Step-by-step explanation: Ants are one of the most abundant insects on our planet and the reasons are their eusocial, complex societal behaviors and their ability to survive in many and various ecosystems. Like most other animal societies, reproduction is one of the core reasons why ants are so prevalent.
Acrobat Ant
Reproduction for ants is a complex phenomenon that involves finding, selecting and successfully fertilizing females to ensure that the eggs laid are able to survive and molt through the successive stages of the ant’s life cycle – larvae, pupae and adults.
Answer:
81
Step-by-step explanation:
Start: 50
After 1 day: 50 * 1.1
After 2 days: 50 * 1.1 * 1.1 = 50 * 1.1^2
After 3 days: 50 * 1.1^2 * 1.1 = 50 * 1.1^3
...
After 5 days: 50 * 1.1^5 = 80.53
Answer: 81
Please help!
Suppose that [tex]\alpha[/tex] is inversely proportional to [tex]\beta[/tex]. If [tex]\alpha=4[/tex] when [tex]\beta=9[/tex], find [tex]\alpha[/tex] when [tex]\beta=-72[/tex]
Answer:
The answer is
[tex] \alpha = - \frac{1}{2} [/tex]Step-by-step explanation:
From the question
[tex]\alpha[/tex] is inversely proportional to [tex]\beta[/tex] is written as
[tex] \alpha = \frac{k}{ \beta } [/tex]where k is the constant of proportionality
When
[tex]\alpha[/tex] = 4[tex]\beta[/tex] = 9Substituting the values into the formula
we have
[tex]4 = \frac{k}{9} [/tex]
cross multiply
k = 4 × 9
k = 36
So the formula for the variation is
[tex] \alpha = \frac{36}{ \beta } [/tex]
when
[tex]\beta[/tex] = - 72
That's
[tex] \alpha = \frac{36}{ - 72} [/tex]
Simplify
We have the final answer as
[tex] \alpha = - \frac{ 1}{2} [/tex]Hope this helps you
SP=2x+3, and LN=5x−14. Find SP.
Answer:
43
Step-by-step explanation:
Using Thales theorem:
● SP/LN = RP /RN
Notice that RN = 2×RP
● SP/LN = RP/2RP
● SP /LN = 1/2
● SP / (5x-14) = 0.5
● (2x+3)/(5x-14) = 0.5
● 2x+3 = 0.5(5x-14)
● 2x+3 = 2.5x -7
Add 7 to both sides
● 2x+3+7 = 2.5x-7+7
● 2x+10 = 2.5x
Sustract 2x brom both sides
● 2x+10-2x = 2.5x-2x
● 10 = 0.5x
Multiply both sides by 2
● 10×2 = 0.5x×2
● 20 = x
Replace x with 20 in Sp expression:
● SP = 2x+3
● SP = 2×20+3
● SP = 43
Point B is on line segment AC. Given BC=9 and AB=11, determine the length AC.
Answer:
20
Step-by-step explanation:
If point B is on line segment AC, then we know for sure AB + BC = AC.
To understand this better, draw a line segment, then put a point anywhere on the line segment. There are two line segment divided by that point. If you combine those two line segments then you have your original figure.
So 11 + 9 = 20.
please this urgent!!
Answer:
Step-by-step explanation:
1)First convert mixed fraction to improper fraction and them prime factorize
[tex]6\frac{1}{4} = \frac{25}{4}\\[/tex]
[tex]\sqrt{\frac{25}{4}}= \sqrt{\frac{5*5}{2*2}}= \frac{5}{2} = 2 \frac{1}{2} \\\\[/tex]
2)
[tex](2 \frac{1}{2}- 1 \frac{1}{2})*1 \frac{1}{7}=( \frac{5}{2}- \frac{3}{2})* \frac{8}{7}\\\\\\= \frac{2}{2}* \frac{8}{7}\\\\=1* \frac{8}{7}= \frac{8}{7}\\\\\\=1 \frac{1}{7}[/tex]
3) 0.00706 = 7.06 * [tex]10^{-3}[/tex]
4) 144 = 12 * 12
12 = 6*2
6 = 2*3
Prime factorization of 144 = 2 * 3 * 2 * 2 * 3 *2
= 2⁴ * 3²
5) To find LCM, prime factorize 96 & 144
96 = 2 * 2 * 2 * 2 * 2 * 3 = 2⁵ * 3
144 = 2⁴ * 3²
LCM = 2⁵ * 3² = 32 * 9 = 288
6) HCF
105 = 7 * 5 * 3
135 = 5 * 3* 3 * 3
180 = 5 * 3 * 3 * 2 * 2
HCF = 5 * 3 = 15
7) 24 = 3 * 2 * 2 * 2 = 3 * 2³
36 = 3 * 3 * 2 * 2 = 3² * 2²
40 = 5 * 2 * 2 * 2 = 5 * 2³
LCM = 5 * 2³ * 3² = 5 * 8 * 9 = 360
HCF = 2² = 4
Difference = 360 - 4 = 356
8) Multiply each digit of the binary number by the corresponding power of 2, solve the powers and add them all
1111 = 1 *2³ + 1*2² + 1*2¹ + 1*2° = 8 + 4 + 2 + 1 = 15
Ans: 15
9) 36₇ = 102₅
10) 6.9163 = 6.916
I knew only this much
hope it's helpful
:)
What are the lower quartile, upper quartile, and median for this box and
whisker plot?
A) LQ = 22 UQ = 10 Median = 18.5
B) LQ = 10 UQ = 22 Median = 18
C) LQ = 10 UQ = 22 Median = 18.5
D) LQ = 10 UQ = 22 Median = 19
Answer:
C
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
The lower quartile range is shown by the bottom of the box which is at 10.
The median is shown in the middle line, which is closer to 18 than 18.5.
The upper quartile range in the end of the box, which is at 22!
(You can also look at the picture attached if that helps.)
In a family with children, the probability that all the children are girls is appoximately . In a random sample of 1000 families with children, what is the approximate probability that or fewer will have girls? Approximate a binomial distribution with a normal distribution.
Answer:
The probability that 100 or fewer will have 3 girls is 0.00734.
Step-by-step explanation:
The complete question is:
In a family with 3 children, the probability that all the children are girls is approximately 0.125. In a random sample of 1000 families with 3 children, what is the approximate probability that 100 or fewer will have 3 girls? Approximate a binomial distribution with a normal distribution.
Solution:
Let X represent the number of families who has 3 girls.
The random variable X follows a Binomial distribution with parameters n = 1000 and p = 0.125.
But the sample selected is too large.
So a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:
1. np ≥ 10
2. n(1 - p) ≥ 10
Check the conditions as follows:
[tex]np=1000\times 0.125=125>10\\\\n(1-p)=1000\times (1-0.125)=875>10[/tex]
Thus, a Normal approximation to binomial can be applied.
So, [tex]X\sim N(\mu=np,\sigma^{2}=np(1-p))[/tex]
The mean and standard deviation are:
[tex]\mu=np=1000\times 0.125=125\\\\\sigma=\sqrt{np(1-p)}=\sqrt{1000\times 0.125\times (1-0.125)}=10.46[/tex]
Compute the probability that 100 or fewer will have 3 girls as follows:
Apply Continuity correction:
[tex]P(X\leq 100)=P(X<100-0.50)[/tex]
[tex]=P(X<99.50)\\\\=P(\frac{X-\mu}{\sigma}<\frac{99.5-125}{10.46})\\\\=P(Z<-2.44)\\\\=0.00734[/tex]
*Use a z-table.
Thus, the probability that 100 or fewer will have 3 girls is 0.00734.
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.
7 = 3x − 1
x − 1 = 3(7)
x over seven = 3(1)
7 + 3x = 1
Answer
Equation : x + 1 + 3x = 7
Miles Lissette biked : 3/2 miles
Step-by-step explanation:
Step 1: Determine the total number of miles biked.
From my understanding. 7 miles is the total number of miles biked by both.
Step 2: Assume the values
Miles Lissette biked = x
Miles Shane biked = 1 + 3x
Step 3: Add miles biked by Lissette and Shane which will be equal to total miles.
Equation for miles Lissette biked: x + 1 + 3x = 7
4x + 1 = 7
x = 6/4
Step 4: Simplify
x = 6/4
x = 3/2
Therefore, the equation for miles Lissette biked is x + 1 + 3x = 7 and Lissete biked for 3/2 miles.
Hope it helped if yes mark me BRAINLIEST
Tysmm
Answer:
7 = 3x - 1
Step-by-step explanation:
Miles Shane biked = y
Miles Lissette biked = x
The equation is
(x ⋅ 3) - 1 = y
And we know y = 7, so
(x ⋅ 3) - 1 = 7
3x - 1 = 7
30 PTS!! Can someone PLEASE rephrase this? The compass and straightedge is more important in constructing geometric structures than other drawing tools such as rulers and protractors. Because steps taken with a compass and straightedge cannot be seen at first glance and this situation become a problem for students.
Answer:
Step-by-step explanation:
This study investigated three mathematics teachers' construction process of geometric structures using compass and straightedge. The teacher-student-tool interaction was analysed. The study consists of the use of a compass and straightedge by the teachers, the ideas of the teachers about their use, and the observations regarding the learning process during the construction of the geometric structures. A semi-structured interview was conducted with the teachers about the importance of the use of a compass and straightedge to construct geometric structures. It was found that teachers taught compass and straightedge constructions in a rote manner where learning is little more than steps in a process. The study concludes with some suggestions for the use of a compass and straightedge in mathematics classes based on the research results. SUMMARY Purpose and significance: For more than 2,000 years, the way in which geometric structures could be constructed with the help of compasses and straightedges has caught the attention of mathematicians. Nowadays, mathematics curriculums place an emphasis on the use of the compass and straightedge. The compass and straightedge is more important in constructing geometric structures than other drawing tools such as rulers and protractors. Because steps taken with a compass and straightedge cannot be seen at first glance and this situation become a problem for students. However, 'doing compass and straightedge construction early in the course helps students to understand properties of figures'
Which of the following is an example of the difference of two squares?
A x2−9
B x3−9
C (x+9)2
D (x−9)2
I know the answer is either A or B i might be wrong tho pls help im not sure.
Answer:
1) What does it mean when a polynomial equation is in standard form?
All terms are on one side of the equation, and zero is on the other side.
2) When factoring 6x2−7x−20 by grouping, how should the middle term be rewritten?
It should be written as 8x−15x.
3) Is the given equation a quadratic equation? Explain.
x(x−6)=−5
The equation is a quadratic equation because there is an x2-term.
4) Which of the following factored forms given below represent the correct factorization of the trinomial x2+10x+16?
(2+x)(8+x)
5) Which of the following is an example of the difference of two squares?
x2−9
Step-by-step explanation:
I hope this helps you out ☺
A binomial whose first term and second term can be squared, and has a subtraction sign between both squared terms represents the difference of two squares, an example of the difference of two squares is:
A. [tex]x^2 - 9[/tex]
Recall:
Difference of two squares is when you have a binomial that is expressed as [tex]x^2 - y^2[/tex].The first and second term of the binomial will have an exponential of 2 wile the subtraction sign will be in the middle.Thus, from the options given, option A: [tex]x^2 - 9[/tex] is an example of a binomial that is the difference of two squares.
This is why:9 can be expressed as [tex]3^2[/tex].
In summary, a binomial whose first term and second term can be squared, and has a subtraction sign between both squared terms represents the difference of two squares, an example of the difference of two squares is:
A. [tex]x^2 - 9[/tex]
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Chantal is driving on a highway at a steady speed. She drives 55 miles every hour. Let d be the total distance in miles and let h be the number of hours.
Write an equation that represents the situation. I'll give out the brainliest if you get it right.
Answer:
[tex] d = 55h [/tex]
Step-by-step explanation:
We are given that Chantal drives at a constant speed of 55 miles per hour.
If, d represents the total distance in miles, and
h represents number of hours, the following equation can be used to express the given situation:
[tex] d = 55h [/tex]
For every hour, a distance of 55 miles is covered.
Thus, if h = 1, [tex] d = 55(1) = 55 miles [/tex]
If h = 2, [tex] d = 55(2) = 110 miles [/tex].
Therefore, [tex] d = 55h [/tex] , is an ideal equation that represents the situation given in the question above.
For a quadratic function y = ax² + bx + c, suppose the constants a, b, and c are consecutive terms of a geometric sequence. Show that the function does not cut the x axis.
Hello, because of the geometric sequence we can say that:
[tex]\alpha = \dfrac{b}{a}=\dfrac{c}{b}\\\\\dfrac{c}{a}=\dfrac{c*b}{a*b}=\dfrac{c}{b}\dfrac{b}{a}=\alpha^2\\\\\text{So the equation becomes.}\\\\ax^2+bx+c=0<=>x^2+\dfrac{b}{a}x+\dfrac{c}{a}=0\\\\<=>x^2+\alpha x+ \alpha^2=0\\\\\Delta=b^2-4ac = \alpha^2-4\alpha^2=-3\alpha^2 < 0[/tex]
So there is no real root, so the function does not cut the x axis.
Thank you
For the given quadratic function, the x-axis is not cut by the function because there is no true root.
What is a quadratic function?To determine values for various parameters, quadratic functions are employed in a variety of scientific and engineering disciplines. A parabola is used to graphically illustrate them. The orientation of the curve is defined by the highest degree factor.
As per provided data in question,
α = b/a = c/b
c/a = (c × b)/(a × b) = (c/b) (b/a) = α²
For the equation,
ax² + bx + c = 0
x² + b/a(x) + c/a = 0
⇒ x² + ax + α² =0
Δ = b² - 4 ac = α² - 4α²
Δ = -3α² < 0, which means that no real root is there.
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in exponential growth functions, the base of the exponent must be greater than 1. How would the function change if the base exponent were 1? How would the function change if the base of the exponent were between 0 and 1?
Answer:
GREAT QUESTION!!
Step-by-step explanation:
Bases of exponential functions CANNOT be 1.
It the base was between 0 and 1, .25 for example, then it would be exponential decay, because as x would increase y would decrease.
Just search up exponential decay to see what it looks like, or type in y=.25^x in google search bar.
if this helped, Please give brainly, I need it! Thank you!
Answer:
If the base of the exponent were 1, the function would remain constant. The graph would be a horizontal line. If the base of the exponent were less than 1, but greater than 0, the function would be decreasing.
Step-by-step explanation:
If the base were 1, the function would be constant.
If the base were 1, the graph would be a horizontal line.
If the base were between 0 and 1, the function would be decreasing.
Dena uses 7.4 pints of white paint and blue paint to paint her bedroom walls. 2/5 of this amount is white paint, and the rest is blue paint. How many pints of blue paint did she use yo paint her bedroom walls
Answer:
4.44 pints
Step-by-step explanation:
7.4 times 3/5
Factorise: 5 x cube + 10 x square + 15 x
Answer:
5x( x^2 + 2x +3)
Step-by-step explanation:
5x^3 + 10x^2 + 15x
What is common to all three terms
5 xxx + 5*2*xx + 5*3*x
We can factor out 5x
5x( x^2 + 2x +3)
Inside the parentheses cannot be factored so we are done
Answer:
5x ( x^2 + 2x +3 )
Step-by-step explanation:
First we hv to take the common terms out from all the three terms...
So......
If we take 5x from 5x^3 it will bcm x^2
If we take 5x from 10^2 it will bcm 2x
if we take 5x from 15x^2 it will bcm 3
Therefore the final expression will bcm
5x ( x^2 + 2x +3 )
Hope this helps.....
Am I doing this right if not please help me
Answer:
Step-by-step explanation:
For the m it would just be -3 because the equation for slope intercept form is y=mx+b
I don’t really understand this
Answer
pretty sure its a or c, sorry I cant be more specific
Step-by-step explanation:
What is the reflection image of
(5,−3)across the line
y=x
Answer: The Answer is (-5,-3)
hope so my answer is correct
Step-by-step explanation:
Finding which number supports the idea that the rational numbers are dense in the real numbers.
Answer:A terminating decimal between -3.14 and -3.15.
Step-by-step explanation:
A natural number includes non-negative numbers like 5, 203, and 18476.
It is encapsulated by integers, which include negative numbers like -29, -4, and -198.
Integers are further encapsulated by rational numbers, which includes terminating decimals like 3.14, 1.495, and 9.47283.
By showing a terminating decimal between -3.14 and -3.15, you are showing that rational numbers include integers (because integers include negative numbers.
how do you find the surface area of this triangular prism?
To find the area of a triangular prism you have to do A 1/2 bh or A bh/2 which means you have to multiply those two fractions and reduce them
Answer:
Find the area of the 2 triangle faces first and then find the area of the 3 rectangle faces and add them together to get [tex]159cm^{2}\\[/tex]
Step-by-step explanation:Step 1: Find the surface area of the 2 triangles
[tex]\frac{(6)(5.5)}{2}[/tex] x2 = [tex]33cm^2\\[/tex]
Step 2: Find the surface area of the 3 rectangles
(6x7) x 3 = [tex]126cm^2[/tex]
Step 3: Add the 2 surface areas together
[tex]33cm^2\\[/tex] + [tex]126cm^2[/tex] = [tex]159cm^2[/tex]
Therefore the surface area of the prism is [tex]159cm^{2}[/tex]
Is a 118 supplementary or complementary?pls ASAP!!
Answer:
[tex]\huge\boxed{Supplementary \ Angle}[/tex]
Step-by-step explanation:
118 is a supplementary angle. It is not a complementary angle because complementary angles add up to 90 and 118 is greater than 90 degrees. So, 118 is a supplementary angle and it is an angle adding up to 180 degrees with any other angle measuring 62 degrees.
Answer:Supplementary
Step-by-step explanation:You should remember that complementary refers to any number from 0-90 and supplementary refers to any number from 90 onwards..
Hereby giving the answer as ''Supplementary''
I need help answering these two questions
Answer:
Step-by-step explanation:
1. Area=3b*b=300 inches^2
3b^2=300
:3 :3
b^2=100
b=V100inches ^2
b=10 inches
2. Area=4b*3b
so 12b^2=4800
:12 :12
b^2=400
b=V400
b=20 inches
The subject is operations on rational expressions.
The instructions are add or subtract the following expressions. Remember to find a common denominator when necessary. Reduce all answers to lowest terms.
Answer:
[tex]\frac{2(x-1)(2x+9)}{(x-3)(x-2)}[/tex]
Step-by-step explanation:
[tex]\frac{4x}{(x-3)}+\frac{6}{(x+2)}[/tex]
= [tex]\frac{4x(x+2)}{(x-3)(x+2)}+\frac{6(x-3)}{(x+2)(x-3)}[/tex]
Now we have done the denominators of each term of the expression equal.
Further we add the terms,
[tex]\frac{4x(x+2)}{(x-3)(x+2)}+\frac{6(x-3)}{(x+2)(x-3)}[/tex]
= [tex]\frac{4x(x+2)+6(x-3)}{(x-3)(x+2)}[/tex]
= [tex]\frac{4x^{2}+8x+6x-18}{(x-3)(x+2)}[/tex]
= [tex]\frac{4x^{2}+14x-18}{(x-3)(x-2)}[/tex]
Now factorize the numerator of the fraction.
4x² + 14x - 18 = 2(2x² + 7x - 9)
= 2(2x² + 9x - 2x - 9)
= 2[x(2x + 9) - 1(2x + 9)]
= 2(x - 1)(2x + 9)
Therefore, [tex]\frac{2(x-1)(2x+9)}{(x-3)(x-2)}[/tex] will be the answer.
How to work out the medium in maths
Answer:
To find the median you cross off the first few numbers and the last few until you get to the middle then when you get the middle number that will be your median
Step-by-step explanation:
Answer:
Below.
Step-by-step explanation:
It's the middle value of a list of numbers arranged in order.
For example the median of the list 1 2 3 4 5 is 3.
If there are an even number of values, the median is the mean of the middle two. For example:
1 3 4 5 7 9:
The middle 2 numbers are 4 and 5 so
the median is (4 + 5) / 2 = 4.5
Please answer this question now
Answer:
Approximately 439.6 square millimeters.
Step-by-step explanation:
The formula for the surface area of a cone is the following:
[tex]A=\pi r^2+\pi r l[/tex]
Where, r is the radius and l is the slant height.
The radius is 7 and the slant height is 13. We also use 3.14 for π Thus:
[tex]A=(3.14)(7)^2+(3.14)(7)(13)\\\text{Use a Calculator}\\A\approx 439.6[/tex]
Answer:
292.77
Step-by-step explanation:
πr(r+[tex]\sqrt{h2+r2}[/tex])
13 x 2 = 26
7 x 2 = 14
26 + 14 = 40
[tex]\sqrt{40}[/tex] = 6.32
7 + 6.32 = 13.32
3.14 x 7 = 21.98
21.98 x 13.32 =
292.77
The sum of two consecutive odd integers is at least 36, find the integers
Answer:
The two integers are greater than or equal to 17 and 19
Step-by-step explanation:
Consecutive odd integers means 1, 3, 5, 7, 9 and so on
That means there is a always a gap of 2 in between each of them. Knowing this, we can set up an equation. Let x represent the first of the consecutive integers.
x+(x+2)=36
x+2 represents the second consecutive interger
x+x=34
2x=34
x=17
The two integers are 17 and 19
kinda confused buttttt anyone know this?
Answer:
Hey there!
The overlapping part is the product.
Thus, the product is 1/8.
Hope this helps :)
PLS ANSWER BRAINLIST AND A THANK YOU WILL BE GIVEN!!!!
Answer:
[tex]\huge\boxed{Option \ D}[/tex]
Step-by-step explanation:
4x + 5x = 180 [They are angles on a "straight" line so they will add up to 180 degrees)
Answer:
D
Step-by-step explanation:
The sum of angles that are formed on a straight line is 180.
4x + 5x = 180
A 250.0 kg rock falls off a 40.0 m cliff. What is the kinetic energy of the rock just before it hits the ground (hint: conservation of energy)?
Answer:
kinetic energy body when it hits the ground is 98000 joule
1000joule = 1 kilojoule
, kinetic energy body when it hits the ground is 98 kilo-joule
Step-by-step explanation:
conservation of energy states that total energy of a system remains constant.
Potential energy of body = mgh
m = mass
g = gravitational pull = 9/8 m/s^2
h = height
kinetic energy = 1/2 mv^2
where v is the velocity of body
________________________________________
Total energy for this at any point is sum of potential energy and kinetic energy
total energy at height h
v= 0
PE = 250*9.8*40= 98,000
KE = 1/2 m0^2 = 0
total energy at when ball hits the ground
h=0
PE = 250*9.8*0 =
KE = 1/2 mv^2
_______________________________________\
Applying conservation of energy
Total energy at height h = total energy at ground
98000 = KE
Thus, kinetic energy body when it hits the ground is 98000 joule
1000joule = 1 kilojoule
, kinetic energy body when it hits the ground is 98 kilo-joule
Given that ∆MTW ≅ ∆CAD, which angles are corresponding parts of the congruent triangles? ∠W ≅ ∠C ∠W ≅ ∠D ∠W ≅ ∠A
Answer:
The Answer would be ∠W ≅ ∠C
Step-by-step explanation:
Only one that is congruent
The measure of the angle ∠TWM is congruent to the measure of the angle ∠ADC. Therefore, the correct option is B.
What are congruent triangles?Two triangles are said to be congruent if their corresponding sides and angles are equal.
A triangle is a three-sided polygon with three edges and three vertices in geometry.
Given that the triangle ∆MTW is congruent to the triangle ∆CAD.
So, we have
∠MTW ≅ ∠CAD
∠WMT ≅ ∠DCA
∠TWM ≅ ∠ADC
If two triangles are equivalent, the ratio of matching sides will stay constant.
The proportion of the point ∠TWM is harmonious with the proportion of the point ∠ADC.
Therefore, at that point, the right choice is B.
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A ship travels due north for 100 miles from point C to point A. From point A the ship travels to point B at 60° east of north. From point B, the ship returns to point C heading 45° west of south. What approximate distance did the ship travel from point A to point B? How far does it travel in total?
Answer:
AandB=80miles
Total=240miles
Step-by-step explanation:
Draw the figure first indicating the figures then find the distance each degrees then find the total
The distance ship travels from A to B is 273.2 miles and total distance covered by ship is 707.82 miles.
What is laws of sines?The law of sines specifies how many sides there are in a triangle and how their individual sine angles are equal. The sine law, sine rule, and sine formula are additional names for the sine law.
The side or unknown angle of an oblique triangle is found using the law of sine. Any triangle that is not a right triangle is referred to as an oblique triangle. At least two angles and their corresponding side measurements should be used at once for the sine law to function.
Given distance from C to A = 100 miles north
From B to A ship travels 60° east of north,
and From B to C 45° west of south,
the figure for problem is attached,
from figure we can calculate the angles of A, B and C
so ∠A makes supplementary with 60°
∠A + 60° = 180°
∠A = 120°
for ∠B we need to draw an imaginary perpendicular on the line extending from A, we get
∠B + 45° + 30° = 90° (30° is angle of imaginary right triangle)
∠B = 90 - 75 = 15°
and ∠C can be found by,
∠A + ∠B + ∠C = 180°
∠C = 180 - 15 - 120
∠C = 45°
now use sine formula for triangles,
sinA/a = sinB/b = sinC/c
where A, B and C are angles of triangle and a, b and c are length of opposite side of angle A, B and C respectively.
a = BC, b = AC, and c = AB
so
sinA/BC = sinB/AC = sinC/AB
we have AC = 100 miles
substitute the values
sinC/AB = sinB/AC
sin(45)/AB = sin(15)/100
AB = 100/(√2sin(15))
AB = 100/0.3659
AB = 273.298 miles
and sinA/BC = sinB/AC
BC = AC sinA/sinB
BC = 100(sin 120/sin15)
BC = 100(0.866/0.2588)
BC = 100 x 3.3462
BC = 334.62 miles
total distance = AB + BC + AC
total distance = 334.62 + 273.2 + 100
total distance = 707.82 miles
Hence the distance from A to B is 273.2 miles and total distance is 707.82 miles.
Learn more about laws of sines;
https://brainly.com/question/17289163
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