To build the fleet of ships, Astrid must consider each of the given rates (i.e. the daily tons of wood, the sailors per ship, etc.). The available deliveries are enough to build ships that can accommodate at least 2100 sailors.
Given that:
Required quantities
[tex]Wood = 40\ tons[/tex]
[tex]Sailors = 300[/tex] per ship
Available quantities
[tex]Wood = 4\ tons[/tex] daily
[tex]Days = 100[/tex] at most
First, we calculate the total tons of woods Astrid can receive.
[tex]Total = Days \times Wood\ Available[/tex]
[tex]Total = 100 \times 4[/tex]
[tex]Total = 400\ tons[/tex] ---- in 100 days
Next, we calculate the number of ships that can be made from the 400 tons.
[tex]Ships = \frac{Total\ tons}{Wood\ Required}[/tex]
So, we have:
[tex]Ships = \frac{400}{40}[/tex]
[tex]Ships = 10[/tex]
This means that Astrid can build up to 10 ships
The number of sailors the ship can accommodate is:
[tex]Sailors = Ships \times Sailors\ per\ ship[/tex]
So, we have:
[tex]Sailors = 10 \times 300[/tex]
[tex]Sailors = 3000[/tex]
It means the 10 ships can accommodate 3000 sailors.
3000 sailors is greater than 2100 sailors.
So, we can conclude that she can build enough ship for the 2100 sailors.
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Answer:
280 tons
Step-by-step explanation:
:)
Company a samples 16 workers, and their average time with the company is 5.2 years with a standard deviation of 1.1. Company b samples 21 workers and their average time with the company is 4.6 years with a standard deviation 4.6 years
Company a samples 16 workers, and their average time with the company is 5.2 years with a standard deviation of 1.1. Company b samples 21 workers and their average time with the company is 4.6 years with a standard deviation 4.6 years
The populations are normally distributed. Determine the:
Hypothesis in symbolic form?
Determine the value of the test statistic?
Find the critical value or value?
determine if you should reject null hypothesis or fail to reject?
write a conclusion addressing the original claim?
Answer:
Step-by-step explanation:
GIven that :
Company A
Sample size n₁ = 16 workers
Mean [tex]\mu[/tex]₁ = 5.2
Standard deviation [tex]\sigma[/tex]₁ = 1.1
Company B
Sample size n₂ = 21 workers
Mean [tex]\mu[/tex]₂ = 4.6
Standard deviation [tex]\mu[/tex]₂ = 4.6
The null hypothesis and the alternative hypothesis can be computed as follows:
[tex]H_o : \mu _1 = \mu_2[/tex]
[tex]H_1 : \mu _1 > \mu_2[/tex]
The value of the test statistics can be determined by using the formula:
[tex]t = \dfrac{\overline {x_1}- \overline {x_2}}{\sqrt{\sigma p^2( \dfrac{1}{n_1}+\dfrac{1}{n_2})}}[/tex]
where;
[tex]\sigma p^2= \dfrac{(n_1 -1) \sigma_1^2+ (n_2-1)\sigma_2^2}{n_1+n_2-2}[/tex]
[tex]\sigma p^2= \dfrac{(16 -1) (1.1)^2+ (21-1)4.6^2}{16+21-2}[/tex]
[tex]\sigma p^2= \dfrac{(15) (1.21)+ (20)21.16}{35}[/tex]
[tex]\sigma p^2= \dfrac{18.15+ 423.2}{35}[/tex]
[tex]\sigma p^2= \dfrac{441.35}{35}[/tex]
[tex]\sigma p^2= 12.61[/tex]
Recall:
[tex]t = \dfrac{\overline {x_1}- \overline {x_2}}{\sqrt{\sigma p^2( \dfrac{1}{n_1}+\dfrac{1}{n_2})}}[/tex]
[tex]t = \dfrac{5.2- 4.6}{\sqrt{12.61( \dfrac{1}{16}+\dfrac{1}{21})}}[/tex]
[tex]t = \dfrac{0.6}{\sqrt{12.61( \dfrac{37}{336})}}[/tex]
[tex]t = \dfrac{0.6}{\sqrt{12.61(0.110119)}}[/tex]
[tex]t = \dfrac{0.6}{\sqrt{1.38860059}}[/tex]
[tex]t = \dfrac{0.6}{1.178388981}[/tex]
t = 0.50917
degree of freedom df = ( n₁ + n₂ - 2 )
degree of freedom df = (16 + 21 - 2)
degree of freedom df = 35
Using Level of significance ∝ = 0.05, From t-calculator , given that t = 0.50917 and degree of freedom df = 35
p - value = 0.3069
The critical value [tex]t_{\alpha ,d.f}[/tex] = [tex]t_{0.05 , 35}[/tex] = 1.6895
Decision Rule: Reject the null hypothesis if the test statistics is greater than the critical value.
Conclusion: We do not reject the null hypothesis because, the test statistics is lesser than the critical value, therefore we conclude that there is no sufficient information that the claim that company a retains it workers longer than more than company b.
Show that the equations x^2-7x+6=0 and y^2-14y+40=0 form a rectangle.Also find the joint equations of diagonals.
Answer:
1) The region between the four lines x = 6, x = 1, y = 4 and y = 10 describing both equations is a rectangle
2) The joint equations of diagonals are;
5·y = 56 - 6·x and 5·y = 6·x + 14.
Step-by-step explanation:
The equations are;
x² - 7·x + 6 = 0......................(1)
y² - 14·y + 40 = 0.................(2)
Factorizing equation (1) and equation (2) , we get
x² - 7·x + 6 = (x - 6)·(x - 1) = 0
Which are vertical lines at points x = 6 and x = 1
For equation (2) , we get
y² - 14·y + 40 = (y - 10)·(y - 4) = 0
Which are horizontal lines at point y = 4 and y = 10
The region between the four lines x = 6, x = 1, y = 4 and y = 10 describing both equations is a rectangle
2) The points of intersection of the equations are;
(1, 4), (1, 10), (6, 4), and (6, 10)
The end point of the diagonals are;
(1, 10), (6, 4) and (1, 4), (6, 10)
The slope of the diagonals are;
(10 - 4)/(1 - 6) = -6/5 and (4 - 10)/(1 - 6) = 6/5
The equation of one of the diagonals are then, y - 10 = -6/5×(x - 1)
y = -6/5·x + 6/5 + 10 = -6/5·x + 56/5
5·y = 56 - 6·x
The other diagonal is therefore;
y - 4 = 6/5×(x - 1)
y = 6/5·x - 6/5 + 4 = 6/5·x + 14/5
5·y = 6·x + 14.
The joint equations of diagonals are therefore;
5·y = 56 - 6·x and 5·y = 6·x + 14.
What is the factored form of 125x6 – 8?
Answer:
Step-by-step explanation:
125 = 5 *5 * 5 = 5³
8 = 2 * 2 *2 = 2³
125x⁶ - 8 = 5³(x²)³ - 2³
= (5x²)³ - 2³ { a³ - b³ = (a -b)(a² + ab + b²)
= (5x² - 2) ([5x²]² + 5x²*2 + 2²)
= (5x² - 2)(25x⁴ + 10x² + 4)
Hint: (5x²)² = 5² * (x²)² = 25* x²ˣ² = 25x⁴
Write and solve an equation to answer the question. How many people must attend the third show so that the average attendance per show is 3000?
Answer:
3250
Step-by-step explanation:
so for the first and 2nd show, the attendance is 2580 and 2920.
The average of both these numbers is 2750
the if the third show had 3000 people, the average attendance would only be 2875.
We need the average number to be 3000.
2750 is 250 less than 3000, so the other number must be 250 more.
3250 is how many people should go to the last show.
=====================================
Explanation:
We have 2580 people attend the first show and 2920 attend the second. So far, that's 2580+2920 = 5500 people. Add on another x people to get 5500+x, which represents the sum of all three days attendance figures. Divide this sum by 3 to get the average attendance
average attendance = (sum of individual attendance values)/(number of days)
average attendance = (5500+x)/3
So that's why (5500+x)/3 goes in the first box. The parenthesis are important to ensure that you divide all of "5500+x" over 3. If you just wrote 5500+x/3, then the computer would think you just want to divide x only over 3.
----------------
We set (5500+x)/3 equal to 3000 as we want the average of the three days to be 3000
(5500+x)/3 = 3000
5500+x = 3*3000
5500+x = 9000
x = 9000-5500
x = 3500
We need 3500 people to show up on day 3 so that the average of all three days is 3000.
3500 goes in the second box.
----------------
Check:
The figures for the three days are 2580, 2920, and 3500
They add to 2580+2920+3500 = 9000
Which divides to 9000/3 = 3000, which is the average we're after. So the answer is confirmed.
Question 1 (
Multiple Choice Worth 3 points)
(07.04)
The cost of 3 slices of pizza is $4.89. What is the cost of each slice of pizza?
O $1.63
$1.89
O $2.45
O $2.88
Answer:
Each slice of pizza cost:
$1.63
Step-by-step explanation:
4.89/3 = 1.63
Answer:
$1.63
Step-by-step explanation:
We want to find the cost per slice of pizza. Therefore, we must divide the total cost by the number of slices of pizza.
cost / slices
It costs $4.89 for 3 slices.
$4.89 / 3 slices
Divide 4.89 by 3 (4.89/3=1.63)
$1.63 / slice
The cost of each slice of pizza is $1.63
Mrs. Yadav purchase 25 kg of vegetable at Rs 20 per kg and sold at a loss of Rs 50 find her
Selling rate and loss percent
Answer:
[tex] \boxed{loss\% \: = 10\%}[/tex][tex] \boxed{selling \: price = Rs 450}[/tex]Step-by-step explanation:
Given,
Cost price of 25 kg of vegetables ( CP ) = 25 × 20
= Rs 500
Loss amount = Rs 50
Selling price ( SP ) = ?
Loss percent = ?
Now, let's find the loss percent :
[tex] \mathsf{ \frac{loss}{cost \: price} \times 100\%}[/tex]
[tex] \mathsf{ = \frac{50}{500} \times 100\%}[/tex]
[tex] \mathsf{ = 10\%}[/tex]
Loss % = 10 %
Now, let's find the selling price:
[tex] \mathsf{ \frac{CP(100 - l\%)}{100} }[/tex]
[tex] \mathsf{ = \frac{500(100 - 10)}{100}} [/tex]
[tex] \mathsf{ = \frac{500 \times 90}{100} }[/tex]
[tex] \mathsf{ = \frac{45000}{100} }[/tex]
[tex] \mathsf{= 450}[/tex]
Hope I helped!
Best regards!
The distance of planet Mercury from the Sun is approximately 5.8. 107 kilometers, and the distance of planet Venus from the Sun is 1.1. 10 kilometers. About how many more kilometers is the
distance of Venus from the Sun than the distance of Mercury from the Sun?
Answer:
I would say about 5 times but I am not sure so if it is wrong am sorry.
Please answer this question now
Answer:
11 yd
Step-by-step explanation:
To find the volume of a rectangular prism, we multiply the width, length and height.
We already know the length, 18, and the height, 11, and the volume, 2178, so we can easily solve for y.
[tex]18\cdot y\cdot11=2178\\192y=2178\\y = 11[/tex]
Hope this helped!
Solve the equation
(If possible please show work)
Using properties of sets show that : a) A ∩ (A’ U B) = A ∩ B b) A ∩ (A U B )’ = Ф
Answer:
a) From A ∩ A' = ∅, we have;
A ∩ (A' ∪ B) = A ∩ B
b) From A ∩ (A' ∩ B') = (A ∩ A') ∩ B' and A ∩ A' = ∅, we have;
A ∩ (A ∪ B)' = ∅
Step-by-step explanation:
a) By distributive law of sets, we have;
A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
From the complementary law of sets, we have;
A ∩ A' = ∅
Therefore, for A ∩ (A' ∪ B) = A ∩ B, we have
A ∩ (A' ∪ B) = (A ∩ A') ∪ (A ∩ B) (distributive law of sets)
A ∩ A' = ∅ (complementary law of sets)
Therefore;
(A ∩ A') ∪ (A ∩ B) = ∅ ∪ (A ∩ B) = (A ∩ B) (Addition to zero identity property)
∴ A ∩ (A' ∪ B) = A ∩ B
b) By De Morgan's law
(A ∪ B)' = A' ∩ B'
Therefore, A ∩ (A ∪ B)' = A ∩ (A' ∩ B')
By associative law of sets, we have;
A ∩ (A' ∩ B') = (A ∩ A') ∩ B'
A ∩ A' = ∅ (complementary law of sets)
Therefore, (A ∩ A') ∩ B' = ∅ ∩ B' = ∅
Which gives;
A ∩ (A ∪ B)' = ∅.
Roselyn is driving to visit her family, which live 150 150150 kilometers away. Her average speed is 60 6060 kilometers per hour. The car's tank has 20 2020 liters of fuel at the beginning of the drive, and its fuel efficiency is 6 66 kilometers per liter. Fuel costs 0.60 0.600, point, 60 dollars per liter. How long can Roselyn drive before she runs out of fuel?
Answer:
She can go 120 km before she runs out of fuel
It will take 2 hours.
Step-by-step explanation:
150 km is the distance
60 km/ h is the speed
The gas tank is 20 liters
We can go 6 km per liter
Fuel costs .60 dollars per liter
We need to determine how far she can go on a tank of gas
20 liters * 6 km / liter = 120 km
She can go 120 km before she runs out of fuel
120 km = 60 km/ h * x hours
Divide each side by 60
120/60 = x
2 hours
Answer:
Hopes this helps!
Step-by-step explanation:
what is the value of this expression when g= -3.5?
8-|2g-5|
a. 20
b. 10
c. 6
d. -4
Answer:
d. -4
Step-by-step explanation:
Let's plug in g
8 - |2(-3.5) - 5|
8 - |-7-5|
8 - |-12|
The absolute value is always positive of any number,
8 - 12
= -4
Answer:
D. -4
Step-by-step explanation:
We are given this expression:
[tex]8-|2g-5|[/tex]
and asked to evaluate when g= -3.5 Therefore, we must substitute -3.5 in for g.
[tex]8-|2(-3.5)-5|[/tex]
First, multiply 2 and -3.5
2 * -3.5 = -7
[tex]8-|-7-5|[/tex]
Next, subtract 5 from -7.
-7-5= -12
[tex]8-|-12|[/tex]
Next, evaluate the absolute value of -12. The absolute value is how far away a number is from 0, and it is always positive. The absolute value of -12 is 12.
[tex]8-12[/tex]
Subtract 12 from 8.
[tex]-4[/tex]
The value of the expression is -4 and D is the correct answer.
Please answer. I need this to be done, Thanks. Will give brainliest
Answer:
The answer is s^26/pq59
Step-by-step explanation:
Answer:
p^ -1 q ^ -59 s ^26
or without negative exponents
s^ 26 /(p q^ 59)
Step-by-step explanation:
When multiplying , we can add the exponents when the bases are the same
p^0 q ^ -60 r^-1 s^25 * p^-1 qrs
When there is no exponent written, there is an implied 1
p^ (0+-1) q^(-60+1) r ^( -1 +1) s ^ ( 25+1)
p^ -1 q ^ -59 r ^0 s ^26
r^0 = 1
p^ -1 q ^ -59 s ^26
If you need the negative exponents written as positive
a^-b = 1/ a^b
s^ 26 /(p q^ 59)
41 =12d-7 d= Math is not my strong suit. I love to read and write but I can not do math without a little bit of help.
Answer:
[tex]\huge\boxed{d = 4 }[/tex]
Step-by-step explanation:
41 = 12d - 7
Adding 7 to both sides
41+7 = 12d
48 = 12 d
Dividing both sides by 12
4 = d
OR
d = 4
Answer:
[tex]\large \boxed{{d=4}}[/tex]
Step-by-step explanation:
[tex]41 =12d-7[/tex]
Add 7 on both sides.
[tex]41 +7=12d-7+7[/tex]
[tex]48=12d[/tex]
Divide both sides by 12.
[tex]\displaystyle \frac{48}{12} =\frac{12d}{12}[/tex]
[tex]4=d[/tex]
Can you write a summation notation of a series that is neither arithmetic nor geometric?
Answer:
Yes, we can.
Step-by-step explanation:
Hello, I found this one.
[tex]\displaystyle \sum_{n=0}^{\infty} \dfrac{1}{n!}[/tex]
We can prove that it exists and it is equal to e.
But this is nor arithmetic nor geometric.
Thank you
Could someone please explain/help me to do this using Pythagoras theorem?
Answer:
[tex]\boxed{478.02}[/tex]
Step-by-step explanation:
→ First understand what Pythagoras theorem is
Pythagoras is a theorem used to find the hypotenuse (the side opposite to the right-angle) of a triangle. We would need the base lengths as well the height in order to use Pythagoras.
→ State the formula and identify the letters
a² + b² = c² ⇒ where 'a' is 380cm, 'b' is 290cm and 'c' is what we are trying to work out
→ Substitute in the values into the formula
380² + 290² = c²
⇒ Simplify
144400 + 84100 = c²
⇒ Collect the numbers together
228500 = c²
⇒ Square root both sides to find 'c'
478.0167361 = c
→ The length of the diagonal is 478.02
Suppose the population of a country is 100 people: 40 work full-time, 20 work half-time but would prefer to work full-time, 10 are looking for a job, 10 would like to work but are so discouraged they have given up looking, 10 are not interested in working because they are full-time students, and 10 are retired. What is the number of unemployed
Answer:
10
Step-by-step explanation:
Those people who are actively seeking for a job are counted as unemployed. Underemployment is not considered as unemployment. Those who have given up looking for jobs are also not considered as unemployed as well. Hence there are 10 unemployed people.
Simplify 7^ -5/6 x 7^-7/6
Answer:
1/49
Step-by-step explanation:
If you add this is the calculator, I think it will come out.
━━━━━━━☆☆━━━━━━━
▹ Answer
1/49
▹ Step-by-Step Explanation
7^-5/6 * 7^-7/6
= 1/7²
= 1/49
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
This is the new one! Please help I’m so lost
Answer:
(a) (f o g)(x) = x^2 - 15x + 54
(b) (g o f)(x) = x^2 + 3x - 9
(c) (f o f)(x) = x^4 + 6x^3 + 12x^2 + 9x
(d) (g o g)(x) = x - 18
Step-by-step explanation:
f(x) = x^2 + 3x
g(x) = x - 9
(a)
(f o g)(x) = f(g(x)) = (g(x))^2 + 3(g(x)) = (x - 9)^2 + 3(x - 9)
(f o g)(x) = x^2 - 18x + 81 + 3x - 27
(f o g)(x) = x^2 - 15x + 54
(b)
(g o f)(x) = g(f(x)) = f(x) - 9 = x^2 + 3x - 9
(c)
(f o f)(x) = f(f(x)) = (x^2 + 3x)^2 + 3(x^2 + 3x)
(f o f)(x) = x^4 + 6x^3 + 9x^2 + 3x^2 + 9x
(f o f)(x) = x^4 + 6x^3 + 12x^2 + 9x
(d)
(g o g)(x) = g(g(x)) = x - 9 - 9 = x - 18
This table represents a quadratic function.
y
x
0
14
1
10.5
2
8
3
6.5
4
5
6.5
What is the value of a in the function's equation?
A.2
B.1/2
C.-1/2
D.1
Answer:
B. 1/2
Step-by-step explanation:
y = ax^2 + bx + c
14 = a(0)^2 + b(0) + c
c = 14
10.5 = a(1)^2 + b(1) + 14
10.5 = a + b + 14 ____(i)
8 = a(2)^2 + b(2) + 14
8 = 4a + 2b + 14
4 = 2a + b + 7 ___ (ii)
i - ii
10.5 - 4 = -a + 7
6.5 = -a + 7
a = 7- 6.5
a = 0.5
Value of a in the quadratic function is 0.5
What is Quadratic function?In algebra, a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic, is a polynomial function with one or more variables in which the highest-degree term is of the second degree
Given,
Quadratic function
y = [tex]ax^{2}+bx+c[/tex]
Consider values in the table x= 0 and y =14
[tex]14=a(0)^{2}+b(0)+c\\ c=14[/tex]
Consider x=1 and y = 10.5
[tex]10.5=a(1^{2})+b(1)+c\\ a+b=10.5-14\\a+b=-3.5[/tex]
Consider x=2 and y =8
[tex]8=a(2^{2})+b(2)+c\\ a\\8=4a+2b+14\\4a+2b=-6\\2a+b=-3[/tex]
Subtract a + b= -3.5 from 2a + b= -3
a=-3--3.5=0.5
Hence, the Value of a in the quadratic function is 0.5
Learn more about Quadratic function here
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You are hiking and are trying to determine how far away the nearest cabin is, which happens to be due north from your current position. Your friend walks 245 yards due west from your position and takes a bearing on the cabin of N 22.6°
e. How far are you from the cabin?
Answer:
589 yards
Step-by-step explanation:
This is a question that requires the use of trigonometric functions.
The trigonometric function to be used here is the tangent function.
tan θ = Opposite side/ Adjacent side
In the question, we are told
Your friend walks 245 yards due west from your position = Opposite side
Your friend's takes a bearing on the cabin of N 22.6° = θ
Your distance from the cabin = Adjacent side
Hence,
tan 22.6 ° = 245/ Adjacent side
Cross Multiply
Adjacent side = 245/ tan 22.6°
Adjacent side = 588.57469726 yards.
Therefore, your distance from the cabin approximately to the nearest yard(whole number) = 589 yards
the product of 5 and z
Answer:
5z
Step-by-step explanation:
As product = multiplication =>
5 x z --> 5(z)
[tex]\text{Find the product of 5 and z}\\\\\text{The key term in this questions is product, and in math it translates to}\\\text{the answer when multiplled}\\\\\text{In this case, you would multiply them together to get your "product"}\\\\\text{Solve:}\\\\5\cdot z\\\\\boxed{5z}[/tex]
Please answer this question now
Answer:
298.3 square centimeters
Step-by-step explanation:
We are given
Slant height (l)= 14cm
Radius (r)= 5cm
Since we are given the slant height ,
the formula for surface area of a cone =
πrl + πr²
πr(l + r)
π = 3.14
Hence,
3.14 × 5(14 + 5)
3.14 × 5(19)
= 298.3 square centimeters
the number of states that entered the union in 1889 was half the number of states "s" that entered in 1788. which expression shows the number of states that entered the union in 1889
Answer:
x = s/2
Step-by-step explanation:
● s states have joined the union in 1788
● half of s have joined in 1889
Let x be the number of states that have joined in 1889
● x = (1/2)× s
● x = s/2
Convert the following:
22 tons is equivalent to
kilograms
Answer:
19958.1
step-by-step explanation:
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
JUST A RANDOM GIRL WANTING TO HELP PEOPLE!
PEACE!
Consider the function represented by 9x + 3y = 12 with x as the independent variable. How can this function be
written using function notation?
O FID = - Šv
O f(x) = - 3x + 4
Of(x) = -x +
O fly) = -34+4
Answer:
f(x) = - 3x + 4
Step-by-step explanation:
Note that y = f(x)
Rearrange making y the subject
9x + 3y = 12 ( subtract 9x from both sides )
3y = - 9x + 12 ( divide all terms by 3 )
y = - 3x + 4 , that is
f(x) = - 3x + 4
What is the volume of the cone below?
A. 432 units 3
B. 1447 units 3
C. 1087 units 3
D. 2167 units 3
Answer:
[tex]144\pi[/tex]
Step-by-step explanation:
To find the volume of a cone use the formula [tex]v = \pi r^2\frac{h}{3}[/tex]
When you substitute that into an equation it will be [tex]v = \pi 4^2\frac{27}{3}[/tex]
First you should evaluate the exponent making it 16
Next divide 27 and 3 which is 9
Since you don't have to multiply by 3.14 ([tex]\pi[/tex]) the equation should be ...
[tex]144\pi[/tex]
Answer:
144
Step-by-step explanation:
PLZ HELP !!!!!! ASAP!!!
Part (a)
BC = opposite side (furthest leg from the reference angle)
AB = adjacent side (closest leg from the reference angle)
AC = hypotenuse (always opposite the 90 degree angle)
=============================================
Part (b)
i. False. Angle B is 90 degrees as shown by the square angle marker.
ii. False. Side AB is opposite angle C. Note how "C" is part of "BC", so that means we cannot have BC be opposite C.
iii. True. Leg AB is the closer leg to angle A. We have "A" in "AB" to see this without having to draw the diagram. Refer to part (a) above.
iv. False. The longest side of any right triangle is always the hypotenuse. The longest side of any triangle is always opposite the largest angle.
==============================================
Part (c)
cos(theta) = adjacent/hypotenuse = AB/AC
tan(theta) = opposite/adjacent = BC/AB
Refer back to part (a) to determine the opposite,adjacent and hypotenuse side lengths.
==============================================
Part (d)
The reference angle has changed, so the opposite and adjacent sides swap. The hypotenuse remains the same regardless of what reference angle you pick.
sin(C) = opposite/hypotenuse = AB/AC
cos(C) = adjacent/hypotenuse = BC/AC
tan(C) = opposite/adjacent = AB/BC
Note the tangent ratio is the reciprocal of what we found back in part (c).
Answer & Step-by-step explanation:
(a)
The hypotenuse is on line CA (the hypotenuse is always opposite the 90° angle (marked by a little square))
The adjacent is on the line BA (adjacent is next to the given angle, but NOT the hypotenuse)
The opposite is on the line CB (this is opposite the given angle)
(b)
i. false (b is a right angle)
ii. false (the side opposite C is BA)
iii. true
iv. false (the side opposite B is the hypotenuse, and the hypotenuse is always the longest side in a triangle)
(c)
cosine ratio: [tex]cos=\frac{adjacent}{hypotenuse}[/tex]
tangent ratio: [tex]tan=\frac{opposite}{adjacent}[/tex]
The cosine and tangent ratios of the given angle:
[tex]cos0=\frac{AB}{CA} \\\\tan0=\frac{CB}{AB}[/tex]
(d)
Remember SOH-CAH-TOA:
Sine=Opposite/Hypotenuse
Cosine=Adjacent/Hypotenuse
Tangent=Opposite/Adjacent
Using the angle C, plug in the appropriate sides:
[tex]sinC=\frac{BA}{CA}\\\\ cosC=\frac{CB}{CA}\\\\ tanC=\frac{BA}{CB}[/tex]
:Done
How many cubes with side lengths of \dfrac12 \text{ cm} 2 1 cmstart fraction, 1, divided by, 2, end fraction, start text, space, c, m, end text does it take to fill the prism? Cubes
Answer:
24
Step-by-step explanation:
Answer
24!
Step-by-step explanation:
Person above me is correct :)
what is -7 + 11 - 14 + 3 + 12
Answer:
5
Step-by-step explanation:
Answer:
5 (Follow PEMDAS left—>right)
