Answers
Answer:
61°
Step-by-step explanation:
Given:
∆MNO,
Side MO (n) = 18
MN (o) = 6
m<O = 17°
Required:
m<N
Solution:
Using the sine rule, [tex] \frac{sin N}{n} = \frac{sin O}{o} [/tex] , solve for N.
Plug in the values of M, n, and m
[tex] \frac{sin N}{18} = \frac{sin 17}{6} [/tex]
Cross multiply
[tex] 6*sin(N) = sin(17)*18 [/tex]
[tex] 6*sin(N) = 0.292*18 [/tex]
Divide both sides by 6
[tex] \frac{6*sin N}{6} = \frac{0.292*18}{6} [/tex]
[tex] sin N = \frac{0.292*18}{6} [/tex]
[tex] sin N = \frac{5.256}{6} [/tex]
[tex] sin N = 0.876 [/tex]
[tex] N = sin^-1(0.876) [/tex]
[tex] N = 61.16 [/tex]
m<N ≈ 61°
Related Questions
The hospital sells raffle tickets to raise funds for new medical equipment. Last year, 2000 tickets sold for $24 each. The fund-raising coordinator estimates that for every $1 decrease in price, 125 more tickets will be sold. a) What decrease in price will maximize the revenue? b) What is the price of a ticket that will maximize the revenue? c) What is the maximum revenue? PLEASE SHOW WORK, Thank you!
Answers
Answer:
a. $4.00
b. $20.00
c. $ 5000
Step-by-step explanation:
a. The given information are;
The number of tickets sold = 2000
The price of tickets sold = $24
The number extra tickets sold per decrease in price = 125
Let the number of tickets sold = y
The price of each ticket = x
Therefore, given that the fund-raising coordinator estimates that the number of tickets sold vary proportionately with the price of the ticket, we have a linear relationship of the form;
y = mx + c
Where:
m = The slope which is change in y divided by change in x
Change in y = 125
Change in x = -1
m = 125/(-1) = -125
Where the change in y = y - 2000 and change in x = x - 24
we have for a linear straight line relation;
(y - 2000)/(x - 24) = m
Which gives
y - 2000 = -125(x - 24)
y - 2000 = -125·x + 3000
y = -125·x + 3000 + 2000 = -125·x + 5000
The revenue = Price × Quantity sold = x × y
Where y = -125·x + 5000, we have
Revenue = x×(-125·x + 5000) = -125·x² + 5000·x
The maximum revenue occur at the point where the slope of the revenue = 0, which is d(yx)/dx =d(-125·x² + 5000·x)/dx = -250·x +5000 = 0
x = -5000/(-250) = 20
Therefore, the price that gives maximum revenue = $20 which is a decrease of $24 - $20 = $4.00
b. The price that will maximize the revenue = $20
c. The quantity sold at maximum revenue = -125 × 20 + 5000 = 2500
The maximum revenue = 2500 × 20 = $5000.00
5x + y = 2
2x-3y = 62
Answers
Hey there! :)
Answer:
x = 4, y = -18 or (4, -18).
Step-by-step explanation:
Given:
5x + y = 2
2x - 3y = 62
We can use substitution to solve this problem. Rearrange the first equation in terms of y:
5x + y = 2 ---> y = -5x + 2
Substitute in this equation for y into the second equation:
2x - 3(-5x + 2) = 62
Distribute -3:
2x + 15x - 6 = 62
Combine like terms:
17x - 6 = 62
Add 6 to both sides:
17x = 68
Divide both sides by 17:
x = 4.
Plug in this value for x into an equation to solve for y:
5(4) + y = 2
20 + y = 2
y = -18.
Therefore, the solutions to this system of equations are:
x = 4, y = -18 or (4, -18).
true or false:
If ab>0 then a>0 and b>0.
Answers
Answer:
false
Step-by-step explanation:
because a<0 and b<0 then ab>0
Answer:
False
Step-by-step explanation:
You don't know what a or b is for example it could be a=-3 b=-4. In that case ab= 12 but a and b indavidually are less than zero making this statment false
Forest fires are most likely to occur when the air temperature (t) is greater than 60°F.
Write an inequality for the situation.
please help me asap!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
The temperature (t) needs to be greater than 60
So you would have t > 60
Answer:
t > 60
Explanation:
In order to answer this question we must determine two things: what two terms will be compared in the inequality and what symbol we will use to compare them. Let's start by finding, 'what two terms will be compared.'
Read the following quote from the problem...
"Forest fires are most likely to occur when the air temperature (t) is greater than 60°F."
Since the temperature (t) must be greater than sixty degrees to start a forest fire, these are the two terms that we will be comparing in the inequality.
Now, let's find out what symbol we will use to compare the terms.
Because the problem uses the phrase "greater than" to represent the comparison between the temperature of the air and an average of sixty degrees, the symbol we will be using in the inequality is the greater than sign, >.
Finally, use all the facts we have established to write the inequality.
· t = air temperature
· > = greater than
· 60 = max temp. before forest fire occurs
Therefore, the inequality for the solution is t > 60.
PLEASE HELP ASAP!!:
explain the answer to this as well, please :)
the difference between two numbers is 4. the sum of the smaller number and theee times the larger number is 36. what are the two numbers?
Answers
I totally typed the right answer for the wrong question sorry
You Identify the ratio of the average number of bass to the averg
Answers
Answer:
Step-by-step explanation:
Using six random samples, the average number of catfish in the samples was 5.7
Answer:
Uhhhh......Hi??
please help me solve
Answers
Answer:
cD /100
Step-by-step explanation:
Change the percent to a fraction
c% = c/100
Multiply by the sale
D * c/100
cD /100
Christine had a six sided dice numbered from 1 to 6. she rolled it a total of 50 times. it landed on a odd number 21 times. ( A ) work out the relative frequency of the dice landing on an odd number. give you answer as a decimal. ( B ) if the dice were fair what would the theoretical probability of it landing on a odd number be give your answer as a decimal. ( C ) is the dice definitely biased or is it impossible to tell write a sentence to explain your answer get brainly plz help
Answers
A) Relative frequency is number of times an event happened over total number of events:
Answer is 21/50 = 0.42
B) On a 6 sides die, there are 3 even numbers and 3 odd numbers, so the theoretical probability of landing on odd would be 3/6 = 0.50
C) Because the die has an equal amount of chance landing on even or odd, both are 3/6, then the dice is not biased.
9. (09.01 LC) The graphs of f(x) and g(x) are shown below: If f(x) = (x + 7)^2, which of the following is g(x) based on the translation? (5 points)
g(x) = (x + 9)^2
g(x) = (x + 5)^2
g(x) = (x − 9)^2
g(x) = (x − 5)^2
Answers
Hey there! :)
Answer:
g(x) = (x + 9)²
Step-by-step explanation:
If we look at the graph g(x), we can see that its vertex is at (-9, 0).
Recall the transformation form of a parabola is f(x) = ±a(b(x-h))+k where (h , k) are the coordinates of the vertex. In this instance it is (-9, 0), therefore:
g(x) = (x + 9)²
Having some problems with this
Answers
Answer: C) 5
Step-by-step explanation:
First let's distribute the left side of the equation.
2/3a - 9 1/3 = -3(a-3)
Then let's distribute the right side of the equation.
2/3a - 9 1/3 = -3a + 9
Then let's move all the a's to one side, and all the constants to the other.
3 2/3a = 18 1/3
Then divide both sides of the equation by 3 2/3.
a = 5
Hope it helps <3
The width of a rectanglular solid is twice the height of the solid, the height of the solid is twice the length of the solid. If x is the length of the solid, what is the surface area in terms of x?
Answers
Answer:
28x^2
Step-by-step explanation:
Set variables:
Width = w
Length = x
Height = h
Set Equation:
w = 2h = 4x
h = 2x
x=x
Now that we have the terms in terms of x, we can find surface area.
We find the first three then multiply answer by 2, because there are 6 sides.
w*h -> first side
w*x -> second side
h*x -> third side
Set them in terms of x:
4x*2x = 8x^2
4x*x = 4x^2
2x*x = 2x^2
Add them and get: 14x^2
Wait, you need to multiply them by 2 and get: 28x^2
Answer: The answer is in the photo I really hope it’s right
Step-by-step explanation: I don’t need a brainly(I’m joking)
Hahahaha I know it’s not the best
Khairul agrees to lay a road 3000m long in 30 days. He employs 50 men,who works for 8 hours a day .After 20 working days, he finds that only 1200 m of the road is completed. Each man now works for 10 hours a day and they have to finish the project in 10 days' time. So , Khairul decides to employ more men to work on the project. How many more men are to be employed to finish the work on time?
Answers
Answer:
10 more men
Step-by-step explanation:
1.5 road made per man
I've got no clue how to do this.
Answers
Answer:
×-10×+21=0
FACTORIZATION of splitting the middle term
Factor 28+56t+28w28+56t+28w28, plus, 56, t, plus, 28, w to identify the equivalent expressions. Choose 2 answers:
Answers
Answer: The factorization of [tex]28+56t+28w[/tex] [tex]=28(1+2t+w)[/tex]
The factors of [tex]28+56t+28w[/tex] are 28 and 1+2t+w.
Step-by-step explanation:
The given expression : [tex]28+56t+28w[/tex]
To factorize it, we need to find the common factor.
As 56 can be written as 2 x 28.
So, the above expression would become
[tex]28+2\times28t+28w[/tex]
Now, taking 28 as common from all the terms, we will get
[tex]28(1+2t+w)[/tex]
Thus, the factorization of [tex]28+56t+28w[/tex] [tex]=28(1+2t+w)[/tex]
And the factors of [tex]28+56t+28w[/tex] are 28 and 1+2t+w.
Answer:
b&d
Step-by-step explanation:
i did khan on it and got it right
The Guzman family lives 240 miles from Mexico City. If the Guzmans travel in
their car at 60 miles per hour, how long does it take for them to get to Mexico
Answers
Answer:
4 hours
Step-by-step explanation:
To find the time it takes to travel the distance, divide the distance by the speed they are going.
(240 miles)/(60 miles per hour) = 4 hours
It will take them 4 hours.
Answer:Answer:
4 hours
Step-by-step explanation:
To find the time it takes to travel the distance, divide the distance by the speed they are going.
(240 miles)/(60 miles per hour) = 4 hours
It will take them 4 hours.
Step-by-step explanation:
Which of the following is a set in correct set notation?(1,2,3){4,5,6} the letters of the alphabet 7,8,9
Answers
Answer: {4,5,6}
Step-by-step explanation: Sets could be explained as a representation of elements which could be numbers, alphabets or a collection of items which are wrapped inside a curly bracket {}. Generally in mathematical or statistical parlance, once elements are wrapped around curly braces, the collection of those emmts is called a set. And therefore, set arithmetic such as union, intersection, complement e.t.c can be performed on elements of the given set. Elements wrapped in curly braces signifies that the elements reperesents an entire entity.
In the question given above, {7,8,9} reperesents a set containing three elements : 7, 8,9.
y
10
1
B(7,9)
Create a rectangle around the parallelogram. The
dimensions of this rectangle are
Find the area of the four right triangles surrounding the
parallelogram. The total area of the triangles is
square units
Subtract the triangle areas from the area of the
rectangle to obtain the area of the parallelogram. The
area of parallelogram ABCD is square units.
6
2
-10
6
-6
A-3,-1)
-2
10
C(8, -1)
D(-2,-11)
Answers
Answer:
rectangle: 11 × 20triangle area: 110 u²parallelogram area: 110 u²Step-by-step explanation:
See below for a graph showing the parallelogram and the rectangle.
The dimensions of the rectangle are 11 by 20. The rectangle area is ...
rectangle area = bh = (11)(20) = 220 . . . square units
There are 2 right triangles with a base of 10 and a height of 1. There are 2 right triangles with a base of 10 and a height of 10. The total area of the triangles is ...
triangle area = 2(1/2)(10)(1) +2(1/2)(10)(10) = 10(1 +10) = 110 . . . square units
The area of the parallelogram is the difference of these, ...
parallelogram area = rectangle area - triangle area
= (220 units²) -(110 units²) = 110 units²
The area of parallelogram ABCD is 110 square units.
_____
Check
The parallelogram has a base of 10√2 and a height of 5.5√2, so an area of (10√2)(5.5√2) = 110 square units. This matches the above result.
Answer:
1) 11 by 20 2) 110 3) 110 correct on edg
Step-by-step explanation:
Create a rectangle around the parallelogram. The dimensions of this rectangle are
11 by 20
Find the area of the four right triangles surrounding the parallelogram. The total area of the triangles is
110 square units.
Subtract the triangle areas from the area of the rectangle to obtain the area of the parallelogram. The area of parallelogram ABCD is
110 square units.
Multiply. 2 3/4* 4/5 Choose 1 answer: (a) 2 7/20 (b) 2 1/5 (c) 1 3/5 (d) 11/20
Answers
Answer:
[tex]\boxed{\red{ \frac{11}{5} = 2 \frac{1}{5} }}[/tex]
Answer B is correct.
Step-by-step explanation:
[tex]2 \frac{3}{4} \times \frac{4}{5} \\ \frac{11}{4} \times \frac{4}{5} \\ \frac{44}{20} \\ = \frac{11}{5} = 2 \frac{1}{5} [/tex]
Answer:
Hello!
_____________________
Exact Form: [tex]\frac{11}{5}[/tex]
Decimal Form: 2.2
Mixed Number Form: [tex]2\frac{1}{5}[/tex]
Step-by-step explanation: Simplify the expression.
So your anwser woould be ( B ) 2 1/5
Hope this helped you!
:D
if -1 and-2 are the zeroes of the cubic polynomial x³-2x²+ax+b, then find the value of a and b
Answers
Answer:
a = - 13, b = - 10
Step-by-step explanation:
Given that x = - 1 and x = - 2 are zeros then
f(- 1) = 0 and f(- 2) = 0, that is substituting value into the polynomial
f(- 1) = (- 1)³ - 2(- 1)² - a + b = 0 , that is
- 1 - 2 - a + b = 0
- a + b = 3 → (1)
f(- 2) = (- 2)³ - 2(- 2)² - 2a + b = 0, that is
- 8 - 8 - 2a + b = 0
- 2a + b = 16 → (2)
Multiply (1) by - 2
2a - 2b = - 6 → (3)
Add (2) and (3) term by term to eliminate a
- b = 10 ( multiply both sides by - 1 )
b = - 10
Substitute b = - 10 into (1) and evaluate for a
- a - 10 = 3 ( add 10 to both sides )
- a = 13 ( multiply both sides by - 1 )
a = - 13
20 POINTS!!! On the following graph F(-5)=?
Answers
Answer:
7
Step-by-step explanation:
Solve for x 4x−2=3x+4
Answers
Answer:
x=6
Step-by-step explanation:
Answer:
x = 6
hope this helps!
An archeologist in Turkey discovers a spear head that contains 27% of its original amount of C-14
Answers
Answer:
it is 13093 i got it correct
PLSSS answer ASAPP plss which statement is true regarding the graphed functions ?
f(0) = 2 and g(-2) = 0
f(0) = 4 and 9(-2) - 4
f(2)= 0 and g(-2) = 0
f(-2) = 0 and g(-2) = 0
Answers
Answer:
f(2)= 0 and g(-2) = 0 is the answer
Step-by-step explanation:
if im seeing this correctly, this is the answer because the bottom end of g(x) is (-2,0) the real coordinates and the bottom end of f(x) the coordinates are (2,0). and the way im seeing this is g(x)=g(-2)=0 and the 0 would =y
f(x)=(2) and once again y=0
so the third option is the answer if im seeing this correctly.
f(2)=0 and g(-2)=0
I’m really not sure what the answer to this question is, can anyone help?
Answers
Answer:
25(sqrt(2)+1)
Some explanation:
The exact form is 25*sqrt(2) + 25.
If we divide by 25, we are left with sqrt(2) + 1.
So 25(sqrt(2) + 1) is the correct answer.
Hope that helps a little!
Please answer it in two minutes
Answers
Answer:
8√3
Step-by-step explanation:
Sin 30 =4√3/DE
DE = 4√3/Sin30 = 8√3
The population of the world was 7.1 billion in 2013, and the observed relative growth rate was 1.1% per year. (a) Estimate how long it takes the population to double. (Round your answer to two decimal places.)
Answers
Answer:
90.91 years
Step-by-step explanation:
If the rate of population of the world was 7.1 billion in 2013, and the observed relative growth rate was 1.1% per year, increase in yearly population = 1.1/100 × 7,100,000,000
= 1.1 × 71,000,000
= 78,100,000
The amount increases by 78.1million every year.
To know how long it will take the population to double.
double of the initial population = 2×7,100,000,000 = 14,200,000,000
Increment per year = 78,100,000
Time it will take for the population to double = 7,100,000,000/78,100,000
= 90.91
≈ 91
This means it will take about 90.91years for the population to double
Tim is investigating the relationship between the number of years since a tree was planted and the height of the tree in feet. His data are shown in the table.
Years Since Tree was Planted vs. Height of Tree
Years since tree was planted, x
Height of tree in feet, y
2
17
3
25
5
42
6
47
7
54
9
69
Using a regression calculator, what is a good prediction for the height of the tree when it is 100 years old?
A calculator screen. A 2-column table with 6 rows titled Data. Column 1 is labeled x with entries 2, 3, 5, 6, 7, 9. Column 2 is labeled y with entries 17, 25, 42, 47, 54, 69. The regression equation is y almost-equals 7.36 x + 3.08; r almost-equals 0.998.
A good prediction for the height of the tree when it is 100 years old is about 315 feet because that is what the trend line, y almost-equals 3.08 x + 7.36, produced by the regression calculator predicts.
A good prediction for the height of the tree when it is 100 years old is about 739 feet because that is what the trend line, y almost-equals 7.36 x + 3.08, produced by the regression calculator predicts.
There is not a good prediction for the height of the tree when it is 100 years old because the trend line produced by the regression calculator does not give a prediction.
There is not a good prediction for the height of the tree when it is 100 years old because the prediction given by the trend line produced by the regression calculator probably is not valid that far in the future.
Answers
Answer: There is not a good prediction for the height of the tree when it is 100 years old because the prediction given by the trend line produced by the regression calculator probably is not valid that far in the future.
Step-by-step explanation:
Years since tree was planted (x) - - - - height (y)
2 - - - - 17
3 - - - - 25
5 - - - 42
6 - - - - 47
7 - - - 54
9 - - - 69
Using a regression calculator :
The height of tree can be modeled by the equation : ŷ = 7.36X + 3.08
With y being the predicted variable; 7.36 being the slope and 3.08 as the intercept.
X is the independent variable which is used in calculating the value of y.
Predicted height when years since tree was planted(x) = 100
ŷ = 7.36X + 3.08
ŷ = 7.36(100) + 3.08
y = 736 + 3.08
y = 739.08
Forward prediction of 100 years produced by the trendline would probably give an invalid value because the trendline only models a range of 9 years prediction. However, a linear regression equation isn't the best for making prediction that far in into the future.
Answer:
D
Step-by-step explanation:
There is not a good prediction for the height of the tree when it is 100 years old because the prediction given by the trend line produced by the regression calculator probably is not valid that far in the future.
Solve for x 4x+8=6x−1 Give your answer as an improper fraction in its simplest form.
Answers
Answer:
Step-by-step explanation:
4x+8=6x-1
-4x . =-4x .
8 = 2x-1
-1+8=2x-1+1
7=2x
7/2= 2x/2
3.5=x
The value of x will be;
⇒ x = 9/2
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 4x + 8 = 6x - 1
Now,
Solve the expression for x as;
⇒ 4x + 8 = 6x - 1
Subtract 6x both side, we get;
⇒ 4x + 8 - 6x = 6x - 1 - 6x
⇒ - 2x + 8 = - 1
Subtract 8 both side,
⇒ - 2x = - 1 - 8
⇒ - 2x = - 9
Divide by - 2 as;
⇒ x = 9/2
Thus, The value of x will be;
⇒ x = 9/2
Learn more about the mathematical expression visit:
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Find the height, x, of the tree.
40°
62 ft
a) 52.02 it
b) 75.23 it
c) 21.27 it
d) 73.89 ft
Answers
Answer:
52.02 ft
Step-by-step explanation:
We can use equation tan θ = opposite/adjacent to solve for the opposite side x.
tan40° = x / 62
62tan40° = x
x = 52.02 ft
The solution is Option A.
The height of the tree is given by x = 52.02 ft
What are trigonometric relations?
Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the triangle be represented as ΔABC
Let the height of the triangle ABC be = x
Now , the base of the triangle ABC is BC = 62 feet
The angle of elevation is θ = 40°
Now , the height of the tree is the height of the triangle ABC and is given by the trigonometric relation ,
tan θ = opposite / adjacent
Substituting the values in the equation , we get
tan θ = x / 62
tan 40° = x / 62
Multiply by 62 on both sides of the equation , we get
x = tan 40° × 62
x = 0.83909963117 × 62
The value of x = 52.024 feet
Therefore , the value of x is 52.02 feet
Hence , The height of the tree is given by x = 52.02 ft
To learn more about trigonometric relations click :
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Hello i need some help
Answers
Answer:
y = 2x - 1
Step-by-step explanation:
(3, 5) (5, 9)
slope = (9-5)/(5-3) = 4/2 = 2
y = mx + b
5 = 2(3) + b
-1 = b
y = 2x -1
Answer:
f(x)=2x-1; y=2x-1
Step-by-step explanation:
First we need to find the slope and to do so you use the equation [tex]\frac{y_{1} -y_{2}}{x_{1}-x_{2}}[/tex] .
Plugging in for the values we get (9-5)/(5-3)=4/2=2, which means we have a slope of 2.
Now we just have to find the y-intercept, and to do this we multiply the x-value by the slope (2) and see what we have to add to that to get the y-value.
For example, 5*2=10, 10-1=9, so -1 is our y-intercept.
This means our equation in slope-intercept form is y=2x-1 and in function form is f(x)=2x-1