100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
Answer:
x = 42
y = 21
Step-by-step explanation:
Since its a right triangle, we have:
sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
\(sin (60) = \frac{21\sqrt{3} }{x} \\\\x= \frac{21\sqrt{3} }{sin (60)} \\\\x= \frac{21\sqrt{3} }{\frac{\sqrt{3} }{2} } \\\\x = \frac{21\sqrt{3} *2 }{\sqrt{3} } \\\\x = 21*2\\\\x = 42\)
\(cos (60) = \frac{y}{x}\\\\cos (60) = \frac{y}{42}\\\\y = cos (60)*42 \\\\y = \frac{1}{2} * 42\\\\y = 21\)
Related Questions
When a radius intersects a chord of a circle at a right angle, what conclusion can be made?
The radius is bisected.
The chord is bisected.
The radius and the chord are congruent.
The radius is twice as long as the chord.
Answers
Answer:
The chord is bisected
Step-by-step explanation:
This problem seek our knowledge on the mensuration of flat shapes, a circle.The chord of a circle is a segment whose endpoints are on the circle. when a perpendicular bisector ( the radius) of any chord passes through the center of the chord at right angle to the chord, the chord is bisected into two. This is a way or could give us a good way to find the center of any circle.
kindly find attached a diagram for your reference
Answer:
B
Step-by-step explanation:
which equation can be used to represent 'three minus the difference of a number and one equals one-half of the difference of three times the same number and four
Answers
Answer:
3 - (x - 1) = 1/2(3x - 4)
Step-by-step explanation:
if y varies jointly as the square of x and the cube of z and inversely as the square root of w. When x = 2, z = 2, and w = 64, then y = 12. Find y when x = 1, z = 3, and w = 4.
Answers
Answer:
40.5
Step-by-step explanation:
if y varies jointly as the square of x and the cube of z and inversely as the square root of w, this is expressed as;
y ∝ x²z³/√w
y = kx²z³/√w
If x = 2, z = 2, y = 12 and w = 64
Substitute;
12 = k (2)²(2)³/√64
12 = 32k/8
12 = 4k
k = 12/4
k = 3
To get y when x = 1, z = 3, and w = 4.
y = 3 (1)²(3)³/√4
y = (3*27)/2
y = 81/2
y = 40.5
Hence the value of y is 40.5
Please help me solve this equation and show the work show me how you got the answer
Answers
Answer: k=3
Step-by-step explanation:
To solve for k, you want to isolate k.
\(\frac{2}{5} (5k+35)-8=12\) [add both sides by 8]
\(\frac{2}{5} (5k+35)=20\) [multiply both sides by 5/2]
\(5k+35=50\) [subtract both sides by 35]
\(5k=15\) [divide both sides by 5]
\(k=3\)
Now, we know that k=3.
Make v the subject of the formula T = v/6 -5
Answers
Answer:
Step-by-step explanation:
T=V/6-5
T+5=V/6
6(T+5)=V
V=6T+30
v= 6(T + 5) is the representation of the given equation 'v' as subject of the formula.
What is subject of the formula?" A subject of the formula is defined as a variable which is expressed in form of other variables."
According to the question,
Given,
T = v/6 - 5
Add 5 both the sides
⇒ T + 5 = v / 6 - 5 +5
⇒v/6 = T + 5
Now represent 'v' as a subject of the formula we get,
v = 6 ( T + 5)
Hence, v= 6(T + 5) is the representation of the given equation 'v' as subject of the formula.
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Which of the following graphs is not a function ?
Answers
If 6 more than the product of a number and - 2 is greater than 10, which of the following could be that number?
Answers
Answer:
-2x + 6 > 10
Step-by-step explanation:
Let the unknown number be x
the product of x and -2 is -2x
6 more than -2x is written as
-2x + 6
if the result of the above is greater than 10, then
-2x + 6 > 10
If z is a standard normal variable, find the probability that z lies between-2.41 and 0
Answers
Step-by-step explanation:
Given: z is a standard normal variable.
We know that probability of z lies lies between
two values a and b is given by :-
Pla<2Now, the probability that z lies between -2.41
and O is given by :-
P(-2.41 < 2 < 0) = P(=<0) - P(2< -2.41)
P(-2.41 < 2 < 0) = 0.5 - 0.0079762 = 0.4920238
[By using z-table for standard normal distribution]
Hence, the probability that z lies between -2.41
and 0 = 0.4920238
Use the approach in Gauss's Problem to find the following sums of arithmetic
sequences.
a. 1+2+3+4+...+99
b. 1+3+5+7+...+1001
c. 3+6+9+ 12 + ... + 300
d. 4+8+12 + 16 + ... + 400
Answers
a. Let S be the first sum,
S = 1 + 2 + 3 + … + 97 + 98 + 99
If we reverse the order of terms, the value of the sum is unchanged:
S = 99 + 98 + 97 + … + 3 + 2 + 1
If we add up the terms in both version of S in the same positions, we end up adding 99 copies of quantities that sum to 100 :
S + S = (1 + 99) + (2 + 98) + … + (98 + 2) + (99 + 1)
2S = 100 + 100 + … + 100 + 100
2S = 99 × 100
S = (99 × 100)/2
Then S has a value of
S = 99 × 50
S = 4950
Aside: Suppose we had n terms in the sum, where n is some arbitrary positive integer. Call this sum ∑(n) (capital sigma). If ∑ is a sum of n terms, and we do the same manipulation as above, we would end up with
2 ∑(n) = n × (n + 1) ⇒ ∑(n) = n (n + 1)/2
b. Let S' be the second sum. It looks a lot like S, but the even numbers are missing. Let's put them back, but also include their negatives so the value of S' is unchanged. In doing so, we have
S' = 1 + 3 + 5 + … + 1001
S' = (1 + 2 + 3 + 4 + 5 + … + 1000 + 1001) - (2 + 4 + … + 1000)
The first group of terms is exactly the sum ∑(1001). Each term in the second grouped sum has a common factor of 2, which we can pull out to get
2 (1 + 2 + … + 500)
so this other group is also a function of ∑(500), and so
S' = ∑(10001) - 2 ∑(500) = 251,001
However, we want to use Gauss' method. We have a sum of the first 501 odd integers. (How do we know there 501? Starting with k = 1, any odd integer can be written as 2k - 1. Solve for k such that 2k - 1 = 1001.)
S' = 1 + 3 + 5 + … + 997 + 999 + 1001
S' = 1001 + 999 + 997 + … + 5 + 3 + 1
2S' = 501 × 1002
S' = 251,001
c/d. I think I've demonstrated enough of Gauss' approach for you to fill in the blanks yourself. To confirm the values you find, you should have
3 + 6 + 9 + … + 300 = 3 (1 + 2 + 3 + … + 100) = 3 ∑(100) = 15,150
and
4 + 8 + 12 + … + 400 = 4 (1 + 2 + 3 + … + 100) = 4 ∑(100) = 20,200
Find value of x in trapezoid
Answers
Answer:
x = 1
Step-by-step explanation:
You want to know the value of x in the trapezoid with adjacent angles (43x+2)° and 135°.
Supplementary anglesThe two marked angles can be considered "consecutive interior angles" where a transversal crosses parallel lines. As such, they are supplementary.
(43x +2)° +135° = 180°
43x = 43 . . . . . . . . . . . . . . divide by °, subtract 137
x = 1 . . . . . . . . . . . . . . . divide by 43
The value of x is 1.
__
Additional comment
Given that the figure is a trapezoid, we have to assume that the top and bottom horizontal lines are the parallel bases.
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A study of the properties of metal plate-connected trusses used for roof support† yielded observations on axial-stiffness index (kips/in.) for plate lengths 4, 6, 8, 10, and 12 in. The axial stiffness data produced the following ANOVA output from Minitab.
Analysis of Variance for stiffness
Source DF SS MS F P
Length 4 43993 10998 10.48 0.000
Error 30 31475 1049
Total 34 75468
Level N Mean StDev
4 7 333.21 36.59
6 7 368.06 28.57
8 7 375.13 20.83
10 7 407.36 44.51
12 7 437.17 26.00
Pooled StDev = 32.39
Tukey's pairwise comparisons
Family error rate = 0.0500
Individual error rate = 0.00693
Critical value = 4.10
Intervals for (column level mean) - (row level mean)
4 6 8 10
6 −85.0
15.4
8 −92.1 −57.3
8.3 43.1
10 −124.3 −89.5 −82.4
−23.9 10.9 18.0
12 −154.2 −119.3 −112.2 −80.0
−53.8 −18.9 −11.8 20.4
(a) Is it plausible that the variances of the five axial stiffness index distributions are identical? Explain.
Yes, it is plausible because the median standard deviation (s2 = 28.57) is within 20 of the largest (s4 = 44.51) and smallest (s3 = 20.83) standard deviation.
Yes, it is plausible because the largest standard deviation (s4 = 44.51) is slightly more than twice the smallest (s3 = 20.83).
No, it is not plausible because the largest standard deviation (s4 = 44.51) is slightly more than twice the smallest (s3 = 20.83).
No, it is not plausible because the median standard deviation (s2 = 28.57) is not within 10 of the largest (s4 = 44.51) and smallest (s3 = 20.83) standard deviation.
(b) Use the output (without reference to our F table) to test the relevant hypotheses.
Fail to reject H0. There is no difference in axial stiffness for the different plate lengths.
Fail to reject H0. There is a difference in axial stiffness for the different plate lengths.
Reject H0. There is a difference in axial stiffness for the different plate lengths.
Reject H0. There is no difference in axial stiffness for the different plate lengths.
(c) Use the Tukey intervals given in the output to determine which means differ, and construct the corresponding underscoring pattern. (Select all that apply.)
4 and 6
4 and 8
4 and 10
4 and 12
6 and 8
6 and 10
6 and 12
8 and 10
8 and 12
10 and 12
There are no significant differences.
Answers
Answer and Step-by-step explanation:
a. Yes, since the highest standard deviation (s4 = 44.51) is significantly more than double the lowest (s3 = 20.83) is plausible.
hence, the second option is correct
(b) The testing of relevant hypothesis using the output is shown below:
As we see that
The 0.05 is more than the F test P-value i.e 0.0000
So ultimately P-value is less
Therefore we have to reject the null hypothesis
Since p-value is less than 0.05 so we reject the null hypothesis.
Therefore, the third option is correct
(c) The construction is shown below:
Since the sample size is the same so for Tuley's HSD it would also same i.e for each pair
Now Tuley's HSD is
\(HSD=4.10\cdot \sqrt{\frac{1049}{7}}=50.19\)
The table that reflects the difference in means in different level is as follows
Levels Difference in mean
4-6 34.85
4-8 41.92
4-10 74.15
4-12 103.96
6-8 7.07
6-10 39.3
6-12 69.11
8-10 32.23
8-12 62.04
10-12 29.81
Now the table of significant difference is
Levels Difference in mean
4-10 74.15
4-12 103.96
6-12 69.11
8-12 62.04
12 + r = 3
I need the answer to this problem?
Answers
Answer:
I think the answer would be r=-9
Step-by-step explanation:
12+r=3
-12 -12
-------------
r=-9
The base of the mountain is 6,500 feet above sea level and AB measures 230 feet across. Given that the measurements for QAP is 20° and QBP is 35°, how far above sea level is peak P ? Express your answer to the nearest foot.
Height above sea level:
Answers
Answer:
6610
Step-by-step explanation:
We have tan(X) = opposite/ adjacent
tan(QBP) = PQ/BQ
tan(35) = PQ/BQ ---eq(1)
tan(QAP) = PQ/AQ
tan(20) = \(\frac{PQ}{AB +BQ}\)
\(=\frac{1}{\frac{AB+BQ}{PQ} } \\\\=\frac{1}{\frac{AB}{PQ} +\frac{BQ}{PQ} } \\\\= \frac{1}{\frac{230}{PQ} + tan(35)} \;\;\;(from\;eq(1))\\\\= \frac{1}{\frac{230 + PQ tan(35)}{PQ} } \\\\= \frac{PQ}{230+PQ tan(35)}\)
230*tan(20) + PQ*tan(20)*tan(35) = PQ
⇒ 230 tan(20) = PQ - PQ*tan(20)*tan(35)
⇒ 230 tan(20) = PQ[1 - tan(20)*tan(35)]
\(PQ = \frac{230 tan(20)}{1 - tan(20)tan(35)}\)
\(= \frac{230*0.36}{1 - 0.36*0.7}\\\\= \frac{82.8}{1-0.25} \\\\=\frac{82.8}{0.75} \\\\= 110.4\)
PQ = 110.4
≈110
Height above sea level = 6500 + PQ
6500 + 110
= 6610
For a science project, Daniel planted 51 flower seeds. Of those seeds, 12 did not grow at all. Of the seeds that did grow, 2/3 of them grew green tomatoes. How many green tomatoes grew?
a) 12
b) 8
c) 26
d) 13
Answers
Answer:
C. 26
Step-by-step explanation:
According to the question,
Daniel planted 51 seeds.
12 seeds did not grow at all,
Therefore, the number of seeds that grew are 51-12= 39
Then, from the 39 seeds that grew, 2/3 of them are green tomatoes.
So, to find out how many green tomatoes grew, we solve
2/3 * 39= 26.
Therefore, the amount of green tomatoes are 26.
3.4z+ 2.8z =
I need help now!!!
Answers
Answer:
6.2z
Step-by-step explanation:
its basically just 3.4 + 2.8 but you add a z.
Answer:
6.2z
Step-by-step explanation:
Basically adding 3.4 +2.8 getting 6.2 then adding z to the end of it
There's another silence as Steve looks toward the crowd and then toward Tommy. He wears a tight grin.
STEVE
Based on the clues in this passage, what will most likely happen next?
• The neighbors will stop doubting Tommy.
Well, I guess what we'd better do then is to run a check on the neighborhood and see which ones of us are really human.
• The neighbors will stop taking Steve seriously.
• The neighbors will continue to joke about the situation.
There's laughter at this, but it's a laughter that comes
from a desperate attempt to lighten the atmosphere. It's a • The neighbors will begin checking to see who is release kind of laugh.
really human.
36. GROUP SHOT - THE PEOPLE 36.
As they look at one another in the middle of their laughter.
-The Monsters Are Due on Maple Street,
Rod Serling
Answers
Answer:
5
Step-by-step explanation:
1.) Look at the figure below.
A
+5
3x
B
What is the measure of ZB?
A 35°
B
71°
С
760
D 105°
Answers
Answer:
D
Step-by-step explanation:
ces
Real GDP, consumption, and the marginal propensity to consume (MPC) for five hypothetical countries are shown in the following table.
Use the table to answer the questions below.
Country
A
B
C
D
E
Real GDP,
Billions
$40
50
70
100
180
Consumption,
Billions
$24
40
82
100
204
MPC
0.75
0.80
0.90
0.95
0.75
Current Level
of Saving,
Billions
$
$
$
$
$
16
10
-12
0
-24
New Level of
Saving,
Billions
Instructions: Enter your answers as a whole number. If you are entering any negative numbers be sure to include a negative sign (-) in
front of those numbers.
a. Enter the current level of saving in the appropriate column in the table.
b. Suppose that GDP increases by $20 billion in each of the five countries. What will be the new level of saving in each country? Enter
your answers in the appropriate column in the table.
Answers
Answer:
Step-by-step explanation:
a. The current level of saving for each country can be calculated as follows:
Country A: Current Level of Saving = Real GDP - Consumption = $40 billion - $24 billion = $16 billion
Country B: Current Level of Saving = Real GDP - Consumption = $50 billion - $40 billion = $10 billion
Country C: Current Level of Saving = Real GDP - Consumption = $70 billion - $82 billion = -$12 billion
Country D: Current Level of Saving = Real GDP - Consumption = $100 billion - $100 billion = $0 billion
Country E: Current Level of Saving = Real GDP - Consumption = $180 billion - $204 billion = -$24 billion
Therefore, the current level of saving for each country is:
Country Real GDP (Billions) Consumption (Billions) MPC Current Level of Saving (Billions)
A 40 24 0.75 16
B 50 40 0.80 10
C 70 82 0.90 -12
D 100 100 0.95 0
E 180 204 0.75 -24
b. If GDP increases by $20 billion in each country, the new level of saving for each country can be calculated as follows:
Country A: New Level of Saving = Real GDP + $20 billion - Consumption = $60 billion - $24 billion = $36 billion
Country B: New Level of Saving = Real GDP + $20 billion - Consumption = $70 billion - $40 billion = $30 billion
Country C: New Level of Saving = Real GDP + $20 billion - Consumption = $90 billion - $82 billion = $8 billion
Country D: New Level of Saving = Real GDP + $20 billion - Consumption = $120 billion - $100 billion = $20 billion
Country E: New Level of Saving = Real GDP + $20 billion - Consumption = $200 billion - $204 billion = -$4 billion
Therefore, the new level of saving for each country is:
Country Real GDP (Billions) Consumption (Billions) MPC Current Level of Saving (Billions) New Level of Saving (Billions)
A 40 24 0.75 16 36
B 50 40 0.80 10 30
C 70 82 0.90 -12 8
D 100 100 0.95 0 20
E 180 204 0.75 -24 -4
c. Based on the table in part (b), which country has the highest MPC, and which country has the lowest MPC?
Country C has the highest MPC of 0.90, while Countries A and E have the lowest MPC of 0.75.
d. Based on the table in part (b), which country has the highest new level of saving, and which country has the lowest new level of saving?
Country A has the highest new level of saving of $36 billion, while Country E has the lowest new level of saving of -$4 billion (or a deficit).
a) The current level of saving for each country is:
Real GDP Consumption MPC Current Level of Saving
A 40 24 0.75 16
B 50 40 0.80 10
C 70 82 0.90 -12
D 100 100 0.95 0
E 180 204 0.75 -24
b) The new level of saving for each country is shown below.
What is GDP?GDP calculates the monetary value of the final goods and services—those purchased by the consumer—produced in a nation during a specific time period (say a quarter or a year). It accounts for all the output produced inside a nation's boundaries.
a. The current level of saving for each country are:
Country A:
Current Level of Saving = Real GDP - Consumption
= $40 billion - $24 billion
= $16 billion
Country B:
Current Level of Saving = $50 billion - $40 billion
= $10 billion
Country C:
Current Level of Saving = $70 billion - $82 billion
= -$12 billion
Country D:
Current Level of Saving = $100 billion - $100 billion
= $0 billion
Country E:
Current Level of Saving = $180 billion - $204 billion
= -$24 billion
b. If GDP increases by $20 billion in each country, the new level of saving for each country can be
Country A:
New Level of Saving = Real GDP + $20 billion - Consumption
= $60 billion - $24 billion
= $36 billion
Country B:
New Level of Saving = $70 billion - $40 billion
= $30 billion
Country C:
New Level of Saving = $90 billion - $82 billion
= $8 billion
Country D:
New Level of Saving = $120 billion - $100 billion
= $20 billion
Country E:
New Level of Saving = $200 billion - $204 billion
= -$4 billion
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What is the average rate of change of this function on the interval from x = 1 to x = 3? f(x)=10(2)x Enter your answer in the box.
Answers
Answer:
30
Step-by-step explanation:
The way to figure out the average rate of change is to divide the change in f(x) and divide that by the change in x. A formula for this is \(\frac{f(x_{1})-f(x_{2})}{x_{1}-x_{2}}\)
1.) By this definition, we need to figure out our x1 and x2. We can say the x1 = 3 and x2 = 1
2.) Next, we plug it into the formula. We will get \(\frac{f(3)-f(1)}{3-1}\).
3.) If we simplify, we will get 10(2)^3 - 10*2 divided by 2, which is equal to 10*4 - 10 = 30.
y = 5 and x = -1
Is it parallel,perpendicular or neither
Answers
Answer: Perpendicular
y = 5 is a horizontal line through 5 on the y axis
x = -1 is a vertical line through -1 on the x axis
The surface of the triangle shown in the picture 15.1 is:
A) 6 B) 21 C) 14 D) 12
I'm not sure I've solved it right.
Answers
Answer:
The coreect answer o
is 14
The joint density function of X and Y is f(x,y) = {210 (2x +y), 2
0, otherwise Find
E(X),
E(Y),
E(XY),
E(X2),
E(Y2),
Var(X),
Var(Y),
Cov(X,Y),
i.p
Answers
Answer:
e(x)
Step-by-step explanation:
i think this is the answer
What is the y-intercept of the line with the equation y = 4 x + 2? a. -2 b. 4 c. 2 d. Negative one-half
Answers
Answer:
the correct answer is c
Bill uses mirrors to augment the “laser experience” at a laser show. At one show he places three mirrors, A, B, C, in a right triangular form. If the distance between A and B is 23m more than the distance between A and C, and the distance between B and C is 23m less than the distance between A and C, what is the distance between mirror A and mirror C? I cannot solve this for the life of me Please help!
Answers
The distance between mirror A and mirror C is 92
How to calculate the distance?Since we are talking for a right triangle and AB is the longer side , we conclude that AB is the hypotenuse of the triangle.
So
AC = x
BC = x- 23
AB = x + 23
Then applying the Pythagorean Theorem we have AB² = AC² + BC²
equivalently ( x + 23 )³ = x² + ( x - 8 )²
x² + 46x + 579 = x² + x² - 46x + 579
x² - x² - x² + 46x + 46x + 579 - 579 = 0
x² - 92x = 0
x = 92
AC = 92
BC = 92 - 23 = 69
AB = 92 + 23 = 115
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Try Again
Suppose that 16 inches of wire costs 48 cents.
At the same rate, how many inches of wire can be bought for 36 cents?
I inches
X Х
$
?
Answers
12 inches
step-by-step explanation:
16 inches of wire = 48 cents
48/16
3 cents for each
36/3
12 inches
The population of a country has been increasing for several decades. In 1990, the population was about 263 million people In 2014, the population was about 307 million people Determine the percent in + The country's population increased by about % during this time period
Answers
Answer:
The country's population increased by about 16.73% during this time period.
Step-by-step explanation:
Percent increase:
The percent increase is given by the change multiplied by 100 and divided by the initial value.
In 1990, the population was about 263 million people In 2014, the population was about 307 million people.
Change: 307 - 263 = 44
Initial population: 263
Percentage increase:
44*100/263 = 16.73%
The country's population increased by about 16.73% during this time period.
The points A, B, C and D lie in order on a straight line
such that
AB:BD = 1:2
AC:CD= 7:2
Find AB:BC:CD
Answers
Answer:
7 + 2 = 9, so AC = 7/9 and CD = 2/9
1 + 2 = 3, so AB = 1/3 = 3/9 and
BD = 2/3 = 6/9
AB + BC = AC
3/9 + BC = 7/9, so BC = 4/9
AB:BC:CD = (3/9):(4/9):(2/9) = 3:4:2
Tyler claims that because he started painting first he will finish painting his side of the fence before Benito finishes painting his side. Is this true? Explain
Answers
Answer:
but
Step-by-step explanation:
yrge sksue dnd djd d d. r e g g h a s. v j u r d. d c g y t
Tyler's claim about finishing his painting first is False because it will take Benito 10 minutes while Tyler will require over 11 minutes to finish up his painting despite starting before Benito.
Size of fence = 150 feet
Benito's rate = 15 ft/min
Tyler's rate = 11 ft/ min
Size already painted by Tyler when Benito started = 39/2 = 19.5 ft
Portion of fence left for Tyler to paint when Benito started = (150 - 19.5) = 130.5 feets
Time required for Tyler to finish :
Time required = 130.5 ÷ 11 = 11.863 minutes
Time required for Benito to finish :
Time required = 150 ÷ 15 = 10 minutes
Time required for Benito to complete his painting is lesser than Tyler's (10 < 11.863)
Hence, Tyler's claim is False
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The time X(mins) for Ayesha to prepare breakfast for her family is believed to have a uniform
distribution with A=25 and B=35.
a) Determine the pdf of X and draw its density curve.
b) What is the probability that time taken by Ayesha to prepare breakfast exceeds 33 mins?
c) What is the probability that cooking or preparation time is within 2 mins of the mean time?
(Hint: Identify mean from the graph of f(x))
Answers
Answer:
(c) \(f_{X}(x)=\left \{ {{\frac{1}{35-25}=\frac{1}{10};\ 25<X<35} \atop {0;\ Otherwise}} \right.\)
(b) The probability that time taken by Ayesha to prepare breakfast exceeds 33 minutes is 0.20.
(c) The probability that cooking or preparation time is within 2 mins of the mean time is 0.40.
Step-by-step explanation:
The random variable X follows a Uniform (25, 35).
(a)
The probability density function of an Uniform distribution is:
\(f_{X}(x)=\left \{ {{\frac{1}{B-A};\ A<X<B} \atop {0;\ Otherwise}} \right.\)
Then the probability density function of the random variable X is:
\(f_{X}(x)=\left \{ {{\frac{1}{35-25}=\frac{1}{10};\ 25<X<35} \atop {0;\ Otherwise}} \right.\)
(b)
Compute the value of P (X > 33) as follows:
\(P(X>33)=\int\limits^{35}_{33} {\frac{1}{10}} \, dx \\\\=\frac{1}{10}\cdot\int\limits^{35}_{33} {1} \, dx \\\\=\frac{1}{10}\times [x]^{35}_{33}\\\\=\frac{35-33}{10}\\\\=\frac{2}{10}\\\\=0.20\)
Thus, the probability that time taken by Ayesha to prepare breakfast exceeds 33 minutes is 0.20.
(c)
Compute the mean of X as follows:
\(\mu=\frac{A+B}{2}=\frac{25+35}{2}=30\)
Compute the probability that cooking or preparation time is within 2 mins of the mean time as follows:
\(P(30-2<X<30+2)=P(28<X<32)\)
\(=\int\limits^{32}_{28} {\frac{1}{10}} \, dx \\\\=\frac{1}{10}\cdot\int\limits^{32}_{28}{1} \, dx \\\\=\frac{1}{10}\times [x]^{32}_{28}\\\\=\frac{32-28}{10}\\\\=\frac{4}{10}\\\\=0.40\)
Thus, the probability that cooking or preparation time is within 2 mins of the mean time is 0.40.
the shadow of a 100 m long vertical pole is of 20 m then what will be the angle of inclination round the answer to the nearest tenth of a degree
Answers
Answer:54.23 m
Step-by-step explanation:I’m not sure this is even close to being right but I tried