Answer:
3.2 miles
Step-by-step explanation:
To approximate the height of the mountain, we need to use the tangent function in trigonometry. We have two angles of elevation and the distance between the observer and the mountain, which we can use to create a right triangle.
Let h be the height of the mountain and d be the distance from the observer to the foot of the mountain.
At the first observation, we have:
tan(3.5°) = h/d
And at the second observation, when the observer is 11 miles closer to the mountain:
tan(9°) = h/(d-11)
Dividing the two equations, we have:
tan(9°) / tan(3.5°) = h/(d-11) / h/d
Solving for h, we have:
h = (d * tan(9°)) / (tan(3.5°) + 1)
We don't have an exact value for d, so we can use an estimate based on the difference in distance between the two observations.
Since d-11 = 11 miles, we have:
d = 11 * 2 = 22 miles
Using this estimate and the given angles, we can approximate the height of the mountain:
h = (22 * tan(9°)) / (tan(3.5°) + 1) = (22 * 0.156434465) / (0.066012183 + 1)
= 22 * 0.156434465 / 1.066012183 = 22 * 0.146838446 = 3.23 miles
The height of the mountain is approximately 3.2 miles to one decimal place.
cost price R600 profit R150 what is loss and selling price?
The loss is given as difference of cost price and selling price and the selling price is R750.
What is profit and loss?Mathematicians use the profit and loss formula to calculate market prices for goods and to assess how lucrative a company is. There is a selling price and a cost price for every goods. We can determine the profit made or loss suffered for a certain product based on the values of these prices. Cost price, fixed, variable, and semi-variable costs, selling price, marked price, list price, margin, etc. are some of the key words that are addressed in this article.
Given that the cost price is R600, and the profit is R150.
The profit is given as:
P = SP - CP
150 = SP - 600
SP = 150 + 600
SP = 750
The loss is given as:
L = CP- SP
Hence, the loss is given as difference of cost price and selling price and the selling price is R750.
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Please help!!
Thankyou!!
The scale factor is: 1.8
because of :
[tex]\frac{36}{20}=1.8\\ \\\\\frac{25.2}{14}=1.8[/tex]
A catapult launches a pumpkin from the base of a hill. The
hill follows an incline with the height in meters, y, in terms
of horizontal distance in meters, x, given by the equation
y=0.9x. The height of the pumpkin, as it is launched up-
hill, is given by the function y = -0.1x² +4.9x¸
What is the height, in meters, where the pumpkin lands on
the hill?
The height where the pumpkin lands on the hill is given as follows:
36 meters.
How to obtain the height where the pumpkin lands on the hill?The equation for the pumpkin's height is given as follows:
y = -0.1x² + 4.9x.
The equation for the hill's height is given as follows:
y = 0.9x.
Hence the pumpkin will land on the hill at a time of:
-0.1x² + 4.9x = 0.9x.
Hence:
0.1x² - 4x = 0.
x(0.1x - 4) = 0.
0.1x - 4 = 0
x = 40.
The height is then given as follows:
y = 0.9(40)
y = 36 meters.
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can someone pls help thank you.
The length of the side BC is 5 unit.
What is distance between two points?The length of the line segment bridging two points on a plane is known as the distance between the points.
The formula to find the distance between the two points is usually given by d=√{(x₂-x₁)² + (y₂-y₁)²}
Given:
A quadrilateral has vertices:
A(0, -3)
B(6, -3)
C(9, 1)
D(3, 1)
The length of the side BC = √{(x₂-x₁)² + (y₂-y₁)²}
= √{(9 - 6)² + (1 + 3)²}
= 5
Therefore, the length is 5 unit.
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shape y is an enlargement of shape x by a scale factor of 4
work out lengths a and b
Answer:
ehhhh
Step-by-step explanation:
Area of a circle with a radius of 15.6
Answer:
Roughly around 764.15
Step-by-step explanation:
The equation to find area is A = π r^2
When you replace the values, you get A = π 15.6^2
15.6 squared is 243.36, so you end up with A = π x 243.36
Once you multiply them, you get 764.15, which is roughly the amount
A survey of 1,029 tourists visiting Orlando was taken. Of those surveyed:
258 tourists had visited the Magic Kingdom
299 tourists had visited Universal Studios
100 tourists had visited both the Magic Kingdom and LEGOLAND
82 tourists had visited both the Magic Kingdom and Universal Studios
76 tourists had visited both LEGOLAND and Universal Studios
12 tourists had visited all three theme parks
68 tourists did not visit any of these theme parks
How many tourists only visited the LEGOLAND (of these three)?
44 tourists only visited LEGOLAND (of these three).
Solving for the tourists only visited the LEGOLAND only:Let's call the number of tourists who visited only LEGOLAND x.
From the information given, we know that:
258 tourists had visited the Magic Kingdom
299 tourists had visited Universal Studios
100 tourists had visited both the Magic Kingdom and LEGOLAND
82 tourists had visited both the Magic Kingdom and Universal Studios
76 tourists had visited both LEGOLAND and Universal Studios
12 tourists had visited all three theme parks
68 tourists did not visit any of these theme parks
We can calculate x as follows:
x = number of tourists who visited LEGOLAND only
number of tourists who visited LEGOLAND - number of tourists who visited LEGOLAND and Magic Kingdom - number of tourists who visited LEGOLAND and Universal Studios + number of tourists who visited all three parks
= 100 - 82 - 76 + 12
= 44
Hence, 44 tourists only visited LEGOLAND (of these three).
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This picture is what i need help with
Answer: [tex]80\%[/tex]
Step-by-step explanation:
[tex]\frac{90-50}{50} \times 100=80\%[/tex]
simple and compound interest
pls tell me answer , asap
The value of interest after 3 years is £2,304.
What is simple interest?Borrowers must pay lenders simple interest as a fee in exchange for a loan. Compound interest is excluded from the calculation and just the original principal is used. Simple interest applies to all loans, not just specific ones. Additionally, it is the kind of interest that banks give their customers on their savings accounts.
Given amount invested = principal = £9600
rate = 8% per year
time = 3 years
simple interest is,
SI = (Prt)/100
SI = (9600*8*3)100
SI = £2,304
Hence value after 3 years is £2,304.
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Which of the values listed is a prime number?
A. 10
B. 15
C. 27
D. 29
Answer:
D. 29
Step-by-step explanation:
A. 10 = 2 × 5 not prime
B. 15 = 3 × 5 not prime
C. 27 = 3³ not prime
D. 29 = 1 × 29 prime
Answer:
29
Step-by-step explanation:
A prime number is a number that can't be divided by any number other than itself or 1.
10
1*10
2*5
5*2
10*1
NOT A PRIME NUMBER
15
1*15
3*5
5*3
15*1
NOT A PRIME NUMBER
27
1*27
3*9
9*3
27*1
NOT A PRIME NUMBER
29
1*29
29*1
PRIME NUMBER
Each of the 23 students in Ms.Evan's class raised $45 for the school by selling coupon books. How much money did the class raise?
Please help me
Answer:
The class raised $45 x 23 = $1035.
Step-by-step explanation:
To find the total amount of money raised by the class:
Identify the amount raised by one student: $45.
Multiply the amount raised by one student by the number of students: $45 * 23.
The total amount raised by the class is $45 * 23 = $1035.
Find the total surface area of this cuboid. 6 cm 5 cm 4 cm
Answer:
solution
given,
length =6cm
breadth =5cm
height =4cm
Now,
area of cuboid =l×b×h
=6cm ×5cm×4cm
=120cm^3
Hence, the total surface area of the given figure of cuboid is 120cm^3
Step-by-step explanation:
given above
Determine if the sequence is arithmetic. If it is, find the common difference, the 52nd term, the
explicit formula, and the recursive formula.
Hence Sequences 4, 16, 36, 64,.. are not arithmetic, however 40, 30, 20, 10,... are, with a common difference of -10 and the 52nd term being -490.
what is arithmetic progression ?An arithmetic progression is defined as a constant discrepancy between terms that follow one another through a series. For instance, the number sequence 5, 7, 9, 11, 13, and 15 is an example of either an exponential manner with a limitation of two. A progression with a set tolerance between any consecutive numbers is referred to as a "arithmetic progression" (A.P.). Two types of mathematical progression are possible: series in mathematics with a finite length A finite geographic progression is a serie with a finite number of terms. The early, delayed, tolerance, and frequency of terms may all be calculated using the terms in the series.
given
First succession
4, 16, 36, 64,
The common difference must be the same for it to be considered AP.
It is not AP since 16 - 4 ≠ 36 - 16.
Second succession;
40, 30, 20, 10, ...
common distinction =30 - 40 = 20 - 30 = 10 - 20 = -10
As a result, it will be an AP because the common difference is -10 and the same.
Now, The nth phrase of AP equals a plus (n - 1) d, where d is a typical difference and an is the initial term.
So, 52nd term = 40 + (52 - 1) (-10), which is -490.
Hence Sequences 4, 16, 36, 64,.. are not arithmetic, however 40, 30, 20, 10,... are, with a common difference of -10 and the 52nd term being -490.
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Please help will mark Brainly
Answer: Y=5
8x5=40
40x5=200
200x5=1000
etc..
Every day last week, Lily biked 7 miles and Charlotte biked 9 miles.
On one day, how many miles did Lily and Charlotte bike together?
• If they biked the same number of miles each day for 3 days, how many miles did they bike in all?
Both Lily and Charlotte biked 9 miles in a day. They biked 48 miles within the space of 3 days
What is an equation?An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.
Every day last week, Lily biked 7 miles and Charlotte biked 9 miles.
The total distance both biked in a day = 7 miles + 9 miles = 16 miles
Both Lily and Charlotte biked 9 miles in a day
They biked the same number of miles each day for 3 days, hence:
Total distance biked = 16 miles per day * 3 days = 48 miles
They biked 48 miles within the space of 3 days
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A model is made of a car. The car is
feet long and the model is
inches long. What is the ratio of the length of the car to the length of the model?
A
131313: 101010
B
101010: 156156156
C
156156156: 101010
D
101010: 131313
The car is 7 feet long and the model is 16 inches long, the ratio of the length of the car to the length of the model is, 21:4 So Option D is correct
What is the ratio?A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.
Given that,
The car is 7 feet long
The model is 16 inches long
The ratio of the length of the car to the length of the model = ?
It is known that,
1 feet = 12 inches
Now, converting length of car into inches
⇒ 7 feet = 7×12 inches = 84 inches
So, Ratio of lengths
⇒ 84/16
⇒ 21/4
Hence, the ratio is 21:4
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Complete question:
A model is made of a car. The car is 7 feet long, and the model is 16 inches long. What is the ratio of the length of the car to the length of the model?
a) 4:21
b) 7:16
c) 16:7
d) 21:4
The amount of liquid in three containers is shown below
Order the liquid measurements from least to greatest.
how your work.
The equivalent of a gallon (gal) is 16 cups, 8 pints, or 4 quarts. The biggest liquid measurement is this one.
What liquid has the largest measurement?The equivalent of a gallon (gal) is 16 cups, 8 pints, or 4 quarts. The biggest liquid measurement is this one.There are various units of measurement that can make your recipes easier to follow, especially when measuring in greater quantities. We typically refer to volume in terms of teaspoons, tablespoons, cups, millilitres, and fluid ounces.A millilitre, which is one thousandth of a litre, is the smallest metric unit for measuring the smallest amount of liquid. Thus, we may state that 1 litre equals 1000 millilitres.The most precise tools for measuring small volumes of liquid are volumetric flasks, burettes, and pipettes, which have tolerances of less than 0.02.The complete question is
What is the biggest measurement of liquid?
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4 Paul sees this advert for a payment plan for a laptop.
Laptop payment plan
normal price £240
pay a deposit of £36 and £15 a month for 12 months
use our payment plan and save 8% of the normal price
(a) Does using the payment plan save 8% of the normal price?
You must show your working
Step-by-step explanation:
by using the paymdnt pkan, the total amount to pay is,
36 + 15×12
= £216
so saving 240-216 = 24. ( 10%)
so it is not 8% saving
Use the following probabilities to answer the question. Round to 4 decimal places.
P(A) = 0.57, P(B) = 0.33, P(A and B) = 0.10.
P(B | A)
Submit Question
P(B|A) = P(A and B) / P(A) = 0.10 / 0.57 = 0.1754.
What do you mean by Probability?Probability is a branch of mathematics that deals with the study of random events and their likelihood of occurring. It provides a framework for understanding the uncertainty and unpredictability of real-world events and helps to make informed decisions based on data and evidence.
The basic concept of probability is the idea that every event has a numerical value between 0 and 1, representing the likelihood of the event occurring. An event with a probability of 1 is considered certain to occur, while an event with a probability of 0 is considered impossible to occur. Events with probabilities between 0 and 1 are considered uncertain, and their likelihood of occurrence can be described using a probability distribution.
There are different methods for calculating probabilities, including classical probability, which assumes that all outcomes are equally likely, and empirical probability, which is based on actual observations of real-world events. The concept of conditional probability is also important, as it allows us to calculate the likelihood of an event occurring given the occurrence of another event.
Probability is widely used in many different fields, including science, engineering, finance, and medicine. In science, it is used to model and understand complex systems, while in engineering it is used to design and test new technologies. In finance, it is used to evaluate investments and make informed decisions, while in medicine it is used to assess the risk of diseases and evaluate the effectiveness of treatments.
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Elizabeth is thinking of a two-digit number. When the tens digit is subtracted from the ones digit, the difference is 2. One-fifth of the number is 1 less than the sun of the digits. What is the number?
The two digit number is 35.
What is equation modelling?Writing a mathematical statement in the form of a mathematical equation for the correct analysis, measurement and solutions.
Given is that Elizabeth is thinking of a two - digit number. When the tens digit is subtracted from the ones digit, the difference is 2. One-fifth of the number is 1 less than the sun of the digits.
Let the number be (xy).
We can write the two digit number as -
xy = 10x + y ... Eq { 1 }
Now, it is given that when the tens digit is subtracted from the ones digit, the difference is 2. We can write -
y - x = 2 ... Eq { 2 }
Also, one - fifth of the number is 1 less than the sun of the digits. We can write -
(1/5)(10x + y) = (x + y) - 1 ... Eq { 3 }
Now, from eq { 1 } and eq { 2 }, we have -
y - x = 2
y = x + 2
and
(1/5)(10x + y) = (x + y) - 1
(1/5)(10x + x + 2) = (x + x + 2) - 1
(1/5)(11x + 2) = 2x - 1
11x + 2 = 10x - 5
x = - 7
y = -5
So, the number would be -
xy = 35
Therefore, the two digit number is 35.
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Select the statement that is true. (Will give brainly points)
0.452 ÷ 2 = 0.226
0.452 ÷ 2 = 2.26
0.452 ÷ 2 = 22.6
0.452 ÷ 2 = 226
Answer: 0.452 ÷ 2 = 0.226 is the correct answer. :)
Please answer my question too, i would appreciate it.
Delilah babysits a fixed number of hours per week. Her friend Laura babysits
5 hours more per week than Delilah. Write an equation that models the tota
number of hours Laura babysits.
An equation that models the total number of hours which Laura babysits is l = d + 5.
How to determine the total cost of y of x rides?In order to write an equation that model this situation, we would assign variables to the number of hours Delilah babysits and the number of hours Laura babysits respectively, and then translate the word problem into algebraic equation as follows:
Let the variable d represent the number of hours Delilah babysits.Let the variable l represent the number of hours Laura babysits.Next, we would translate the word problem into an algebraic equation based on the fact that Laura babysits 5 hours more per week than Delilah as follows;
l = d + 5
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The sides of a square field are 12 meters. A sprinkler in the center of the field sprays a circular area with a diameter that corresponds to a side of the field. How far does the sprinkler travel in 2 revolutions? How much of the field is not reached by the sprinkler? Round your answer to the nearest hundredth.
There are 30.90 meters squared of the field is not reached by the sprinkler.
What is Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
First, get the area of the square field. The area of the square is side multiplied by side.
A = S x S
A = 12 X 12
A = 144 meters squared
Second, get the area of the circle formed by the sprinkler.
The circle is formed inside the square with a radius of 6 meters (half of the diameter which is 12 meters).
A = πr²
A = 3.1415 x 6²
A = 113.09733 meters squared.
In order to get the not sprinkled area, subtract the area of the square by the area of the circle.
Hence, Not Sprinkled Area = 144 meters squared - 113.09733 meters squared
Thus, The final answer is 30.90 meters squared.
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To isolate the variable on one side of the equal sign, divide both sides of the equation by .
To isolate the variable on one side of the equal sign, divide both sides of the equation by the coefficient of the variable.
5. Health and Fitness Tyler does squats and pushups. He wants to increase the number of each type of exercise by 20% by the end of the month. He currently does 25 pushups. If Tyler meets his goal, he will do a total of 13 more squats and pushups than he does now. Write an equation to find how many squats Tyler does now?
If Health and Fitness Tyler does squats and pushups. He wants to increase the number of each type of exercise by 20% by the end of the month. The equation is 0.2(x+25)=13 and the number of squats is 40.
How to find the number of squats?Let x represent the number of squats Tyler currently have
Given the equation:
0.2(x + 25) = 13
Expanding the parentheses on the left side:
0.2x + 5 = 13
Subtracting 5 from both sides:
0.2x = 8.
Dividing both sides by 0.2 to isolate x:
x = 8/0.2
x = 40
Therefore Tyler currently does 40 squats.
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How can you rewrite -8
−
− 10 as an addition problem
Answer:
When using inverse operations with negative numbers, when you change subtraction to addition, the negative turns to a positive.
-8 - -10 can be changed to:
8 + 10
8 + 10 = 18
Step-by-step explanation:
Hope it helps! =D
Sorry took so log to answer. My internet is being slow some reason. -_-
Work out the following sheet
Answer:
Subtract two angles together to get the answer 19.(22) 20.(12)
The blueprint for a circular gazebo has a scale of 2 inches=5 feet. The blueprint shows that the gazebo has a diameter of 5.1 inches. What is the actual diameter of the gazebo? What is its area? Use 3.14 for π.
The actual diameter of the gazebo is 12.75 feet and has an area of
127.6 square inches.
What is a scale factor?The scale factor defines a variable in a ratio of two different measurements.
Sometimes drawings of large models are represented in a scale factor of a smaller unit.
Given, The blueprint for a circular gazebo has a scale of 2 inches = 5 feet.
So, The scale factor is (5/2) = 2.5 or 1 inch = 2.5 feet.
Also given, The gazebo has a diameter of 5.1 inches.
Therefore, The actual diameter of the gazebo is = 5.1×2.5 = 12.75 feet.
The area of the gazebo is π(12.75/2)² = 127.6 square inches.
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I need a answer with solution please help
Answer: b because i searched it up and thats what it is
707 divided by 6 with remainder