Answer:
x=30h
Step-by-step explanation:
First, you need to figure out how much she actually paid for lessons, so you need to subtract 45 from 165.
165-45=120
Now you know she paid 120 dollars in total for lessons.
You know she took four hours of lessons, so you divide 120 by 4.
120/4=30
It takes $30 an hour for lessons.
Now you can form an equation.
Since you know it takes $30 per hour of lessons, it will be 30h.
x is the full amount of money paid
You don't need to add 165-45 to your equation because not everyone will need to rent skis when they come to White Peaks.
Hope this helps!
x=30h is the equation used to find how much White Peaks charges, h, for each hour of group skiing lessons.
What is a fixed charge?A fixed charge is any type of expense that recurs on a regular basis, regardless of the volume of business.
First, we need to find out how much she actually paid for lessons, so we need to subtract 45 from 165.
165-45=120
Now we know that she paid 120 dollars in total for lessons.
Given that she took four hours of lessons, divide 120 by 4 to get the fixed charge of a lesson.
120/4=30
It takes $30 an hour for lessons.
Now we can form an equation.
Since it takes $30 per hour of lessons, it will be 30h.
x is the full amount of money paid.
No need to add 165-45 to equation because not everyone will need to rent skis when they come to White Peaks.
Hence, the equation formed to find the cost of each ession is x=30h
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What are the sine and cosine ratios for a 30°–60°–90° triangle with a hypotenuse of 6, when θ = 60°?
Answer:
There are two ways to do this problem algebraically or trigonometrically.
Algebraically/geometrically
The ratios of the sides of a 30/60/90 tri. are x, x√3, 2x (short leg, long leg, hyp). Therefore, if the long leg is 6 'units'. then 6 = x√3. x = 6√3.
The hyp is 2x then the hypotenuse is 2(6√3) = 12√3, rationalizing is 12√3/3 = 4√3
Using Trig.
We can use sinx = y/r = opp/hyp. The long leg of 6 is opposite 60 degrees (pi/3).
Therefore, sin(pi/3) = 6/r =
r = 6/sin(pi/3) = 6/(√3/2) = 12/√3, when you rationalize you get 12√3/3 = 4√3
The sine and cosine ratios for a 30°–60°–90° triangle with a hypotenuse of 6, when θ = 60° are 6√3 and 4√3.
What is a Hypotenuse?This is defined as the longest side of a right-angled triangle and is opposite to the right angle.
The ratios of the sides of a 30/60/90 triangle are x, x√3, 2x (short leg, long leg, hyp). We can infer that the long leg is 6 'units' which is
6 = x√3
x = 6√3.
The hypotenuse is 2x then the hypotenuse is 2(6√3)
= 12√3 when rationalized
= 12√3/3 = 4√3.
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Select the correct solution for the expression.
Answer:
= B
[tex]\frac{16}{40} +\frac{15}{40} = \frac{31}{40} \\\\\frac{2}{5} +\frac{3}{8} =\frac{31}{40}[/tex]
4. Solve the following equation: 6x + 12 = 4x - 8
Answer:
-10 is the correct answer
Step-by-step explanation:
hope this helps
Answer:
-10
Because I worked it out on paper
What is the area of the triangle below
PROJECT MATH - ANGLE OF ELEVATION AND DEPRESSION
- Guys can anyone help me of this project
- I have to write a story about the picture
- Then questions
- Traingles
That’s all i would be thankful if someone helped me Due is tmrw and i really need help with it !!!
Answer:
Story
Jane is 1.7 m tall. She stands 250 m away from the base of the Eiffel tower and looks up at the top of the building. The angle of elevation from her eyeline to the top of the building is 45°.
Question
Calculate an estimate of the height of the building. Give your answer to the nearest meter.
Calculation
Label the sides of the triangle O, A and H (where O is the side opposite to the angle, A is the side adjacent to the angle and H is the hypotenuse).
In the triangle, the angle and side A is known, and O must be calculated.
Therefore, use the trig ratio tan(x) = O/A:
⇒ tan(40) = O/250
⇒ 250tan(40) = O
⇒ O = 209.7749078...
Assume Jane's eye-level is approximately 1.5 m above the ground.
Therefore, the Eiffel tower is approximately:
209.7749078... + 1.5 = 211.2749078.. meters tall
Rounding to the nearest meter ⇒ 211 m
I'm not good at linear equations and I need help fast.
Answer:
B. nonlinear
Step-by-step explanation:
Difference Difference
in x x y in y
0 -2
1 1
1 -1
1 7
2 6
1 19
3 25
The difference between any two consecutive x-coordinates is 1. Each difference between any two consecutive y-coordinates is different. This means it is a nonlinear function.
Use the Internet to conduct research on real-world applications of chaos theory. Some examples of search terms to use are chaos theory, the butterfly effect, and fractal. Write 2-3 paragraphs on how chaos theory is used in today's world in various fields.
Chaos theory has a wide range of real-world applications and is used in fields such as weather prediction, finance, and biology.
What is Chaos theory?Chaos theory is a branch of mathematics that studies the behavior of systems that are highly sensitive to initial conditions. The "butterfly effect" is a popular term used to describe the idea that small variations in initial conditions can lead to vastly different outcomes over time. This theory has many real-world applications in various fields.
One of the fields that makes use of chaos theory is weather prediction. Meteorologists use chaos theory to understand how small variations in atmospheric conditions can lead to large-scale weather patterns. They use computer simulations to model how different initial conditions can lead to different weather outcomes. This helps them make more accurate weather predictions and plan for extreme weather events.
Another field that uses chaos theory is finance. Financial analysts use chaos theory to understand how small fluctuations in financial markets can have a significant impact on the economy. They use mathematical models to analyze stock prices and interest rates and determine how small changes can lead to large market movements. This helps them make informed investment decisions and minimize risk.
Chaos theory is also used in biology to study the behavior of populations of animals, plants, and microorganisms. Biologists use chaos theory to understand how small changes in the environment can have a major impact on the growth and survival of populations. This helps them make informed decisions about the conservation and management of natural resources.
In conclusion, chaos theory has a wide range of real-world applications and is used in fields such as weather prediction, finance, and biology. The idea that small variations in initial conditions can lead to vastly different outcomes over time is a powerful tool for understanding complex systems and making informed decisions.
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The area of a rectangle is 18 cm. It's length is double than that breadth, (1) Find its length and breadth (2) Find its perimeter?
Answer:
3 cm, 6 cm18 cmStep-by-step explanation:
Let the width is x, then the length is 2x.
Area of rectangle:
x*2x = 182x² = 18x² = 9x = 3Dimensions are:
3 cm and 6 cmPerimeter is:
P = 2(3 + 6) = 18 cmLet dimensions be x and 2x
Now
Area=18LB=182x(x)=182x²=18x²=9x=3Now
Breadth=3
Length=2(3)=6
Perimeter
2(3+6)=2(9)=18cm8x+14y=4
-6x-7y=-10
Please help by solving the problem as a system of equation by elimination
Step-by-step explanation:
8x+ 14y= 4
-6×-7y= -10
For elimination method we can decide to eliminate either the y or x variable I'm going to eliminate the x variable so either of the one am eliminating we multiply the first equation by the coefficient of the variable we are eliminating in other words
8x +14y=4.....*-6
-6×-7y= -10......*8
-48x-84y= -24
-48x-56y= 80
then we multiply the second equation all through by -1
-48x-84y= -24
48x+ 56y= -80
28y=-104
y= 26/7
x= 8/3
Complete the following:
Multiply these numbers the quickest and easiest way possible: 87 x 5 x 2
Explain how you were able to quickly determine the product. Justify your reasoning using a property of multiplication.
Diamond started the day with $280 in her bank account. She purchased 14 books that were all the same price. After she left the store, she had -$20 in her account. How much did each book cost? (Round your answer to the nearest hundredths place)
Answer:
21.43
Step-by-step explanation:
280+20=300=total spent
300÷14=21.4285714
21.4285714 to the nearest hundredths place= 21.43
Help me I really need help
Answer:
Question 1 is A (7/10) Question 2 is b (39/56)
Step-by-step explanation:
what is the point of intersection of the linear system
x=5 and y = - 4
Please help with this question :`D
Answer:
The 4th term is geometric
Step-by-step explanation:
For geometry series we use Tn = a•r^n-1
r = -3
a = 3
Use the equation Tn = 3(-3)^n-1 and you'll see that it's geometric.
Order the following numbers from greatest (on top) to least (on bottom). Click on the arrows and drag to move the numbers around.
1 1.
-2/8
-3/7
-0.2
A manager is assessing the correlation between the number of employees in a plant and the number of products produced yearly. The table shows the data: Number of employees (x) 0 50 100 150 200 250 300 350 400 Number of products (y) 100 1,100 2,100 3,100 4,100 5,100 6,100 7,100 8,100 Part A: Is there any correlation between the number of employees in the plant and the number of products produced yearly? Justify your answer. (4 points) Part B: Write a function that best fits the data. (3 points) Part C: What does the slope and y-intercept of the plot indicate? (3 points).
The correlation coefficient of the number of employees and the number of products is 0.1.
What is the correlation coefficient?The correlation coefficient helps us to know how strong is the relation between two variables. Its value is always between +1 to -1, where, the numerical value shows how strong is the relation between them and, the '+' or '-' sign shows whether the relationship is positive or negative.
1 indicates a strong positive relationship.-1 indicates a strong negative relationship.A result of zero indicates no relationship at all, therefore, independent variable.
A.) In order to find the correlation between the two quantities we need to know the mean of the two values, therefore, the mean of the number of employees can be written as,
The mean of the number of employees
[tex]\text{Mean of the number of employees} = \dfrac{0+50+100+150+200+250+300+350+400}{9}[/tex]
[tex]\text{Mean of the number of employees} = 200[/tex]
The mean of the number of products
Mean of the number of Products [tex]= \dfrac{100+1100+2100 +3100+ 4100 +5100+ 6100+ 7100+ 8100}{9}\\\\\\=4100[/tex]
Now, the table can be written in the following manner as shown below, using the formula of the correlation,
[tex]r =\dfrac{\sum\left(x_{i}-\bar{x}\right)\left(y_{i}-\bar{y}\right)}{\sqrt{\sum\left(x_{i}-\bar{x}\right)^{2} \sum\left(y_{i}-\bar{y}\right)^{2}}}[/tex]
[tex]r =\dfrac{(30 \times 10^4)}{\sqrt{(15 \times 10^4)\times (60 \times 10^6)}}\\\\r = 0.1[/tex]
B.) The given data follows the linear relationship, therefore, the function of the given data will follow the general equation of a line.
y = mx + C
If we look at the value of y when the value of x was 0,
[tex]y = mx +C \\\\100 = m(0) + C\\\\C = 100[/tex]
Substitute the value of C in any other data point we will get,
[tex]y = mx+C\\\\1100 = m(50) +100\\\\m = 20[/tex]
Hence, the function that best fits the data is y=20x+100.
C.) The slope and y-intercept of the plot indicate that as the number of employees in the organization increases the number of products increases as well. The y-intercept shows us that if there are no employees in the company at that point the company will be able to produce 100 products on its own.
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Find ST. Round to the nearest tenth.
HELP PLEASEEEE SHOW WORK!!
Answer:
Step-by-step explanation:
sin 44° = [tex]\frac{63}{ST}[/tex]
ST = [tex]\frac{63}{sin44}[/tex]
ST ≈ 90.7
!WILL MARK AS BRAINLIEST! I would really appreciate the help!
Answer: 1) 36 m and 60 m^2 2) 15π/2 + 10 m and 75π/4 m^2
Step-by-step explanation:
Using the pythagorean theorem in the first question, we get that the slope is 10 m so the perimeter = 10 + 14 + 6 + 6 = 36 m and the area is
(14 + 6)*6/2 = 60 m^2
So in the next question, the arc of the circle has a length of
2π*5*3/4 = 15π/2
So the perimeter is 15π/2 + 5 + 5 = 15π/2 + 10 m
And the area is 3/4*π*5*5=75π/4 m^2
Hope it helps
Help pls asap so confused PLS
Answer:
the answer is x=12√2
hope it helps
) An outdoor staircase has a total vertical elevation of 21 feet from the road level to the first floor. The 1st floor to the 2nd floor is also 21 feet. If the angle of elevation is 32 degrees and the landing of each step is 12 inches, answer the following questions showing each step of your work:
a) What is the vertical rise per step (in inches, rounded to the nearest inch)?
b) Find the number of steps needed to climb from road level to the 2nd floor.
Answer:
a) 7 in
b) 72 steps
Step-by-step explanation:
Angle of elevation formula: [tex]tan(\theta)=\dfrac{y}{x}[/tex]
where [tex]\theta[/tex] is the angle of elevation, y is the vertical distance (rise) and x is the horizontal distance.
a) Given:
[tex]x=12[/tex][tex]\theta=32[/tex][tex]\implies tan(32)=\dfrac{y}{12}[/tex]
[tex]\implies y=12tan(32)[/tex]
[tex]\implies y=7 \ \textsf{in (nearest inch)}[/tex]
b) Given:
1st floor = 21 feet2nd floor = 21 feet⇒ Total height = 21 + 21 = 42 feet
1 foot = 12 inches
⇒ 42 feet = 42 x 12 = 504 inches
Using vertical rise of 7 in per step found in part (a):
Number of steps = 504 ÷ 7 = 72
Increased accuracy
Using unrounded vertical rise of 12tan(32):
Number of steps = 504 ÷ 12tan(32) = 67 steps to the nearest step
A person invests 8000 dollars in a bank. The bank pays 4.75% interest compounded daily. To the nearest tenth of a year , how long must the person leave the money in the bank until it reaches 20400 dollars?
The number of days for which the money is left to reach the 20,400$ mark is; 21.28 days
Compound interestThe final amount to be reached is; $20400
The principal amount is; $8,000 and at. rate of 4.75 % compounded.
Hence, it follows that;
20400 = 8000(1+0.045)^(x)Divide both sides of the equation by 8000; we have;
20400/8000= 1.045^(x)2.55 = 1.045^(x)Take log of both sides;
x = 0.4065/0.0191x = 21.28 days.Read more on compound interest;
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Which expression below produces the nth term in the sequence?
4,4, -12, -20, -28, ...
Answer:
-28, -20, -12, 4, 4
Step-by-step explanation:
I really dont know how to explain this but yeah pretty much thats the answer.
A person walks 4 miles per hour for 2.5 hours. How far do they walk?
Answer:
10 miles
Step-by-step explanation:
Distance walked in 1 hour = 4 miles
So, distance walked in 2.5 hours
= 4 miles × 2.5
= 10 miles
A farmer saw some chickens and pigs in a field. He counted 51 heads and 172 legs. Determine
exactly how many chickens and pigs he saw.
How many chickens?
How many pigs?
Answers:
16 chickens
35 pigs
========================================================
Explanation:
x = number of chickens
y = number of pigs
There are 51 heads, so x+y = 51 which solves to y = 51-x
2x = number of legs just from the chickens (2 legs per chicken)
4y = number of legs just from the pigs (4 legs per pig)
2x+4y = 172 legs total
----------
Plug in y = 51-x and solve for x.
2x+4y = 172
2x+4(51-x) = 172
2x+204-4x = 172
-2x+204 = 172
-2x = 172-204
-2x = -32
x = -32/(-2)
x = 16
Now use this to find y
y = 51-x
y = 51-16
y = 35
Since x = 16 and y = 35, this means there are 16 chickens and 35 pigs.
----------
Check:
x+y = 16+35 = 51 which works
2x+4y = 2*16+4*35 = 172 and that also works.
Both equations are confirmed.
Please answer this (who ever answers correctly gets brainlest)
Answer:
last one "kiki" is true...
Answer:
Option 2 and 4
Step-by-step explanation:
2) Number of science questions = (3/4) of total questions
= [tex]\dfrac{3}{4}*24[/tex]
4) Number of marbles in the jar = (3/4) of the total marbles
[tex]=\dfrac{3}{4}*24[/tex]
The perimeter of a rectangle bathroom mirror is 24 feet . The mirror is 10 feet wide how tall is it
Write the ratio for cosB
Answer:
11/61
Step-by-step explanation:
cos b = adj side/hypotenuse
=11/61
Answer:
CosB = B/H
Base(B)= 11
Perpendicular (P)=60.
Hypotenuse (H)= 61
CosB = B/H
CosB= 11/61
Please help this is due in 20 minutes. If you get I right I will give you 100 points.
It should cut into
2 right angle traingles.One rectangle for baseOne rectangle for b ack.One rectangle for fronti.e 3 rectangles and 2 right angles2 ne t is accurate
Answer:
A) net A
B) AB = 3 in BC = 5 in CD = 8.6 in
C) 106.6 in²
Step-by-step explanation:
Part A:
net A is the correct net for the prismPart B:
From inspection of the diagram:
AB = 3 inBC = 5 inCD = 8.6 inPart C:
Area of a rectangle = width x length
Area of a triangle = 1/2 x base x height
Surface area = 2(4 x 8.6) + (3 x 8.6) + 2(1/2 x 4 x 3)
= 68.8 + 25.8 + 12
= 106.6 in²
8.15 = e + 6
Solving one step equations
Addition and subtraction
Answer:
e= 2.15
Step-by-step explanation:
Subtract both sides by 6
2.15=e
Thus e is 2.15
Hope this helps!
Find the value of x.
Answer:
37
Step-by-step explanation:
（x+10)+x+(3x-5)=180
5x=185
x=37
The sum of angles in the triangle is 180 degrees. Therefore, the value of x in the triangle is 35
Angles of a triangleThe sum of angles of a triangle is 180 degrees. This simply implies the sum of the three angles in a triangle is equals to 180 degrees.
Therefore,
x + 10 + 3x - 5 + x = 180
combine like terms
x + x + 3x + 10 - 5 = 180
5x + 5 = 180
subtract 5 from both sides of the equation
5x + 5 - 5 = 180 - 5
5x = 175
divide both sides by 5
5x / 5 = 175 / 5
x = 35
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