Answer: True
Step-by-step explanation:
The probability of an event occurring lies between zero and one. A probability of 0 means that the event has no chance of happening for example, rolling a die once and getting a number greater than 6 while a probability of 1 means the event will definitely happen for example, getting a number less than 7 when you roll a die once.
Every other probability falls in-between this range so probability can never be 154.
The instructor wants to give an A to the students whose scores were in the top of the class. What is the minimum score needed to get an A
Answer:
The minimum svore required to get an A is 85.3.
Step-by-step explanation:
Complete Question
Exam grades: Scores on a statistics final in a large class were normally distributed with a mean of 75 and a standard deviation of 8.
The instructor wants to give an A to the students whose scores were in the top 10% of the class. What is the minimum score needed to get an A?
Solution
Scores in the top 10% of the class will have a minimum greater than the remaining bottom 90% of the class.
If the minimum score for the top 10% of the class is x'
P(X ≤ x') = 90% = 0.90
If the z-score of this minimum score of the top 10%, x', is z'.
P(X ≤ x') = P(z ≤ z') = 0.90
using the z-distribution tables
z' = 1.282
But the z-score of any value is given as the value minus the mean divided by the standard deviation.
z = (x - μ)/σ
So,
z' = (x' - μ)/σ
Mean = 75
Standard deviation = 8
z' = 1.282
1.282 = (x' - 75)/8
x' = (1.282 × 8) + 75 = 85.256
= 85.3 to 3 s.f.
Hope this Helps!!!
The _________ measures the strength and direction of the linear relationship between the dependent and the independent variable.
Answer:
Correlation Coefficient
Step-by-step explanation:
if the focus of an ellipse are (-4,4) and (6,4), then the coordinates of the enter of the ellipsis are
Answer:
The center is (1,4)
Step-by-step explanation:
The coordinates of the center of an ellipse are the coordinates that are in the middle of the two focus.
Then if we have a focus on [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], we can say that the coordinates for x and y can be calculated as:
[tex]x=\frac{x_1+x_2}{2}\\ y=\frac{y_1+y_2}{2}[/tex]
So, replacing [tex](x_1,y_1)[/tex] by (-4,4) and [tex](x_2,y_2)[/tex] by (6,4), we get that the center is:
[tex]x=\frac{-4+6}{2}=1\\ y=\frac{4+4}{2}=4[/tex]
If a dozen eggs cost $1.35, what is the unit cost?
A) $0.11
B) $0.13
C) $1.23
D) $4.29
Answer:
A) $0.11
Step-by-step explanation:
Since a dozen (12) eggs cost $1.35. You will divide $1.35 by 12. And it will equal 0.1125. Round it up it equals to 0.11.
Connor has a collection of dimes and quarters with a total value of $6.30. The number of dimes is 14 more than the number of quarters. How many of each coin does he have?
Answer:
14 Quarters and 28 dimes
Step-by-step explanation: 14 quarters $3.50
28 dimes is $2.80 total is $6.30
Which statement must be true if ?
A.
B.
C.
D.
Answer:
D
Step-by-step explanation:
D because they are congruent try measuring it.
Answer:
[tex]\boxed{\mathrm{D}}[/tex]
Step-by-step explanation:
The triangles are congruent.
The angles that are corresponding on both triangles must be congruent.
Angle Q in triangle PQR must be congruent to angle T in triangle STU.
Two types of survey questions are open questions and closed questions. An open question allows for any kind of response; a closed question allows for only a fixed response. An open question and a closed question with its possible choices are given below. List the advantages and disadvantages of each question.
Open question: What can be done to get students to eat healthier foods?
Closed question: How would you get students to eat healthier foods?
1. Mandatory nutrition course
2. Offer only healthy foods in the cafeteria and remove unhealthy foods
3. Offer more healthy foods in the cafeteria and raise the prices on unhealthy foods
What are the advantag?
A. It is easy to compare the results of surveys with open questions.
B. An open question allows for new solutions to be introduced.
C. It is easy to quantify the responses of open questions.
D. An open question allows the respondent to go in-depth with their answer.
What are the disadvantages of an open question?
A. It is difficult to compare the results of surveys with open questions.
B. It is difficult to quantify the responses of open questions.
C. The form of the question may influence the opinion of the respondent.
D. An open question limits the possible responses of the respondent.
Answer and explanation:
Advantages of open questions:
B. An open question allows for new solutions to be introduced.
D. An open question allows the respondent to go in-depth with their answer.
Disadvantages of open questions:
A. It is difficult to compare the results of surveys with open questions.
B. It is difficult to quantify the responses of open questions.
Advantages of closed questions:
- It is easy to compare the results of surveys with closed questions.
- It is easy to quantify the responses of closed questions.
Disadvantages of closed questions:
- A closed question limits the possible responses of the respondent.
-The researcher must spend time to generate a satisfactory list of possible responses from the respondent.
- possible answers may also be insufficient to be useful.
Open questions and closed questions in research questionnaires are two popular methods of getting data from respondents. They both have advantages and disadvantages and can be used interchangeably or together in questionnaires.
Closed Questions have defined answer alternatives or answer categories. Eg: Which is your favourite time of the day? (Morning or Evening etc)
Open Questions have free answers, not clear defined alternatives or categories. Eg : Why do you like morning/ evening time the most ?
Closed Questions give brief concrete answers, Open Questions have more essence of subjective & personal elaboration.
Advantages of Open Questions
Open questions allows for new solutions to be introduced. Open questions allows the respondent to go in-depth with their answer.Disadvantages of Open Questions
It is difficult to compare the results of surveys with open questions.It is difficult to quantify the responses of open questions.Advantages of Closed Questions
It is easy to quantify the responses, with these questions. It is easy to compare the results, with these questionsDisadvantages of Closed Questions
The form of question may influence potential of respondent. It limits the possible responses of respondentTo learn more, refer https://brainly.com/question/2855510?referrer=searchResults
please help it's Factorisation with Numbers
Answer:
C.
6a + 18x + 18p
Step-by-step explanation:
3(2a + 6 (x + p)) firs multiply (x + p) with 6
3 (2a + 6x + 6z) now multiply inside the parenthesis with 3 and the answer would be 6a + 18x + 18p
Use the Alternating Series Remainder Theorem to determine the smallest number of terms required to approximate the sum of the series with an error of less than 0.0001.
Answer:
yeyyyaya
Step-by-step explanation:
Graph image of figure using transformation given. Reflection across x-axis.
Answer:
Q(1,1), N(3,2) A(2,5)
Step-by-step explanation:
540 beads are shared in the ratio 4:5. The larger share of beads is
Answer:
300
Step-by-step explanation:
A(dd): 4+5= 9
D(ivide): 540/9 = 60
T(imes): 4 x 60= 240 beads
5 x 60= 300 beads
I hope this helped :)
Number of larger share of beads is 300 seeds
Given that;
Number of total beads = 540
Beads ratio = 4:5
Find:
Number of larger share of beads
Computation:
Number of larger share of beads = 5[540 / (4+5)]
Number of larger share of beads = 5[540 / 9]
Number of larger share of beads = 5[60]
Number of larger share of beads = 300 seeds
Learn more:
https://brainly.com/question/13419413?referrer=searchResults
Square root of 5 + square root of 3 the whole divided by sqaure root of 5 - square root of 3
Answer:
The answer is 4 + √15 .
Step-by-step explanation:
You have to get rid of surds in the denorminator by multiplying it with the opposite sign :
[tex] \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } [/tex]
[tex] = \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } \times \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} + \sqrt{3} } [/tex]
[tex] = \frac{ {( \sqrt{5} + \sqrt{3} ) }^{2} }{( \sqrt{5} - \sqrt{3} )( \sqrt{5} + \sqrt{3}) } [/tex]
[tex] = \frac{ {( \sqrt{5} )}^{2} + 2( \sqrt{5} )( \sqrt{3}) + {( \sqrt{3}) }^{2} }{ {( \sqrt{5}) }^{2} - { (\sqrt{3} )}^{2} } [/tex]
[tex] = \frac{5 + 2 \sqrt{15} + 3 }{5 - 3} [/tex]
[tex] = \frac{8 + 2 \sqrt{15} }{2} [/tex]
[tex] = 4 + \sqrt{15} [/tex]
Prove that a cubic equation x 3 + ax 2 + bx+ c = 0 has 3 roots by finding the roots.
That's a pretty tall order for Brainly homework. Let's start with the depressed cubic, which is simpler.
Solve
[tex]y^3 + 3py = 2q[/tex]
We'll put coefficients on the coefficients to avoid fractions down the road.
The key idea is called a split, which let's us turn the cubic equation in to a quadratic. We split unknown y into two pieces:
[tex]y = s + t[/tex]
Substituting,
[tex](s+t)^3 + 3p(s+t) = 2q[/tex]
Expanding it out,
[tex]s^3+3 s^2 t + 3 s t^2 + t^3 + 3p(s+t) = 2q[/tex]
[tex]s^3+t^3 + 3 s t(s+t) + 3p(s+t) = 2q[/tex]
[tex]s^3+t^3 + 3( s t + p)(s+t) = 2q[/tex]
There a few moves we could make from here. The easiest is probably to try to solve the simultaneous equations:
[tex]s^3+t^3=2q, \qquad st+p=0[/tex]
which would give us a solution to the cubic.
[tex]p=-st[/tex]
[tex]t = -\dfrac p s[/tex]
Substituting,
[tex]s^3 - \dfrac{p^3}{s^3} = 2q[/tex]
[tex](s^3)^2 - 2 q s^3 - p^3 = 0[/tex]
By the quadratic formula (note the shortcut from the even linear term):
[tex]s^3 = q \pm \sqrt{p^3 + q^2}[/tex]
By the symmetry of the problem (we can interchange s and t without changing anything) when s is one solution t is the other:
[tex]s^3 = q + \sqrt{p^3+q^2}[/tex]
[tex]t^3 = q - \sqrt{p^3+q^2}[/tex]
We've arrived at the solution for the depressed cubic:
[tex]y = s+t = \sqrt[3]{q + \sqrt{p^3+q^2}} + \sqrt[3]{ q - \sqrt{p^3+q^2} }[/tex]
This is all three roots of the equation, given by the three cube roots (at least two complex), say for the left radical. The two cubes aren't really independent, we need their product to be [tex]-p=st[/tex].
That's the three roots of the depressed cubic; let's solve the general cubic by reducing it to the depressed cubic.
[tex]x^3 + ax^2 + bx + c=0[/tex]
We want to eliminate the squared term. If substitute x = y + k we'll get a 3ky² from the cubic term and ay² from the squared term; we want these to cancel so 3k=-a.
Substitute x = y - a/3
[tex](y - a/3)^3 + a(y - a/3)^2 + b(y - a/3) + c = 0[/tex]
[tex]y^3 - ay^2 + a^2/3 y - a^3/27 + ay^2-2a^2y/3 + a^3/9 + by - ab/3 + c =0[/tex]
[tex]y^3 + (b - a^2/3) y = -(2a^3+9ab) /27 [/tex]
Comparing that to
[tex]y^3 + 3py = 2q[/tex]
we have [tex] p = (3b - a^2) /9, q =-(a^3+9ab)/54 [/tex]
which we can substitute in to the depressed cubic solution and subtract a/3 to get the three roots. I won't write that out; it's a little ugly.
In the figure below, which term best describes point L?
Explanation:
The tickmarks show which pieces are congruent to one another, which in turn show the segments have been bisected (cut in half). The square angle markers show we have perpendicular segments. So we have three perpendicular bisectors. The perpendicular bisectors intersect at the circumcenter. The circumcenter is the center of the circumcircle. This circle goes through all three vertex points of the triangle.
A useful application is let's say you had 2 friends and you three wanted to pick a location to meet for lunch. Each person traveling from their house to the circumcenter's location will have each person travel the same distance. We say the circumcenter is equidistant from each vertex point of the triangle. In terms of the diagram, LH = LJ = LK.
Answer: B.) Circumcenter
Step-by-step explanation:
Find the slope of the line that passes through (1, 14) and (4,9)
Which two numbers in the points represent x values? Select both in the
list.
In any coordinate pair, the first number is the x-value and the second number is the y-value.
To find the slope, simply take the difference of the y values and divide by the difference in the x values: (14-9)/(1-4) is equal to -5/3.
The slope of the line that passes through (1, 14) and (4,9) is -5/3.
It is find the slope of the line.
what is slope?The slope of any line, ray, or line segment is the ratio of the vertical to the horizontal distance between any two points on it (“slope equals rise over run”).
The slope is always calculated from the rise divided by the run. Typically, the equation is presented as:
m = Rise/Run
If you have two points, the points should be [tex]P_{1} (x_{1} ,y_{1} )[/tex] and [tex]P_{2} (x_{2} ,y_{2} )[/tex] So, the equation would be:
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
In any coordinate pair, the first number is the x-value and the second number is the y-value.
The difference of the y values and divide by the difference in the x values:
m=(14-9)/(1-4) is equal to -5/3.
The slope of the line that passes through (1, 14) and (4,9) is -5/3.
Learn more about slope here:
https://brainly.com/question/17114095
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Given that r = ( 7, 3, 9) and v = ( 3, 7, -9), evaluate r + v
a. (-21,-21,81)
b. (10,10,0)
c. (21,21,-81)
d. (-10,-10,0)
Answer:
b. (10,10,0)
Step-by-step explanation:
r+v can be evaluated if the vectors/matrices have the same dimensions.
These do. They are both 1 by 3 vectors.
Just add first to first in each.
Just add second to second in each.
Just add third to third in each.
Example:
(5,-5,6)+(1,2,3)
=(5+1,-5+2,6+3)
=(6,-3,9)
Done!
In general, (a,b,c)+(r,s,t)=(a+r,b+s,c+t).
r+v
=(7,3,9)+(3,7,-9)
=(7+3,3+7,9+-9)
=(10,10,0)
Done!
Which interval contains a local minimum for the graphed
function?
Answer:
[2.5 ,4]
Step-by-step explanation:
The graph in this interval has a vertex while opening up wich means it's a minimum
Base: z(x)=cosx Period:180 Maximum:5 Minimum: -4 What are the transformation? Domain and Range? Graph?
Answer:
The transformations needed to obtain the new function are horizontal scaling, vertical scaling and vertical translation. The resultant function is [tex]z'(x) = \frac{1}{2} + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)[/tex].
The domain of the function is all real numbers and its range is between -4 and 5.
The graph is enclosed below as attachment.
Step-by-step explanation:
Let be [tex]z (x) = \cos x[/tex] the base formula, where [tex]x[/tex] is measured in sexagesimal degrees. This expression must be transformed by using the following data:
[tex]T = 180^{\circ}[/tex] (Period)
[tex]z_{min} = -4[/tex] (Minimum)
[tex]z_{max} = 5[/tex] (Maximum)
The cosine function is a periodic bounded function that lies between -1 and 1, that is, twice the unit amplitude, and periodicity of [tex]2\pi[/tex] radians. In addition, the following considerations must be taken into account for transformations:
1) [tex]x[/tex] must be replaced by [tex]\frac{2\pi\cdot x}{180^{\circ}}[/tex]. (Horizontal scaling)
2) The cosine function must be multiplied by a new amplitude (Vertical scaling), which is:
[tex]\Delta z = \frac{z_{max}-z_{min}}{2}[/tex]
[tex]\Delta z = \frac{5+4}{2}[/tex]
[tex]\Delta z = \frac{9}{2}[/tex]
3) Midpoint value must be changed from zero to the midpoint between new minimum and maximum. (Vertical translation)
[tex]z_{m} = \frac{z_{min}+z_{max}}{2}[/tex]
[tex]z_{m} = \frac{1}{2}[/tex]
The new function is:
[tex]z'(x) = z_{m} + \Delta z\cdot \cos \left(\frac{2\pi\cdot x}{T} \right)[/tex]
Given that [tex]z_{m} = \frac{1}{2}[/tex], [tex]\Delta z = \frac{9}{2}[/tex] and [tex]T = 180^{\circ}[/tex], the outcome is:
[tex]z'(x) = \frac{1}{2} + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)[/tex]
The domain of the function is all real numbers and its range is between -4 and 5. The graph is enclosed below as attachment.
Suppose that you expect SugarCane stock price to decline. So you decide to ask your broker to short sell 2000 shares. The current market price is $40. The proceeds from the short sale $80,000 is credited into your account. However, a few days later the market price of the stock jumps to $80 per share and your broker asks you close out your position immediately. What is your profit or loss from this transaction?
Answer:
Loss = $80000
Step-by-step explanation:
To determine if it's a profit or loss is simple.
He predicted the sugar cane stock to fall so he sold , but few days later the stock grew and went bullish.
He sold at$ 40 for 2000 shares
=$ 80000
But the stock went up to $80 per share that is gaining extra $40
So it was actually a loss.
The loss is =$40 * 2000
The loss = $80000
4.5/y = 12.5/4 PLEASE HELP!!! SOS
Answer:
y = 1.44
Step-by-step explanation:
What are you aiming to do here? Please share all instructions with each problem.
If you want to solve 4.5/y = 12.5/4 for y: Multiply both sides by 4y:
18 = 12.5y. Then y = 1.44
1. Which of the following ordered pairs are solutions to the system of equations below?
4x + 4y = -9
Y = 2x - 13
A : (-3, -7)
B : (3-7)
C : (3,7)
D : (-3,7)
Answer:
43\ 12 , 35/ 6
Step-by-step explanation:
43\ 12 , 35/ 6
Answer: B: (3, -7)
Step-by-step explanation:
4x + 4y = -9
y = 2x - 13
Use Substitution:
4x + 4(2x - 13) = -9
4x + 8x - 52 = -9
12x - 52 = -9
12x = 43
[tex]x=\dfrac{43}{12}[/tex]
None of the options provided are valid so either there is a typo on your worksheet or you typed in one of the equations wrong.
Plan B: Input the choices into the equation to see which one makes a true statement.
4x + 4y = -9
A) (x, y) = (-3, -7)
4(-3) + 4(-7) = -9
-12 + -28 = -9
-40 ≠ -9
B) (x, y) = (3, -7)
4(3) + 4(-7) = -9
12 + -28 = -9
-16 ≠ -9
C) (x, y) = (3, 7)
4(3) + 4(7) = -9
12 + 28 = -9
40 ≠ -9
D) (x, y) = (-3, 7)
4(-3) + 4(7) = -9
-12 + 28 = -9
16 ≠ -9
Obviously there is something wrong with the first equation because none of the options provide a true statement.
y = 2x - 13
A) (x, y) = (-3, -7)
-7 = 2(-3) - 13
-7 = -6 -13
-7 ≠ -19
B) (x, y) = (3, -7)
-7 = 2(3) - 13
-7 = 6 -13
-7 = -7 this works!!!
C) (x, y) = (3, 7)
7 = 2(3) - 13
7 = 6 -13
7 ≠ -7
D) (x, y) = (-3, 7)
7 = 2(-3) - 13
7 = -6 -13
7 ≠ -19
Option B is the only one that provides a true statement so this must be the answer.
A sample of 150 CBC students was taken, and each student filled out a
survey. The survey asked students about different aspects of their college
and personal lives. The experimenter taking the survey defined the
following events:
A=The student has children
B = The student is enrolled in at least 12 credits
C = The student works at least 10 hours per week
The student found that 44 students in the sample had children, 73 were
enrolled in at least 12 credits, and 105 were working at least 10 hours per
week. The student also noted that 35 students had children and were
working at least 10 hours per week.
Calculate the probability of the event BC for students in this sample. Round
your answer to four decimal places as necessary.
Answer:
The probability of the event BC
= the probability of B * C = 48.6667% * 70%
= 34.0667%
Step-by-step explanation:
Probability of A, students with children = 44/150 = 29.3333%
Probability of B, students enrolled in at least 12 credits = 73/150 = 48.6667%
Probability of C, students working at least 10 hours per week = 105/150 = 70%
Therefore, the Probability of BC, students enrolled in 12 credits and working 10 hours per week
= 48.6667% * 70%
= 34.0667%
The altitude of an airplane is decreasing at a rate of 41 feet per second. What is the change in altitude of the airplane over a period of 32 seconds?
Answer:
1312 feet
Step-by-step explanation:
41 ft=1 sec
how about 32 sec
41 x 32=1312/1=1312
Determine which expression could represent a polynomial with a factor of (x - √3i)
Answer:
Option (3)
Step-by-step explanation:
[tex](x-i\sqrt{3})[/tex] is a factor of a polynomial given in the options, that means a polynomial having factor as [tex](x-i\sqrt{3})[/tex] will be 0 for the value of x = [tex]i\sqrt{3}[/tex].
Option (1),
3x⁴ + 26x² - 9
= [tex]3(i\sqrt{3})^{4}+26(i\sqrt{3})^2-9[/tex] [For x = [tex]i\sqrt{3}[/tex]]
= 3(9i⁴) + 26(3i²) - 9
= 27 - 78 - 9 [Since i² = -1]
= -60
Option (2),
4x⁴- 11x² + 3
= [tex]4(i\sqrt{3})^4-11(i\sqrt{3})^2+3[/tex]
= 4(9i⁴) - 33i² + 3
= 36 + 33 + 3
= 72
Option (3),
4x⁴ + 11x² - 3
= [tex]4(i\sqrt{3})^4+11(i\sqrt{3})^2-3[/tex]
= 4(9i⁴) + 33i² - 3
= 36 - 33 - 3
= 0
Option (4),
[tex]3x^{4}-26x^{2}-9[/tex]
= [tex]3(i\sqrt{3})^4-26(i\sqrt{3})^{2}-9[/tex]
= 3(9i⁴) - 26(3i²) - 9
= 27 + 78 - 9
= 96
Therefore, [tex](x-i\sqrt{3})[/tex] is a factor of option (3).
tje mean of 12 scores is 8.8 what is the sum of tue 12 scores
Answer:
105.6
Step-by-step explanation:
If the mean is 8.8, than that means that in total the sum must be (8.8 * 12) which equals 105.6.
This is because the sum of all the numbers in a list divided by the amount of numbers in a list equals the mean.
Please Help!!! Find X for the triangle shown.
Answer:
[tex] x = 2 [/tex]
Step-by-step explanation:
Given a right-angled triangle as shown above,
Included angle = 60°
Opposite side length = 3
Adjacent side length = x
To find x, we would use the following trigonometric ratio as shown below:
[tex] tan(60) = \frac{3}{x} [/tex]
multiply both sides by x
[tex] x*tan(60) = \frac{3}{x}*x [/tex]
[tex] x*tan(60) = 3 [/tex]
Divide both sides by tan(60)
[tex] \frac{x*tan(60)}{tan(60} = \frac{3}{tan(60} [/tex]
[tex] x = \frac{3}{tan(60} [/tex]
[tex] x = 1.73 [/tex]
[tex] x = 2 [/tex] (approximated to whole number)
the sum of place value of 5 in 15954
Answer:
5050
Step-by-step explanation:
Place value of a digit is the value of digit based on its position the given number.
to determine the place value of a digit
we multiply the digit by number of 10's which is equal to number of digits in its right.
example
for a number 1234687
the place value of 3 is
we take 3 and
multiply it by number of 10' in its right
number of 10's in the right is 4
thus place value of 3 = 3*10*10*10*10 = 30000
________________________________________________
15954
place value of 5 at thousandth position = 5*10*10*10 = 5000
place value of 5 at tens position = 5*10 = 50
Thus, sum of place value of 5 in 15954 = 5000+50 = 5050
plz help.... 2|x-3|-5=7
Answer:
x = -3 and x = 9.
Step-by-step explanation:
2|x - 3| - 5 = 7
2|x - 3| = 12
|x - 3| = 6
x - 3 = 6
x = 9
-(x - 3) = 6
-x + 3 = 6
-x = 3
x = -3
Hope this helps!
Answer:
x=9 x=-3
Step-by-step explanation:
2|x-3|-5=7
Add 5 to each side
2|x-3|-5+5=7+5
2|x-3|=12
Divide by 2
2/2|x-3|=12/2
|x-3|=6
There are two solutions to an absolute value equation, one positive and one negative
x-3 =6 x-3 = -6
Add 3 to each side
x-3+3 = 6+3 x-3+3 = -6+3
x=9 x = -3
need help with these 3 questions (giving brainiest if you can answer with equations)
Problem 10
Answer: approximately 57.39159 kmExplanation: You'll use the equation cos(28) = d/65 to solve for d to get d = 65*cos(28) = 57.39159 approximately. We use the cosine ratio because it ties together the adjacent and hypotenuse.
=====================================
Problem 11
Answer: approximately 10.46162 metersExplanation: This time we use the sine rule. We have the height as the opposite side (which is unknown, call it x) and the hypotenuse is the ladders length (11). So we have sin(72) = x/11 which solves to x = 11*sin(72) = 10.46162
=====================================
Problem 12
Answer: approximately 16.05724 cmExplanation: Now we use the tangent rule to connect the opposite and adjacent sides.
tan(37) = 12.1/x
x*tan(37) = 12.1
x = 12.1/tan(37)
x = 16.05724 approximately
a person can do a job in 6 day days . another can do the same job in 4days . if they work together, how long do they need to finish the job?
Answer:
It will take them 2 2/5 days working together
Step-by-step explanation:
To find the time worked
1/a + 1/b = 1/t
Where a and b are the times worked individually and t is the time worked together
1/4 + 1/6 = 1/t
Multiply each side by 12t to clear the fractions
12t( 1/4 + 1/6 = 1/t)
3t + 2t =12
Combine like terms
5t = 12
Divide by 5
t = 12/5
t = 2 2/5
It will take them 2 2/5 days working together