteristics of the data.
If the data on patient wait times is very tightly clustered around the 2-hour mark, such that there is very little variation or dispersion in the data, then it is possible that the mean time for all patients is 2 hours. However, in most real-world situations, it is unlikely that all patients would have exactly the same wait time, so it is unlikely that the mean time for all patients would be exactly 2 hours.
Furthermore, the statement that the mean time for all patients is 2 hours may be misleading or inaccurate if it does not take into account other factors that may affect wait times, such as the time of day, the day of the week, the severity of patients' conditions, and the efficiency of the hospital's operations. Therefore, it is important to consider not only the mean time but also other measures of central tendency and dispersion, as well as other factors that may impact patient wait times, in order to fully understand and interpret the data.
Multiply 13. 5 x 12. 1 using a regrouping strategy. Explain your answer and each step that you take
Answers
The product of 13.5 and 12.1 using a regrouping strategy is 163.35.
To begin with, we can start by breaking down each number into its place value components, which are the ones, tenths, and hundredths places. We can represent 13.5 as 13 + 0.5 and 12.1 as 12 + 0.1.
So, we can rewrite 13.5 as (10 + 3) + 0.5 and 12.1 as (10 + 2) + 0.1. Now, we can use the distributive property of multiplication to multiply 13.5 by 12.1 as follows:
13.5 x 12.1 = (10 + 3 + 0.5) x (10 + 2 + 0.1)
= 10 x 10 + 10 x 2 + 10 x 0.1
+ 3 x 10 + 3 x 2 + 3 x 0.1
+ 0.5 x 10 + 0.5 x 2 + 0.5 x 0.1
Next, we can simplify each of these products by multiplying the numbers in the ones and tenths places separately, and then adding the results. For example, 10 x 10 = 100, 10 x 2 = 20, 10 x 0.1 = 1, 3 x 10 = 30, and so on.
So, continuing from the previous step, we get:
13.5 x 12.1 = 100 + 20 + 1
+ 30 + 6 + 0.3
+ 5 + 1 + 0.05
Finally, we can add up all these products to get the final answer:
13.5 x 12.1 = 163.35
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i need the answer loololololololol
Answers
The standard format of the polynomial given in the image is given as follows:
0.5x^5 - x^4 - 5x² - 6.
How to obtain the standard format of the polynomial?The standard format of a polynomial is to write it in descending order of the exponents of the variable, with each term separated by a plus or minus sign. For example, the standard format of a polynomial with one variable (x) is:
a_nx^n + a_{n-1}x^{n-1} + ... + a_2x^2 + a_1x + a_0
The exponents of the polynomial in this problem are given as follows:
5, 0, 4, 2.
Hence the descending order is:
5, 4, 2, 0.
And the standard format of the polynomial is of:
0.5x^5 - x^4 - 5x² - 6.
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the resultant data are: forty mothers have taken the suspected drug during their pregnancies. of these mothers, 35 have delivered malformed infants. in addition, 10 other infants are born with malfunctions. the number of individuals who both did not take the drug and did not give birth to infants who were malformed was:
Answers
No. of individuals Suspected drug and didn't give birth to in infants malformed is 10.
Number of individuals who did not take the drug and did not give birth to malformed infants.
subtract the number of individuals who took the drug and gave birth to malformed infants.
The total number of mothers, and then subtract the number of infants born with malfunctions.
Total number of mothers = 40
Number of mothers who gave birth to malformed infants after taking the drug = 35
Number of infants born with malfunctions = 10
the number of mothers who did not take the
drug = 40 - 35 = 5
The number of infants born without malfunctions = Total number of infants - Number of infants born with
malfunctions = (40 - 35) + 5 = 10
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Find the measure of angle a and B. Round to the nearest degree.
Answers
The measure of angle A and angle B are 32° and 58° respectively.
What is the measure of anglw A and B?The figures in the image are right-triangle.
To find the measure of angle A and B, we use the trigonometric ratio.
For angle A:
Angle θ = ?
Opposite to angle θ = 8
Hypotensue = 15
Note that: sine = opposite / hypotensue
sinθ = 8 / 15
Take th sine inverse
θ = sin⁻¹( 8/15 )
θ = 32°
Angle A = 32°
For angle B:
Angle B = ?
Adjacent to angle B = 8
Hypotensue = 15
Note that: cosine = adjacent / hypotensue
cosB = 8/15
Take th cosine inverse
B = cos⁻¹( 8/15 )
B = 58°
Therefore, angle B measures 58 degrees.
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in par 12.2 cm 9.3 cm 9.3 cm 7.9 cm 26.5 cm 9.3 cm 17.2 cm 9.3 cm. ? 21.5 cm
Answers
Stop using brainly. This whole website has became a big money grab over the last few months and they will remove all your posts and answers unless you pay them money. I've had it happen several times now.
the president of doerman distributors, inc., believes that 30 %of the firm's orders come from first-time customers. a simple random sample of 100 orders will be used to estimate the proportion of first-time customers. use z-table. a. assume that the president is correct and . what is the sampling distribution of for this study?
Answers
The probability of success (p) would be 0.30 and the probability of failure (q) would be 0.70.
Binomial distributions are probability distributions of the number of successes in a fixed number of trials.
The probability of success (p) and the probability of failure (q) must remain the same for each trial.
The probability of success and failure can be represented as a proportion, a percentage, or a decimal.
The sum of the probabilities of success and failure must equal 1.
The mean of the binomial distribution is equal to np.
Where n is the number of trials and p is the probability of success.
The standard deviation of the binomial distribution is equal to npq, where n is the number of trials, p is the probability of success, and q is the probability of failure.
The z-table can be used to calculate the probability of a given number of successes or failures in a binomial distribution.
The sampling distribution of this study would be a binomial distribution, as it is a study of the proportion of first-time customers out of 100 orders.
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A rectangular prism is shown in the image.
A rectangular prism with dimensions of 5 yards by 5 yards by 3 and one half yard.
What is the volume of the prism?
twenty eight and one half yd3
forty one and one fourth yd3
eighty seven and one half yd3
166 yd3
Answers
The volume of the prism is 87 and 1/2 cubic yards or 87.5 [tex]yd^{3}[/tex]
What is the volume of the prism?The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height.
In this case, the length is 5 yards, the width is 5 yards, and the height is 3 and 1/2 yards. We can convert the height to a mixed number fraction of 7/2 yards.
Therefore, the volume of the prism is:
V = lwh = 5 yards × 5 yards × 7/2 yards = 87.5 cubic yards
So, the volume of the prism is 87 and 1/2 cubic yards or 87.5 [tex]yd^{3}[/tex]
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A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days:
f(d) = 7(1.06)d
Part A: When the biologist concluded her study, the radius of the algae was approximately 13.29 mm. What is a reasonable domain to plot the growth function? (4 points)
Part B: What does the y-intercept of the graph of the function f(d) represent? (2 points)
Part C: What is the average rate of change of the function f(d) from d = 4 to d = 11, and what does it represent? (4 points)
Answers
Part A: A reasonable domain to plot the growth function would be from d = 0 to d = 11.
Part B: The y-intercept of the graph of the function f(d) is 7
Part C: The average rate of change of the function f(d) from d = 4 to d = 11 is approximately 0.64 mm/day.
Domine and y-intercept of a function:
The domain of a function represents the set of input values for which the function is defined and can produce a meaningful output.
The y-intercept of a function represents the value of the function when the input is equal to zero.
The average rate of change of a function from x = a to x = b is given by the slope of the secant line passing through the points (a, f(a)) and (b, f(b)).
Here we have
A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days:
=> f(d) = 7(1.06)^d
Since it is given that the radius of the algae was approximately 13.29 mm when the biologist concluded her study, we can set f(d) = 13.29
=> 13.29 = [tex]7(1.06)^{d}[/tex]
=> ln(13.29/7) = d ln(1.06)
=> d = ln(13.29/7)/ln(1.06) ≈ 11
Therefore, A reasonable domain to plot the growth function would be from d = 0 to d = 11.
Part B: The y-intercept of the graph of the function f(d) represents the value of the function when d = 0.
Substituting d = 0 into the given equation, we get:
f(0) = 7(1.06)⁰ = 7
Therefore, The y-intercept of the graph of the function f(d) is 7
Part C: The average rate of change of the function f(d) from d = 4 to d = 11 is given by the slope of the secant line passing through the points (4, f(4)) and (11, f(11)). Using the given equation, we can evaluate f(4) and f(11):
f(4) = 7(1.06)⁴ ≈ 8.84
f(11) = 7(1.06)¹¹ ≈ 13.29
The slope of the second line passing through these two points is:
Slope = (f(11) - f(4))/(11 - 4) = [ 13.29 - 8.84]/7 = 0.64
Therefore,
The average rate of change of the function f(d) from d = 4 to d = 11 is approximately 0.64 mm/day.
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A particular pancake recipe calls for 3 cups of flour to 1 cup of milk. What is the ratio of flour to milk if you double this
Answers
Answer: It should be the same?
(edit) Answer: The direct answer is 6:2 or 6 (cups) flour 2 (cups) milk
Step-by-step explanation: I'm Confused, the ratio is 3:1 or 1:0/3 even if you double the ratio it would be 6:2 the portions of flour will always 3 times the amount (measurement) of the milk. Correct me if i'm wrong, a bit perplexed why this question is asked.
This is due today. PLEASE HELP
Answers
Answer:
The first, third, fifth and 6th statements are true.
Step-by-step explanation:
Answer:
Here are the ones you should select:
The slope of AB is equal to slope of ACThe slope of AB is equal to the slope of the lineSlope of the line is equal to BE/AEThe slope of the line is equal to CD/ADStep-by-step explanation:
1) The slope of AB is equal to slope of AC
Rise over run for AB =2/4=1/2
Rise over run for AC=3/6=1/2
so they are equal
2) Slope of AB is not equal to BE because of visual reasons but if you need an explanation I can provide it
3) AB is a segment on the line, so the slopes are equal as you can see in the illustration provided in the question
4/5) Slope=[tex]\frac{rise}{run}[/tex], but AE/AB is not that, BE/AB is rise/run, so it's correct
6) CD/AD=rise/run, so it's correct
sorry if i got anything wrong!
Find the three trigonometric ratios. If needed, reduce fractions.
Answers
Sin= 15/17 opposite/hypotenuse
Cos= 8//17 adjacent/ hypotenuse
Tan= 15/8 opposite/ adjacent
Question 8(Multiple Choice Worth 2 points)
(Creating Graphical Representations MC)
The number of milligrams of Vitamin C from 100 different gummy vitamins sold in the world was collected.
Which graphical representation would be most appropriate for the data, and why?
Box plot, because the median can easily be determined from the large set of data
Stem-and-leaf plot, because you can see the shape of the data
Histogram, because it shows each individual data point
Bar chart, because the data is categorical
Answers
Histogram would be the most appropriate graphical representation for the collected data, because it shows each individual data point.
How to plot a histogram?A histogram is a graphical representation of a distribution of continuous data that is used to visualize the underlying frequency distribution of a set of data. Here are the general steps to plot a histogram:
1. Choose the appropriate number of bins: The first step in creating a histogram is to choose the number of bins or intervals that the data will be divided into. This decision is based on the number of data points and the range of the data.
2. Determine the range of the data: Determine the range of the data, which is the difference between the largest and smallest values in the data set.
3. Calculate the width of each bin: Divide the range of the data by the number of bins to determine the width of each bin.
4. Plot the horizontal axis: The horizontal axis of the histogram represents the range of the data and is divided into the chosen number of bins.
5. Plot the vertical axis: The vertical axis of the histogram represents the frequency or density of the data.
6. Count the number of observations: Count the number of observations that fall into each bin.
7. Plot the bars: Plot the bars of the histogram such that the height of each bar corresponds to the number of observations in each bin.
8. Label the axes and title: Finally, label the horizontal and vertical axes appropriately and give the histogram an appropriate title.
Histogram would be the most appropriate graphical representation for the collected data of milligrams of Vitamin C from 100 different gummy vitamins sold in the world.
A histogram is a graph that displays the distribution of a continuous data set using bars. It is useful for showing the frequency distribution of a large data set and helps to identify patterns or outliers in the data.
In this case, the milligrams of Vitamin C is a continuous variable, and the histogram would display the frequency of different milligram ranges. It would show the concentration range of the vitamin C in the gummy vitamins sold worldwide and provide an overall picture of the distribution of the data.
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Write 35% as a fraction in lowest term
Answers
Answer:7/20
Step-by-step explanation:
35% [tex]= 0.35 = \frac{35}{100} = \frac{35/5}{100/5} = \frac{7}{20}[/tex]
5.
Records of randomly selected births were obtained and
categorized according to the day of the week that they occurred.
A reasonable claim is that births occur on the different days with
equal frequency. Use a 0.01 significance level to test that claim.
Find the test statistic and critical value for the goodness-of-fit
needed to test the claim.
Day
Number
of Births
Sun
77
Mon
110
Tues Wed
124
122
test statistic x² = 21.005, critical value x² = 12.592
test statistic x² = 21.005, critical value x² = 16.812
Thurs
120
Fri
123
Sat
97
Answers
The critical value from the chi-square distribution table is 15.51 for 11 degrees of freedom and a 0.01 significance level. Since the chi-square statistic (23.9) is greater than the critical value (15.51), we can reject the null hypothesis
What is chi-square goodness-of-fit test?Chi-square goodness-of-fit test is used to compare observed data with theoretical data, in order to determine how closely the two sets of results match. It is used to assess whether a sample data fits a given distribution.
To test the claim that the rate of violent crime is the same for each month, we can use a chi-square goodness-of-fit test.
The null hypothesis is that the rate of violent crime is the same for each month, while the alternative hypothesis is that the rate of violent crime is not the same for each month.
The chi-square statistic is calculated as follows:
X₂ = Σ(Oi - Ei)2 / Ei
where Oi is the observed number of crimes for each month and Ei is the expected number of crimes for each month.
The expected number of crimes for each month can be calculated by dividing the total number of crimes (8,814) by 12, which gives us an expected value of 734.5.
Using these values, we can calculate the chi-square statistic:
X₂ = (786 - 734.5)2 / 734.5 + (704 - 734.5)2 / 734.5 + (835 - 734.5)2 / 734.5 + (826 - 734.5)2 / 734.5 + (900 - 734.5)2 / 734.5 + (868 - 734.5)2 / 734.5 + (920 - 734.5)2 / 734.5 + (901 - 734.5)2 / 734.5 + (856 - 734.5)2 / 734.5 + (862 - 734.5)2 / 734.5 + (783 - 734.5)2 / 734.5 + (797 - 734.5)2 / 734.5
X₂ = 23.9
We can compare this value to the critical value from the chi-square distribution table, which is 15.51 for 11 degrees of freedom and a 0.01 significance level.
Since the chi-square statistic (23.9) is greater than the critical value (15.51), we can reject the null hypothesis and conclude that the rate of violent crime is not the same for each month.
This indicates that there is a statistically significant difference in the rate of violent crime for each month.
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The principal of a school claims that 30 % of grade 3 pupils stay in the playground after their classes. A survey among 500 grade 3 pupils revealed that 150 of them stay in the playground after their classes. Use 99% confidence to conduct a test of proportions.
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The margin of error for the school's claim is 0.055 or approximately 5.5%.
To find the margin of error, we need to use the formula:
Margin of error = Critical value x Standard error
For a sample size of 500, the critical value can be found by:
critical value = 1.96
Next, we need to find the standard error. The formula for the standard error is:
standard error = sqrt(p_hat * (1 - p_hat) / n)
In this case, the sample proportion is 150/500 = 0.3.
standard error = sqrt(0.3 * (1 - 0.3) / 500) = 0.028
Finally, we can calculate the margin of error:
Margin of error = 1.96 x 0.028 = 0.055
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--The complete Question is, What is the margin of error for the school's claim that 30% of grade 3 pupils stay in the playground after their classes, given the results of the survey of 500 grade 3 pupils, which revealed that 150 of them stay in the playground after their classes? Assume a confidence level of 95%.--
I NEED HELP ON THIS ASAP!
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Answer:
I believe the answer would be 4 to the power of x?
Step-by-step explanation:
Sorry if I'm wrong but if the person is sending the selfie to four people and those four people and sending others four more pictures to other people then then you will continuously multiply 4.
Using the yearfrac function in excel - In 2017, the Christian celebration of Easter occurred on Sunday, 16 April. What fraction of the year was this? (to 1 decimal place)
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The fraction of the year representing the Christian celebration of Easter on April 16 is equal to 0.3.
In 2017, there were 365 days in the year.
It was not a leap year.
Easter Sunday occurred on April 16th.
Number of days in months before Easter,
January = 31
February = 28
March = 31
April = 16
Total days in Easter = 31 + 28 + 31 +16
= 106th day of the year
January 1 is the first day of the year.
Total number of days in a year = 365
Fraction of the year
= the number of days up to and including April 16th / the total number of days in the year
= 106 / 365
= 0.2904
= 0.3 (rounded to 1 decimal place)
Therefore, Easter Sunday in 2017 represented as 0.3 fraction of the year.
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The above question is incomplete , the complete question is:
In 2017, the Christian celebration of Easter occurred on Sunday, 16 April. What fraction of the year was this? (to 1 decimal place).
please help me with this question!!!!
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The distance between building B and C is 10√2 meters, or 9.38 meters, rounded to two decimal places.
What is triangle?Triangle is a three-sided geometric shape. It has three vertices which join together to form three sides. The sum of the three angles in a triangle is always equal to 180°. It can be classified into three types, namely equilateral, isosceles, and scalene based on the length of the sides. Triangles can also be classified as right, obtuse, or acute depending on the angles. Triangles are one of the most basic shapes in geometry and are used in many real-world applications such as architecture and engineering.
To answer this question, we need to use the Pythagorean theorem, which states that the sum of the squares of the two sides of a right triangle is equal to the square of the hypotenuse.
Using the given information, we can set up the equation:
10² + x² = (x√2)²
Where x is the distance between building B and C.
We can solve this equation with algebra to find x:
100 + x² = 2x²
x² = 100
x = 10√2
Therefore, the distance between building B and C is 10√2 meters, or 9.38 meters, rounded to two decimal places.
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(COMPOUND INTEREST)
-$17,525 deposit, interest at 1/2% for 3 years; find interest earned.
20 points reward
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Answer:
Step-by-step explanation:
Principal = 17,525. Rate = 1/2% = 0.005 time,t = 3
Interest, I = principal x rate x time
Interest, I = 17525 x 0.005 x 3
Interest, I = $262.875
there are 12 sides and 1 side is 8 so 8 x 12 is 96 so 96 is the perimeter and i need the area
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Therefore, the area of the regular dodecagon with a side length of 8 units is approximately 1,843.21 square units.
What is area?In mathematics, area refers to the measure of the amount of space inside a two-dimensional shape or region. It is a measure of the size of a flat surface, and is typically expressed in square units, such as square meters (m²), square centimeters (cm²), or square feet (ft²). The area of a shape can be calculated using various formulas, depending on the type of shape. The concept of area is used in many areas of science and engineering, including physics, geometry, and architecture. It is particularly important in fields such as construction and landscaping, where the amount of material needed to cover a given area is often a key factor in planning and budgeting.
Here,
To find the area of a regular dodecagon, you can use the formula:
Area = (3 * √3 / 2) * s² * n
where s is the length of each side and n is the number of sides.
Substituting s = 8 and n = 12, we get:
Area = (3 * √3 / 2) * 8² * 12
Area = 3 * √3 * 64 * 12
Area = 1,843.21 square units (rounded to two decimal places)
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