Answer:
AE = 7.5
Step-by-step explanation:
Since <BAC = [tex]90^{0}[/tex], then;
<BAD = <DAE = <CAE = [tex]30^{0}[/tex] (complementary angles)
From ΔABC, applying the Pythagoras theorem to determine the length of side AC;
[tex]/BC/^{2}[/tex] = [tex]/AC/^{2}[/tex] + [tex]/AB/^{2}[/tex]
[tex]/10/^{2}[/tex] = [tex]/AC/^{2}[/tex] + [tex]/5/^{2}[/tex]
100 = [tex]/AC/^{2}[/tex] + 25
[tex]/AC/^{2}[/tex] = 100 - 25
[tex]/AC/^{2}[/tex] = 75
AC = [tex]\sqrt{75}[/tex]
Applying trigonometric function to ΔCAE,
Cos [tex]30^{0}[/tex] = [tex]\frac{AE}{\sqrt{75} }[/tex]
AE = [tex]\sqrt{75}[/tex] × Cos [tex]30^{0}[/tex]
= 7.5
Therefore, AE = 7.5
Does anyone know the answers to the graded activities on plato?
Answer:
Explanation
There are some activities in Courseware content that report scores and some that just report mastery and/or completion status.
Resolution
Dynamic vs. Non-dynamic mastery tests
Mastery tests give mastery status if the score is 80% or higher, but not all tests report a score. There are two types of mastery tests in Courseware content:
Non-dynamic tests: Those that do report a score, such as those in the Writing Process and Practice titles, in the Grammar and Mechanics modules, give the same number of questions each time; these are non-dynamic tests. For example, Splitting Fused Run-ons: Mastery Test presents ten questions. Even if the Learner answers the first three questions incorrectly and is, at that point, no longer able to answer eight correctly to achieve mastery, the remaining seven questions are presented.
Dynamic tests: Mastery tests from some content titles, such as Essential Reading Skills, however, are dynamic, which means they adapt to the Learner's responses. These tests do not always give the maximum number of questions; instead, they will end sooner if 80% is either achieved or no longer achievable. These tests show mastery if 80% or better was achieved, but do not show a score. For example, in Essential Reading Skills, Pronouns: Mastery Test, the maximum number of questions presented is five; mastery requires four questions are answered correctly. The test will end early if the student answers the first four correctly or two incorrectly out of the first four. Mastery is still based on achieving 80% or better, but the score is not fully determined, so no score is reported, by design.
Step-by-step explanation:
A box is dragged across 20 meters with a force of 60 Newtons, which are kg*m/s^2
Answer:
Mass= 6kg
Acceleration= 10 ms^-2
Work done = 1200Nm
Step-by-step explanation:
kg*m/s^2 represent the force.
The kg represent the mass
The m/s^2 represent the acceleration
The acceleration here will be due to gravity force= 10 ms^-2
Then the mass= 60/10
Mass= 6 kg
The force = 60 Newton
Distance covered in the direction of the the force= 20 Meters
The work done in the direction of the force= force* distance
The work done in the direction of the force=60*20
The work done in the direction of the force=1200 Nm
Answer: 20 • 60
Step-by-step explanation:
An operator wants to determine the standard deviation for a machine relative to its ability to produce windshield wipers conforming within their specifications. To do this, she wants to create a p-chart. Over a month's time, she tests 100 units every day and records the number of manufacturing defects. The average proportion of non-conforming windshield wipers is found to be 0.042. What is the standard deviation of this sample
Answer:
the standard deviation of the sample is less than 0.1
Step-by-step explanation:
Given that :
The sample size n = 100 units
The average proportion of non-conforming windshield wipers is found to be 0.042 which is the defective rate P-bar
The standard deviation of the machine([tex]S_p[/tex]) can be calculated by using the formula:
[tex]S_p =\dfrac{ \sqrt{ \overline P \times (1 - \overline P)} }{n}[/tex]
[tex]S_p =\dfrac{ \sqrt{0.042 \times (1 -0.042)} }{100}[/tex]
[tex]S_p =\dfrac{ \sqrt{0.042 \times (0.958)} }{100}[/tex]
[tex]S_p =\dfrac{ \sqrt{0.040236} }{100}[/tex]
[tex]S_p =\dfrac{ 0.2005891323 }{100}[/tex]
[tex]S_p =0.002[/tex]
Thus , the standard deviation of the sample is less than 0.1
According to the Empirical Rule, 99.7% of scores in a normal distribution fall within 2 standard deviations of the mean.
a. True
b. False
Answer:
False
Step-by-step explanation:
Here, we want to check the validity of the given statement. The statement is false.
Under the empirical rule, following a normal distribution, 99.7% of observed data lies within 3 standard deviations from the mean while 95% of observed data lies within 2 standard deviation from the mean and 68% of observed data lies within 1 standard deviation of the mean.
Please check attachment for diagrammatic representation of the empirical rule.
A random sample of 1400 Internet users was selected from the records of a large Internet provider and asked whether they would use the Internet or the library to obtain information about health issues. Of these, 872 said they would use the Internet
1. The standard error ˆp SE of the proportion pˆ that would use the Internet rather than the library is:_______
a. 0.013.
b. 0.25.
c. 0.485.
d. 0.623.
2. If the Internet provider wanted an estimate of the proportion p that would use the Internet rather than the library, with a margin of error of at most 0.02 in a 99% confidence interval, how large a sample size would be required? (Assume that we don’t have any prior information about p).
a. 33
b. 3909
c. 2401
d. 4161
Answer:
1 [tex]\sigma_{\= x } = 0.0130[/tex]
2 [tex]n = 3908.5[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n_p = 1400[/tex]
The number of those that said the would use internet is [tex]k = 872[/tex]
The margin of error is [tex]E = 0.02[/tex]
Generally the sample proportion is mathematically evaluated as
[tex]\r p = \frac{k}{n_p}[/tex]
substituting values
[tex]\r p = \frac{ 872}{1400}[/tex]
substituting values
[tex]\r p = 0.623[/tex]
Generally the standard error of [tex]\r p[/tex] is mathematically evaluated as
[tex]\sigma_{\= x } = \sqrt{\frac{\r p (1- \r p)}{n} }[/tex]
substituting values
[tex]\sigma_{\= x } = \sqrt{\frac{0.623 (1- 0.623)}{1400} }[/tex]
[tex]\sigma_{\= x } = 0.0130[/tex]
For a 95% confidence interval the confidence level is 95%
Given that the confidence interval is 95% the we can evaluated the level of confidence as
[tex]\alpha = 100 - 99[/tex]
[tex]\alpha = 1\%[/tex]
[tex]\alpha = 0.01[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from normal distribution table (reference math dot armstrong dot edu) , the value is
[tex]Z_{\frac{\alpha }{2} } = 2.58[/tex]
Give that the population size is very large the sample size is mathematically represented as
[tex]n = [ \frac{Z_{\frac{\alpha }{2} ^2 * \r p ( 1 - \r p )}}{E^2} ][/tex]
substituting values
[tex]n = [ \frac{2.58 ^2 * 0.623 ( 1 -0.623 )}{0.02^2} ][/tex]
[tex]n = 3908.5[/tex]
Find the sum of 1 + 3/2 + 9/4 + …, if it exists.
Answer:
Option (4)
Step-by-step explanation:
Given sequence is,
[tex]1+\frac{3}{2}+\frac{9}{4}..........[/tex]
We can rewrite this sequence as,
[tex]1+\frac{3}{2}+(\frac{3}{2})^2.............[/tex]
There is a common ratio between the successive term and the previous term,
r = [tex]\frac{\frac{3}{2}}{1}[/tex]
r = [tex]\frac{3}{2}[/tex]
Therefore, it's a geometric sequence with infinite terms. In other words it's a geometric series.
Since sum of infinite geometric sequence is represented by the formula,
[tex]S_{n}=\frac{a}{1-r}[/tex] , when r < 1
where 'a' = first term of the sequence
r = common ratio
Since common ratio of the given infinite series is greater than 1 which makes the series divergent.
Therefore, sum of infinite terms of a series will be infinite Or the sum is not possible.
Option (4) will be the answer.
If the solutions for a quadratic equation are -2 and 5 what is the equation
Answer:
f(x) = x^2 - 3x -10
Step-by-step explanation:
If the solutions are {-2, 5}, the factors of the quadratic are (x + 2) and (x - 5).
The equation is f(x) = (x + 2)(x - 5) = x^2 - 3x -10
The development of AstroWorld ("The Amusement Park of the Future") on the outskirts of a city will increase the city's population at the rate given below in people/year t yr after the start of construction. 5,700 t 11,000 The population before construction is 67,000. Determine the projected population 16 yr after construction of the park has begun. people
Complete question :
The development of AstroWorld ("The Amusement Park of the Future") on the outskirts of a city will increase the city's population at the rate given below in people/year t yr after the start of construction. 5,700√t + 11,000 The population before construction is 67,000. Determine the projected population 16 yr after the construction of the park has begun. people
Answer:
486,200
Step-by-step explanation:
Given that the rate of change in population is represented by the function:
f(t) = 5,700√t + 11,000
To get the original function, we take the integral of the rate function because the rate of change is obtained by taking the derivate of the original equation
f(t) = 5,700t^1/2 + 11,000
Taking the integral of f with respect to t:
∫(5,700t^1/2 + 11,000)
[5700t^(1/2 + 1)] / (1/2 + 1) + 11000t + C
[(5700t^3/2)/ 3/2] + 11000t + C
Where C = constant
If population before construction = 67000
Then C = 67000
t = time = 16 years
Substitute values into the original change equation:
[(5700(16)^3/2)/ 3/2] + 11000t + 67000
[(5700 * 64) / 1.5] + 11000(16) + 67000
243200 + 176000 + 67000
= 486,200
The isotope of plutonium 238Pu is used to make thermoelectric power sources for spacecraft. Suppose that a space probe was launched in 2012 with 4.0 kg of 238Pu.
Required:
a. If the half-life of 238Pu is 87.7 yr, write a function of the form Q(t)= Q0e- kt.to model the quantity Q(t) of 238Pu left after t-years.
b. If 1.6 kg of 238Pu is required to power the spacecraft's data transmitter, for how long will scientists be able to receive data?
Answer:
A) Q(t) = 4e^-(0.0079t)
B) t = 115.99 ≈ 116
Therefore scientist will be able to receive data after 116 years
Step-by-step explanation:
a)
to write a function of the form Q(t)= Q₀e⁻^kt to model the quantity Q(t) of ²³⁸Pu left after t-years.
so given that; half-life of ²³⁸Pu is 87.7 years,
∴ t = 87.7 years , Q(t) = 0.5Q₀
Now we substitute these value in the form Q(t)= Q₀e⁻^kt
Q(t)= Q₀e⁻^kt
0.5Q₀ = Q₀e^ -(87.7k)
0.5 = e^ -(87.7k)
now we take the natural logarithm of both sides
In(0.5) = Ine^ -(87.7k)
Now using the property logₙnᵃ = a
-87.7k = In(0.5)
k = - In(0.5) / 87.7
k = 0.0079
ALSO it was given that Q₀ = 4.0 kg
Therefore , model quality Q(t) of ²³⁸pu left after t years is:
Q(t) = 4e^-(0.0079t)
b)
to find the time left after 1.6kg of ²³⁸pu
we simple substitute Q(t) = 1.6 into Q(t) = 4e^-(0.0079t)
so we have
1.6 = 4e^-(0.0079t)
e^-(0.0079t) = 1.6/4
e^-(0.0079t) = 0.4
again we take the natural logarithm of both sides,
Ine^-(0.0079t) = In(0.4)
again using the property logₙnᵃ = a
-0.0079t = In(0.4)
t = - in(0.4) / 0.0079
t = 115.99 ≈ 116
Therefore scientist will be able to receive data after 116 years
What is the x-coordinate of the point shown in the graph?
______
Answer:
Hey there!
The x coordinate would be -5.
Let me know if this helps :)
As we can see in the Graph,
x-coordinate = - 5y-coordinate = - 7
Shane biked 1 mile less than three times the number of miles Lissette biked. Shane biked a total of 7 miles. Write an equation to determine how many miles Lissette biked.
Answer:
2.67 miles (or 8/3 miles which is also 3 2/3 miles)
Step-by-step explanation:
S (shane) = 7
L (lissette) = ??
S = 3(L) - 1
7 = 3L - 1
8 = 3L
L = 2.67 miles
Suppose you were exploring the hypothesis that there is a relationship between parents’ and children’s party identification. Would we be correct in inferring that such a relationship also exists in the population? Explain your answer. What is the probability that any relationship we found is due to pure chance?
Answer:
No
It could be purely due to chance.
Step-by-step explanation:
A population is defined as the whole group which has the same characteristics. For example a population of the college belongs to the same college . But a sample may be an element of a population.
So it is not necessary for a population to have the same characteristics as the sample.
But it is essential for the sample to have at least one same characteristics as the population.
So we would not be correct in inferring that such a relationship also exists in the population.
It is a hypothesis which can be true or false due to certain conditions or limitations as the case maybe.
For example in a population of smokers some may be in the habit of taking cocaine. But a sample of cocaine users does not mean the whole population uses it.
It could be purely due to chance if we find out that there is a relationship between parents’ and children’s party identification in the population.
how many meters are in 250 centimeters
Answer:
2.5 meters
Step-by-step explanation:
Find the surface area of the solid given the net.
Answer:
288
Step-by-step explanation:
Area of two triangles=2(½bh)
=bh
=8×6
=48
For the rectangles=lb + lb +lb
l(b+b+b)
=12(8+6+6)
=12×20
=240
Total area=240 +48=288
3x18 = 3 (10+8) is an example of the _________ property of multiplication.
Answer:
3x18 = 3 (10+8) is an example of the commutative property of multiplication
Step-by-step explanation:
Answer: commutative property of multiplication
Step-by-step explanation:
a sheet metal worker earns $26.80 per hour after receiving a 4.5% raise. what was the sheet metal worker's hourly pay before raise? Round your answer to the nearest cent
Answer
$25.59
Step-by-step explanation:
subtract by percentage or you can also do:
100% - 4.5% = 95.5%
95.5% x $26.80 = $25.594
IF ROUNDED: $25.59
Answer:
$25.65
Step-by-step explanation:
Let the original hourly rate be r.
Then 1.045r + $26.80/hr.
Dividing both sides by 1.045, we get:
$26.80/hr
r = ------------------ = $25.65 This was the before-raise pay rate.
1.045
Use the two highlighted points to find the
equation of a trend line in slope-intercept
form.
Answer: y=(4/3)x+2/3
Step-by-step explanation:
Slope-intercept form is expressed as y=mx+b
First, find the slope (m):
m= rise/run or vertical/horizontal or y/x (found between the highlighted points)
m = 4/3
Second, find b:
Use one of the highlighted points for (x, y)
2=4/3(1)+b
6/3=4/3+b
2/3=b
b=2/3
Plug it into the equation:
You get y=(4/3)x+2/3 :)
A shopping centre wants to examine the amount of space required for parking. Studies indicated that 50% of staff and shoppers use public transportation. A survey of 1002 was taken, and 483 responded that they used public transportation. At 5% level of significance, is it reasonable to conclude that the survey results indicate a change?
Answer:
The survey result doesn't indicate the change
Step-by-step explanation:
Previous study result is 50%
Survey result:
483/1002 = 0.482 = 48.2%Comparing with previous result:
50% - 48.2% = 1.8% < 5%Since this result is within 5% level of significance, it can be concluded that the survey result doesn't indicate the change
Find the vertex of this parabola:
y = x2 + 2x - 3
Answer:
(-1,-4)
Step-by-step explanation:
The equation of a parabola os written as: ax^2+bx+c
This parabola's equation is x^2+2x-3
● a= 1
● b= 2
● c = -3
The coordinates of the parabola are: ( (-b/2a) ; f(-b/2a) )
● -b/2a = -2/2 = -1
● f(-b/2a) = (-1)^2+2×(-1)-3=1-2-3= -4
So the vertex coordinates are (-1,-4)
Answer:
-1+2X
Step-by-step explanation:
Identify whether the sampling method is simple random, systematic, stratified, cluster, or convenience. Explain.
In a nationwide study of registered voters conducted by The New York Times, 390 people are randomly selected out of those registered as Republicans, 430 people are randomly selected out of those registered as Democrats, and 180 people are randomly selected out of those registered as Independents.
Answer: stratified
Step-by-step explanation:
In stratified sampling, you divide the population into subgroups, or strata, with similar characteristics, like here we have divided the population into subgroups that depend on their political alignment. This is used when you can expect that the results have a noticeable variation between the different subgroups. Usually, you want to have the same number of population for eac subgroup, but sometimes it is hard for different reasons (not enough people in one subgroup, for example)
In cluster sampling we also use subgroups, but the subgroup itself is the unit of the sampling, while in this case, we are randomly selecting individuals of the given subgroups.
So this would be a "stratified sampling".
PLEASE HURRY! i walked north 8 miles, the west 4 miles, and finally south 5 miles, at the end how far was i from where i started
Answer:
5 miles away
Step-by-step explanation:
If you walked north 8 miles, then west 4 miles, then south 5 miles, you have, in total, travelled 4 miles west and [tex]8-5=3[/tex] miles north.
This creates a triangle, in which we can find the the length of the hypotenuse to find how far away you are now.
We can use the Pythagorean theorem since this is a right triangle.
[tex]a^2+b^2=c^2\\3^2+4^2=c^2\\9+16=c^2\\25=c^2\\c=5[/tex]
Hope this helped!
Answer:
5 miles away
Step-by-step explanation:
In a mathematics class, half of the students scored 87 on an achievement test. With the exception of a few students who scored 52, the remaining students scored 71. Which of the following statements is true about the distribution of scores?
Answer:the mean is greater than the median
Step-by-step explanation:
The mean is less than the median. Then the correct option is A.
What are statistics?Statistics is the study of collection, analysis, interpretation, and presentation of data or to discipline to collect, and summarise the data.
Half the students scored 87.
The next highest score is 71.
Then the median will be
(71+ 87) / 2 = 79
A few students scored 52, so the mean is slightly lower than the mean of 71 and 87.
Thus, the mean is less than the median.
Then the correct option is A.
The missing options are given below.
A. The mean is less than the median.
B. The mean and the median is the same.
C. The mean is greater than the mode.
D. The mean is greater than the median.
More about the statistics link is given below.
https://brainly.com/question/10951564
#SPJ2
Put 0.9,0.1038,0.10299,0.1037 in order from least to greatest
Answer: 0.10299,0.1037 ,0.1038 ,0.9
Step-by-step explanation:
In all the numbers we could see that 0.9 is the greatest because it has the greatest tenth value. The rest three have the same tenth value which is one and the same hundredth value which is 0 so we will compare the numbers using their thousandth values.
In the numbers 0.1038,0.10299, 0.1037 The first one has a thousandth value of 3, the second one has a thousandth value of 2, and the third one has a thousandth value of 3. Which means the first and the second have the same thousandths value so using their last numbers which is 8 and 7 , 8 is greater than 7 so 0.1038 is greater than 0.1037 and 0.10299. The same way 0.1037 is greater than 0.10299.
So to order them from least to greatest,
0.10299 will be first
0.1037 will be second
0.1038 will be the third
0.9 will be the last.
Johnny and a robot standing 5 melo (units of length) apart (in a flat area) on the
planet Rote. They spot a flying object hovering in the sky at the same time. If the
angle of elevation from Johnny to the flying object is 29°, and the angle of elevation
from the robot to the flying object is 42°, find the distance from the flying object to
the ground. For this problem, assume that the heights of Johnny and the robot are
neligible. [8 marks]
Answer:
distance from the flying object to
the ground
= 7.2 melo(unit of measurement)
Step-by-step explanation:
The distance between the robot and Jo is 5 melo( unit Of measurement)
Let the distance between the flying object and the ground= y
Let's the remaining length of the closest between robot and Jonny and the ground be x.
Y/(x+5)= tan 29.... equation 1
Y/x= tan 42.... equation 2
Equating the value of y
Tan 29(x+5) = tan42(x)
Tan29/tan 42 = x/(x+5)
0.61562(x+5)= x
3.0781= x- 0.61562x
3.0781= 0.38438x
3.0781/0.38438= x
8.008= x
8= x
Y/x= tan 42
Y/8= 0.9004
Y= 7.203
Y= 7.2 melo (unit of measurement )
A manufacturer claims that the calling range (in feet) of its 900-MHz cordless telephone is greater than that of its leading competitor. A sample of 19 phones from the manufacturer had a mean range of 1160 feet with a standard deviation of 32 feet. A sample of 11 similar phones from its competitor had a mean range of 1130 feet with a standard deviation of 30 feet.
Required:
Do the results support the manufacturer's claim?
Complete question is;
A manufacturer claims that the calling range (in feet) of its 900-MHz cordless telephone is greater than that of its leading competitor. A sample of 19 phones from the manufacturer had a mean range of 1160 feet with a standard deviation of 32 feet. A sample of 11 similar phones from its competitor had a mean range of 1130 feet with a standard deviation of 30 feet. Required:
Do the results support the manufacturer's claim?
Let μ1 be the true mean range of the manufacturer's cordless telephone and μ2 be the true mean range of the competitor's cordless telephone. Use a significance level of α = 0.01 for the test. Assume that the population variances are equal and that the two populations are normally distributed
Answer:
We will fail to reject the null hypothesis as there is no sufficient evidence to support the manufacturers claim.
Step-by-step explanation:
For the first sample, we have;
Mean; x'1 = 1160 ft
standard deviation; σ1 = 32 feet
Sample size; n1 = 19
For the second sample, we have;
Mean; x'2 = 1130 ft
Standard deviation; σ2 = 30 ft
Sample size; n2 = 11
The hypotheses are;
Null Hypothesis; H0; μ1 = μ2
Alternative hypothesis; Ha; μ1 > μ2
The test statistic formula for this is;
z = (x'1 - x'2)/√[(σ1)²/n1) + (σ2)²/n2)]
Plugging in the relevant values, we have;
z = (1160 - 1130)/√[(32)²/19) + (30)²/11)]
z = 2.58
From the z-table attached, we have a p-value = 0.99506
This p-value is more than the significance value of 0.01,thus,we will fail to reject the null hypothesis as there is no sufficient evidence to support the manufacturers claim.
Transform the given parametric equations into rectangular form. Then identify the conic. x= 5cos(t) y= 2sin(t)
Answer:
Solution : Option D
Step-by-step explanation:
The first thing we want to do here is isolate the cos(t) and sin(t) for both the equations --- ( 1 )
x = 5cos(t) ⇒ x / 5 = cos(t)
y = 2sin(t) ⇒ y / 2 = sin(t)
Let's square both equations now. Remember that cos²t + sin²t = 1. Therefore, we can now add both equations after squaring them --- ( 2 )
( x / 5 )² = cos²(t)
+ ( y / 2 )² = sin²(t)
_____________
x² / 25 + y² / 4 = 1
Remember that addition indicates that the conic will be an ellipse. Therefore your solution is option d.
Write 8x8x88888 as power
Answer:
8[2]×88888
Step-by-step explanation:
[8×8]=8[2]×88888
How to find which ratio is largest
Need help with this as soon as possible pls
Answer:
i think
x=6.77
y=11.33
please help me out! <3
Answer:
[tex]-1 \frac{3}{4}[/tex]
Step-by-step explanation:
Using this number line, we can plot our original number - [tex]\frac{3}{4}[/tex] (see picture attached)
Adding a negative is the same thing as subtracting - so we are subtracting [tex]2\frac{1}{2}[/tex] from [tex]\frac{3}{4}[/tex].
To subtract this, we can break up [tex]2\frac{1}{2}[/tex] into 3 parts: 1, 1, and [tex]\frac{1}{2}[/tex]. We can subtract each of these from the current number and see where we land up. (again see picture)
We land up at [tex]-1 \frac{3}{4}[/tex].
Hope this helped!
