A surveyor leaves her base camp and drives 43km
on a bearing of 032 degrees. She then drives 28km
on a bearing of 154 degrees. How far is she then
from her base camp and what is her bearing from
it?
Answers
Answer:
1. The distance from the base camp is 37 Km
2. The bearing from the base camp is 72°
Step-by-step explanation:
Please see attached photo for explanation.
1. Determination of the distance from the base camp.
In the attached photo, x is the distance from the base camp. The value of x can be obtained by using the cosine rule formula. This is illustrated below:
Side opposite A = a = 28 Km
Side opposite C = c = 43 Km
Angle B = 58°
Side opposite B = b = x =?
b² = a² + c² – 2ac Cos B
x² = 28² + 43² – 2 × 28 × 43 Cos 58
x² = 784 + 1849 – 2408 × 0.52991
x² = 2633 – 1276
x² = 1357
Take the square root of both side
x = √1357
x ≈ 37 Km
Thus, the distance from the base camp is 37 Km.
2. Determination of the bearing from the base camp
We'll begin by calculating the value of θ in the attached photo. This can be obtained by using sine rule formula as shown below:
Side opposite A = a = 28 Km
Side opposite B = b = x = 37
Angle B = 58°
Angle A = θ =?
a/Sine A = b/SineB
28/Sine θ = 37/Sine 58
Cross multiply
37 × Sine θ = 28 × Sine 58
Divide both side by 37
Sine θ = 28 × Sine 58 /37
Sine θ = 28 × 0.8480 / 37
Sine θ = 0.6417
Take the inverse of sine
θ = Sine¯¹ 0.6417
θ = 40
Finally, we shall determine the bearing from the base camp. This can be obtained as follow:
Bearing from the base camp = 32 + θ
θ = 40
Bearing from the base camp = 32 + 40
Bearing from the base camp = 72°
Related Questions
solve the system of equations -8x+7y=6 and 3x-2y=4 by combining the equations
Answers
Answer:
x=8, y=10. (8, 10).
Step-by-step explanation:
-8x+7y=6
3x-2y=4
--------------
2(-8x+7y)=2(6)
7(3x-2y)=7(4)
-----------------------
-16x+14y=12
21x-14y=28
-------------------
5x=40
x=40/5
x=8
3(8)-2y=4
24-2y=4
2y=24-4
2y=20
y=20/2
y=10
In the diagram, R, S, and T are all points of tangency. What is the perimeter of Triangle
XYZ?
Answers
Answer:
54 cm
Step-by-step explanation:
Perimeter = TZ + TX + RX + RY + SY + SZ
TZ = 5 cm
TX = 13 cm
RY = 9 cm
RX = TX = 13 cm (tangents drawn from and external point)
SY = RY = 9 cm (tangents drawn from and external point)
SZ = TZ = 5 cm (tangents drawn from and external point)
Plug in the values:
Perimeter = 5 + 13 + 13 + 9 + 9 + 5 = 54 cm
Select all the expressions that have the same value
Answers
so what was the question again?
Answer:
Step-by-step explanation:
The equation of the line passing through (2, 3) with a slope of 5 is y = []x- []
Answers
Answer: y = 5x - 7
Step-by-step explanation:
y = mx + b, where m = slope
We plug in the point, where x = 2, and y = 3
y = 5x - b
3 = 5(2) - b
3 = 10 - b
b + 3 = 10
b = 7
y = 5x - 7
A rectangular box is to have a square base and a volume of 63 ft3. If the material for the base costs $0.22/ft2, the material for the sides costs $0.09/ft2, and the material for the top costs $0.20/ft2, determine the dimensions (in ft) of the box that can be constructed at minimum cost.
Answers
9514 1404 393
Answer:
3 ft square base, 7 feet high
Step-by-step explanation:
For minimum cost, each pair of opposite sides costs the same as any other pair of opposite sides.
If s is the edge length of the base, then the areas of the top and bottom are s² and their total cost is ...
(s²)(0.22 +0.20) = 0.42s² . . . . cost of top and bottom
__
For a volume of 63 ft³, the height of the side of the box is ...
63/s² = h
and the area of one side of the box is ...
hs = 63/s
A pair of opposite sides will have a cost of ...
(63/s)(0.09 +0.09) = 11.34/s . . . . cost of a pair of opposite sides
__
We want these two costs to be the same, so we have ...
0.42s² = 11.34/s
s³ = 11.34/0.42 = 27
s = ∛27 = 3 . . . . feet
h = 63/s² = 7 . . . . feet
__
The box dimensions are 3 feet square by 7 feet tall.
_____
Additional comment
Each pair of opposite sides will cost $3.78, so the total cost of the box is $11.34.
For the non-believers, we have shown a graph of the total cost of the box as a function of the base dimension (s). It has a minimum at $11.34 when s=3. You can find that by differentiating the cost function and and finding the zero(s) of that (or by reading the values from the graph).
Merit verification
1+1+1+1=R
2+2+2+2=T
3+3+3+3=E
4+4+4+4=N
5+5+5+5=?
Answers
Explanation: The letter represents the last letter of the total. For example, 1+1+1+1= 4 (fouR), 3+3+3+3=12(twelvE), therefore 5+5+5+5=20(twentY)
Hey guys I need some help; I would really appreciate it :)
Answers
When adding two rational
numbers tell what the sign of the
sum will be if:
Both rational numbers are
negative
Answers
Answer:
it's going to be negative
Pls help I need a good grade
Answers
Answer:
Step-by-step explanation:
13). [tex]-\frac{q}{7}\geq -1[/tex]
[tex]\frac{q}{7}\leq 1[/tex]
[tex](\frac{q}{7}\times 7)\leq (1\times 7)[/tex]
q ≤ 7
14). -12x < 60
12x > -60
[tex]\frac{12x}{12}>\frac{-60}{12}[/tex]
x > -5
15). 5 > z - 3
5 + 3 > z - 3 + 3
8 > z
16). 0.5 ≤ [tex]\frac{y}{8}[/tex]
0.5 × 8 ≤ [tex]\frac{y}{8}\times 8[/tex]
4 ≤ y
Now we can draw these inequalities on a number line.
Select the correct answer from each drop-down menu.
A camp director developed the function m(c) = 12c + 80 to model the total cost of taking c campers on a field trip to the movies.
In the camp director’s function, the number of campers is the _______ variable and the total cost of the trip _________
1. ( independent, dependent )
2. ( changes by a constant factor per camper, Changes by a constant amount per camper )
.
Answers
Answer:
(a) Independent variable
(b) The constant factor is 12
Step-by-step explanation:
Given
[tex]m(c) = 12c + 80[/tex]
c = campers
m = total cost
Solving (a) What type of variable is the number of campers (c)
The total cost (m) is dependent on the number of campers (c) for its own value.
In other words, if c changes from 5 to say 7, the value of m will also change.
This implies that the number of campers is an Independent variable
Solving (b): Constant factor
This in other words means, rate of change (or slope)
A linear function is:
[tex]y = ax + b[/tex]
Where a represents the slope
By comparison with: [tex]m(c) = 12c + 80[/tex]
Hence, the constant factor is 12
Answer:
dependent, changes by a constant factor per camper.
Step-by-step explanation:
A gadget company randomly selects 10 toys per hour to inspect. The number of defective toys in the last six samples is shown in the table.
Based on this information, how many toys are likely to be defective in a sample of 500?
A: 1
B: 5
C: 50
D: 300
Answers
Answer:
50
Step-by-step explanation:
Using proportions, it is found that the number of toys that is likely to be defective in a sample of 500 is given by:
C: 50
What is a proportion?A proportion is a fraction of a total amount.
For the samples of 10, the mean number of errors is of:
( 0 + 2 + 1 + 1 + 2 + 0)/6 = 1
Hence, for samples of 500, the expected number of defective toys will be given by:
E = (500/10) x 1 = 50
Hence, option C is correct.
More can be learned about proportions at https://brainly.com/question/24372153
The temperatures at 6:00 am one morning in four cities are given below.
Paris
-5 °C
Oslo
-12 °C
-3°C
London
Brussels
-1 °C
a) Which city was the warmest?
Brussels
b) Give the difference in temperature between Oslo and London.
°C
At 6:00 pm, the temperature in Paris was 3°C higher than at 6:00 am.
c) What was the temperature at 6:00 pm in Paris?
°C
Answers
Answer:
-9
Step-by-step explanation:
The city of Brussels will be the warmest. The difference in temperature between Oslo and London is -9°C and the temperature at 6:00 pm in Paris will be -2°C.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
(a)
A city which has the lowest temperature will be warmest since -1°C is the lowest so Brussels will have the warmest city.
(b)
The difference in temperature between Oslo and London will be as,
-12 °C - (-3 °C) = -9 °C.
(c)
At 6.:00 pm the temperature will be -5 °C + 3 °C = -2 °C.
Hence "The city of Brussels will be the warmest. The difference in temperature between Oslo and London is -9°C and the temperature at 6:00 pm in Paris will be -2°C".
To learn more about the arithmetic operators,
brainly.com/question/25834626
#SPJ2
HURRY ASAP ?!?!?!?!?!?!?!?Which of the following is the inverse of
Answers
Answer:
[tex]f^{-1}(x) = \sqrt[3]{\frac{x -4}{5}} +2[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 5(x - 2)^3 + 4[/tex]
Required
Determine the inverse
[tex]f(x) = 5(x - 2)^3 + 4[/tex]
Replace f(x) with y
[tex]y = 5(x - 2)^3 + 4[/tex]
Swap the positions of x and y
[tex]x = 5(y - 2)^3 + 4[/tex]
Make y the subject
[tex]x -4= 5(y - 2)^3[/tex]
Divide by 5
[tex]\frac{x -4}{5}= (y - 2)^3[/tex]
Take cube roots of both sides
[tex]\sqrt[3]{\frac{x -4}{5}}= y - 2[/tex]
Add 2 to both sides
[tex]\sqrt[3]{\frac{x -4}{5}} +2 = y[/tex]
[tex]y = \sqrt[3]{\frac{x -4}{5}} +2[/tex]
Replace y with [tex]f^{-1}(x)[/tex]
[tex]f^{-1}(x) = \sqrt[3]{\frac{x -4}{5}} +2[/tex]
What if I had 1/3x^3, would this be a vertical stretch or vertical compression?
Answers
Vertical compression
Please Help Quickly :)
The area of the top of a rectangular coffee table, in square units, is represented by the expression: (2x-11)(2x+11). Which expression represents an equivalent area?
A.) (4x^2-121) Square units
B.) (4x^2-44x+121) Square units
C.) (4x^2 +44x-121) Square units
D.) (4x^2+121) Square units
I will gve you brainliest if it is the correct awnser and if you help me quickly
Answers
Answer:
Step-by-step explanation:
2x * 2x = 4x^2 and -11 * 11 = -121
Find the mean, median, and
mode of this data set:
2, 3, 4, 5, 5, 6, 8
Answers
Answer:
Mean: 4.71
Mode: 5
Median: 5
Step-by-step explanation:
A recent survey was conducted to compare the cost of solar energy to the cost of gas or electric energy. Results of the survey revealed that the distribution of the amount of the monthly utility bill of a 3-bedroom house using gas or electric energy had a mean of $93 and a standard deviation of $11. Three solar homes reported monthly utility bills of $56, $54, and $51. Which of the following statements is true?
A. Homes using solar power always have lower utility bills than homes using only gas and electricity.
B. Homes using solar power may have lower utility bills than homes using only gas and electricity.
C. Homes using solar power may actually have higher utility bills than homes using only gas and electricity.
D. The utility bills for homes using solar power are about the same as those for homes using only gas and electricity.
Answers
Answer:
A. Homes using solar power always have lower utility bills than homes using only gas and electricity.
Step-by-step explanation:
Gas and Electricity
[tex]\bar x = 93[/tex]
[tex]\sigma = 11[/tex]
Solar
Bills: 56, 54 and 51
Required
Determine which of the statements is true
First, we calculate the mean of the given data
[tex]\bar x = \frac{\sum x}{n}[/tex]
[tex]\bar x = \frac{56 + 54 + 51}{3}[/tex]
[tex]\bar x = \frac{161}{3}[/tex]
[tex]\bar x = 53.67[/tex]
Then, the standard deviation
[tex]\sigma = \sqrt{\frac{\sum(x - x_i)^2}{n}}[/tex]
[tex]\sigma = \sqrt{\frac{(56 - 53.67)^2 + (54 - 53.67)^2 + (51 - 53.67)^2}{3}}[/tex]
[tex]\sigma = \sqrt{\frac{12.67}{3}}[/tex]
[tex]\sigma = \sqrt{4.223}[/tex]
[tex]\sigma = 2.05[/tex]
So, we have:
Gas or Electricity
[tex]\bar x = 93[/tex]
[tex]\sigma = 11[/tex]
Solar
[tex]\bar x = 53.67[/tex]
[tex]\sigma = 2.05[/tex]
By comparison.
The mean and standard deviation of homes using solar panel is less than home using gas and electricity.
This implies that: (a) is true.
What is 0.69 expressed as a fraction in simplest form
Answers
Answer:
the answer is 69/100
Select all the choices below that show three lengths that could be the lengths of a triangle?
2 cm, 3 cm, 8 cm
2 cm, 5 cm, 6 cm
4 cm, 8 cm, 11 cm
10 in, 5 in, 13 in
Answers
Answer:
The last three,
2 cm, 5 cm, 6 cm
4 cm, 8 cm, 11 cm
10 in, 5 in, 13 in
As long as any two sides added together are long than the third side, it works as a triangle!
In a survey of 300 college graduates, 53% reported that they entered a profession closely related to their college major. If 9 of those survey subjects are randomly selected with replacement for a follow-up survey, what is the probability that 3 of them entered a profession closely related to their college major
Answers
Answer:
0.1348 = 13.48% probability that 3 of them entered a profession closely related to their college major.
Step-by-step explanation:
For each graduate, there are only two possible outcomes. Either they entered a profession closely related to their college major, or they did not. The probability of a graduate entering a profession closely related to their college major is independent of other graduates. This, coupled with the fact that they are chosen with replacement, means that we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
53% reported that they entered a profession closely related to their college major.
This means that [tex]p = 0.53[/tex]
9 of those survey subjects are randomly selected
This means that [tex]n = 9[/tex]
What is the probability that 3 of them entered a profession closely related to their college major?
This is P(X = 3).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 9) = C_{9,3}.(0.53)^{3}.(0.47)^{6} = 0.1348[/tex]
0.1348 = 13.48% probability that 3 of them entered a profession closely related to their college major.
Two companies manufacture a rubber material intended for use in an automotive application. The part will be subjected to abrasive wear in the field application, so we decide to compare the material produced by each company in a test. Twenty-five samples of material from each company are tested in an abrasion test, and the amount of wear after 1000 cycles is observed. For company 1, the sample mean and standard deviation of wear are
xÌ… = 20 milligrams / 1000cycless
s1= 2 milligrams/1000cycles and for company 2, you obtain
xÌ… 2 = 15 milligrams /1000cycles
and
s2= 8 milligrams / 1000cycles
Required:
a. Do the data support the claim that the two companies produce material with different mean wear? Use α = 0.05, and assume that each population is normally distributed but that their variances are not equal. What is the P-value for this test?
b. Do the data support a claim that the material from company 1 has higher mean wear than the material from company 2? Use the same assumptions as in part (a).
c. Construct confidence intervals that will address the questions in parts (a) and (b) above.
Answers
Step-by-step explanation:
Due to the time it took to solve this question, I had little time to type the answers fully
The answers are contained fully in the attachment I have uploaded.
A. H0: u1 = u2
H1: u1 not equal to u2
The t statistics was solved to be 3.03
The degree of freedom was solved to be 26
Given this information, this is a 3 tailed test, critical value at 5% = +-2.056
T stat > critical value
We therefore reject the null hypothesis at 5% and conclude they have different mean wear
The p value is calculated using excel and the result is 0.00544
We reject null at 5% since p value is less than 0.05
B. H0: u1 = u2
H1: u1>u2
Alpha = 0.05
Following a,
Test stat = 3.03
Df = 26
Critical value for 1 tailed test = 1.706
Test stat > 1.706
We reject H0 and conclude company 1 has higher mean wear.
We find p value for a right tailed distribution using excel
Tdist(3.03,26,1)
= 0.002722
We reject h0
C. Confidence interval
1.610 < u < 8.390
Is this a rational number
Answers
Answer:
Note that it is not a perfectly elastic result so it is irrational
A 4-column table with 4 rows titled Population Data. Column 1 has entries 4, 5, 9, 15. Column 2 has entries 8, 2, 20, 1. Column 3 has entries 6, 9, 10, 8. Column 4 has entries 10, 8, 1, 2.
If Serena selects 4 samples from the table, which row will give her largest mean?
Which row will give her the smallest mean?
The actual population mean will be between
.
Answers
Answer:
row 3
row 2
6 and 10
Answer:
The answers are 1( row 3 ) 2( row 2 ) 3( 6 and 10 )
Step-by-step explanation:
I got it right on edge and also the person above me is correct have a wonderful day. (✿◠‿◠)
please help me thanks
Answers
Answer:
1/14
Step-by-step explanation:
What's 9 mil time 400 can you please answer
Answers
Answer:
The answer is 3,600,000,000
Step-by-step explanation:
Simply multiply 9,000,000 * 400 which equals 3,600,000,000.
Please Help No fake answers
Answers
Answer:
5.09 or 5.10(if u round up)
Step-by-step explanation:
When you convert √24 it will be 5.099
The decimal point must lie between 5 and 0
Hope this helps:)
what is 1/2 + 1/3 i know it’s so simple i’m just so bad at maths
Answers
What is the m∠J, to the nearest tenth? JLK is right angle triangle. The length of JL is 9.4 and length of LK is 15.1.
Answers
Answer:
58.1
Step-by-step explanation:
The staircase has three parallelogram-shaped panels that are the same size. The horizontal distance between each panel is 4.25 inches. What is the area of one panel?
Item 19
The staircase has three parallelogram-shaped panels that are the same size. The horizontal distance between each panel is 4.25 inches. What is the area of one panel?
Answers
Answer:
636
8u2b4c9....°73vaultx8 3_2144,773,90=636
Step-by-step explanation:
993yuei92u83vaultx21564=636
pls hurry if you can. A What is the volume of this cube?
Question 5 options:
26.46 cm3
9.261 cm3
6.3 cm3
Answers
Answer:
9.261 cm³
Step-by-step explanation:
2.1x2.1x2.1=9.261
Answer:
9.2
Step-by-step explanation:
the answer is 9.2 yo multiplu 2.1x2.1x2.1