Two planes leave an airport at the same time. Their speeds are 120 miles per hour and 110 miles per hour, and the angle between their courses is 33° How far apart are they after 2.5 hours? Round answers to the nearest whole number
Answers
165.09 miles far apart are they after 2.5 hours.
What is the law of cosines?
The law of cosine establishes a link between the lengths of a triangle's sides and the cosine of its angles. In trigonometry, the cosine rule generalizes the Pythagorean theorem, which applies to a right triangle.
Here, we have
Given: Let plane A travel at 120 mph and plane B travel at 110 mph.
After 2.5 hours, the total distance traveled by each plane is:
A = 2.5 × 120 = 300 miles
B = 2.5 × 110 = 275 miles
The law of cosines can be used to find the distance (D) between both planes as follows:
D² = A² + B² - 2ABcosθ
D = \(\sqrt{A^2+B^2-2ABcos(33)}\)
D = \(\sqrt{300^2+275^2-2(300)(275)cos(33)}\)
D = 165.09 miles
Hence, 165.09 miles far apart are they after 2.5 hours.
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Related Questions
I need help with this question I beeen stuck on it
Answers
Answer:
The question is already simplified completely
Step-by-step explanation:
s^5 can not be simplified any further. I see you are currently learning exponent rules, the main thing you have to remember is as long as exponents have the same bases if you divide them you subtract exponents and if you multiply you add exponents.
Allison has a part-time job at an ice skating rink selling hot cocoa. She decided to plot the number of hot cocoas she sold relative to the day's high temperature and then draw the line of best fit. What does the line's y-intercept represent?
Answers
The Y intercept tells us of the number of the cocoas soald based on the temperature
How to determine the y interceptIn the context of Allison's plot of hot cocoas sold relative to the day's high temperature, the y-intercept of the line of best fit represents the value of the dependent variable (number of hot cocoas sold) when the independent variable (day's high temperature) is zero.
The y-intercept helps establish the initial starting point of the line's slope and can provide insights into the general behavior of the relationship between the two variables.
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Sophie made 5 identical batches of dinner rolls for a restaurant. There was a total of 1,265 rolls. If each batch contained the same number of rolls, how many rolls were in 3 batches? Select whether the group size or the number of groups is unknown
Answers
Answer:
759 rolls
Step-by-step explanation:
Total rolls = 1265
Number of batches = 5
Since each batch hs the same number of rolls:
Number of rolls per batch :
1265 / 5
= 253 rolls per batch
Number of rolls in 3 batches :
253 * 3 batches
= 759 rolls
Under what operation are the set of integers closed? Explain your answer
Answers
Answer:
a set of integers is closed under addition, subtraction, and multiplication because when you add, subtract, or multiply any integers, the result is always an integer.
Step-by-step explanation:
Which image shows a reflection ABC
Answers
Answer:
A I think
Step-by-step explanation
Answer:
A
Step-by-step explanation:
I am not sure but I think it's A
Whats 952.80 ↩ hundreds?
Answers
Answer:
If you mean rounding it would be 1000
Step-by-step explanation:
Is that the question?
For the following, write down the largest and smallest number in the group:
a)-10, -4, -16, -1, -21
b)-19, -8, -45, -5, -2
c)-4, 0, 3, -2, 7
d)-17, -6, -19, -10, -5
Answers
In the group of numbers given above, the largest and the smallest number in each group is given below respectively:
a.) -1 and -21
b.) -2 and -45
c.) 7 and -4
d.) -5 and -19
What is a number line?A number line is defined as the representation of numbers in the order of negative and positive numbers with zero at the center of the structure.
In a number line, the figures that are at the right of zero are the positive and larger numbers while the numbers that are on the left of zero are the negative numbers and are smaller numbers.
Therefore, -1 is greater than -2 which is in turn greater than -3.
Therefore the largest and smallest numbers of each number group respectively include the following
a.) -1 and -21
b.) -2 and -45
c.) 7 and -4
d.) -5 and -19
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Levi needed to get his computer fixed. He took it to the repair store. The technician at
the store worked on the computer for 5.5 hours and charged him $59 for parts. The
total was $361.50. Which equation could be used to determine c, the cost of labor per
hour?
Answers
Answer:
$55
Step-by-step explanation:
Let c = cost of labour per hour
1) Set up an equation, where hours is denoted by c.
5.5c + 59 = 361.50
5.5c = 361.50 - 59
5.5c = 302.50
c = 302.50/5.5
c = 55
Therefore, the technician took $55 per hour.
1., express the following properties in propositional logic:
(a) For every location that is a cliff, there is an
adjacent location to it that contains some
non null quantity of resource r3.
(b) For every location that contains some
non null quantity of resource r2,
there is exactly one adjacent location that is a hill
.
(c) Resource r1 can only appear in the corners of the
grid (the corners of the grid are the locations
(1, 1), (K, 1), (1, K), (K, K)).
Answers
(a) The proposition can be expressed as ∀x(Cliff(x) → ∃y(Adjacent(x, y) ∧ NonNull(y, r3))).
(b) The proposition can be expressed as ∀x(NonNull(x, r2) → (∃y(Adjacent(x, y) ∧ Hill(y)) ∧ ¬∃z(Adjacent(x, z) ∧ Hill(z) ∧ ¬(z = y)))).
(c) The proposition can be expressed as ∀x(Resource(x, r1) → (Corner(x) ∧ ¬∃y(Resource(y, r1) ∧ ¬(x = y) ∧ Adjacent(x, y)))).
(a) In propositional logic, we use quantifiers (∀ for "for every" and ∃ for "there exists") to express the properties. The proposition (a) states that for every location that is a cliff (Cliff(x)), there exists an adjacent location (Adjacent(x, y)) to it that contains some non-null quantity of resource r3 (NonNull(y, r3)).
(b) The proposition (b) states that for every location that contains some non-null quantity of resource r2 (NonNull(x, r2)), there is exactly one adjacent location (y) that is a hill (Hill(y)), and there are no other adjacent locations (z) that are hills (¬(z = y)).
(c) The proposition (c) states that resource r1 (Resource(x, r1)) can only appear in the corners of the grid (Corner(x)), and there are no other adjacent locations (y) that contain resource r1 (Resource(y, r1)).
By using logical connectives (∧ for "and," ∨ for "or," ¬ for "not"), quantifiers (∀ for "for every," ∃ for "there exists"), and predicate symbols (Cliff, NonNull, Resource, Hill, Corner), we can express these properties in propositional logic to represent the given statements accurately.
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A dolphin was swimming 28 meters below the ocean's surface. It changed its depth to avoid a predator and ended up 21 meters below the surface.
What was the change in the dolphin's depth?
Answers
Answer:
7 meters
Step-by-step explanation:
Now write an equation that represents the situation. You want to find the change in the dolphin's depth, so subtract its beginning depth from its final depth.
The change in the dolphin's depth is negative 7 meters.
What is Subtraction?Subtraction of two or more numbers or algebraic expressions is the method of taking away a certain value from a number. This operation is also called difference of numbers.
Subtraction is one of the basic operations in mathematics along with division, multiplication and addition.
Initial depth that Dolphin was swimming = 28 meters
Then the Dolphin changed it's depth to avoid predator.
Final depth that Dolphin was swimming = 21 meters
Change in depth = Final depth - Initial depth
= 21 - 28
= -7 meters
This implies that depth of the Dolphin decreases with -7 meters.
Hence the change in the Dolphin's depth is -7 meters if the initial depth was 28 meters and final depth was 21 meters.
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If you answer correctly I will give you brainlest 5 stars and a thank you
A baseball field has four bases that form the shape of a quadrilateral. If someone invented a
new game similar to baseball that had four extra bases in the field, what type of polygon would
the bases form?
Apentagon
Boctagon
Chexagon
Ddecagon
Answers
4 bases plus 4 more makes 8, an octagon has 8 sides.
Part A: A statement about rational numbers is shown.
The product of two negative rational numbers is greater than either factor. Is the statement always true, sometimes true, or never true? Explain your answer. Provide at least two examples to support your answer.
Part B: A different statement about rational numbers is shown.
The product of two positive rational numbers is greater than either factor. Provide at least two examples to show that this statement is only sometimes true.
Answers
i didn’t realize u were chill like that
Please HELPPPPPPPPP please please please I beg
Answers
Answer:
A = {1,2,3} and B = {1,2,A,B}
A U B = { 1,2,3,A,B}
A U B means, the union of both sets. So, all the members in both sets are written together.
NB: An element is written only once even if it appears in both sets.
HOPE IT HELPS........✨✨✨
What does it mean when a forecaster says 70% chance of rain?
Answers
A 70% chance of rain means that there is a higher likelihood of rain occurring compared to other possible weather conditions, but it is not a guarantee.
When a forecaster says there is a 70% chance of rain, it means that, based on their analysis of various weather factors, they believe there is a 70% probability of rain occurring. This percentage represents the likelihood or chance of rain happening.
It's important to note that this is not a definitive prediction that it will rain. Weather forecasting is not an exact science, and there is always some level of uncertainty involved. The forecaster is indicating that, given the current conditions and their expertise, rain is more likely to happen than not.
To put it into perspective, if this weather scenario were repeated 100 times, it is expected that rain would occur in approximately 70 of those instances. The remaining 30 instances would not experience rain.
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3x² - 5x+2
5x²-2x-6
Which of the following is the sum of the two
polynomials shown above?
A) 8x²-7x-4
B) 8x² +7x-4
C) 8x4-7x²-4
D) 8x² +7x²-4
Answers
combine like terms
Arnold's credit card has a balance of $1,543. The annual percentage rate for his credit card is 18.25%. What is the daily interest rate ( 365 day in 1 year) and what amount of simple interest will Arnold owe after 30 days? Round the answer to the nearest penny.
Answers
To convert an annual interest rate to a daily interest rate based on simple interest, divide the annual interest rate by 365, the number of days in a year.
This way,
\(\frac{18.25}{365}=0.05\)The daily interest rate is 0.05%
To get the simple interest in a 30 day period, we use the formula for simple interest and get:
\(1543(\frac{0.05}{100}\cdot30)\Rightarrow23.15\)The interest for a 30 day period is $23.15
2. In his bakery, Al Pastore decorated 18
cakes at a time. Al's daughter, Noamy,
decorated 6 cakes at a time. If they
ended up decorating the same number of
cakes by the end of the day, what is the
smallest number of cakes that each must
have decorated? (Hint: LCM or GCF?)
Answers
(144-4)×(12÷4)+3=???
Answers
423
To solve the above equation follow the BODMAS rule
That is,
Brackets of Division Multiplication Addition Subtraction
BODMAS rule states that mathematical expressions with multiple operations need to be solved from left to right in the order of BODMAS.
so,
first, calculate the value in the brackets
(144-4)*(12/4)+3 = (140)*(12/4)+3
=140*(3)+3
According to the rule, a division operation is to be performed but there is no division operation in the equation we skip this step and proceed to the next operation
so, multiply 140*3
=420+3
the next operation is the addition
=423
the next operation according to the rule is subtraction which is not required to be performed in the equation.
therefore,
(144-4)*(12/4)+3 = 423
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for the exponential random variable, you should then test the empirical expectation and variance of the random variables you generated. assume you have generated random variables ????1,????2,????3,…,???????? calculate the empirical mean ????^
Answers
To test the empirical mean and variance of an exponential random variable generated with rate parameter λ, generate a sequence of n random variables and calculate the empirical mean and variance using appropriate formulas. Compare with theoretical values.
To test the empirical expectation and variance of the exponential random variable from a sample of n random variables X1, X2, ..., Xn generated with parameter λ, we can use the following formulas:
Empirical mean: Ȳ = (X1 + X2 + ... + Xn)/n
Empirical variance: s^2 = ((X1 - Ȳ)^2 + (X2 - Ȳ)^2 + ... + (Xn - Ȳ)^2)/(n - 1)
We can then compare the empirical mean and variance with the theoretical mean and variance of an exponential random variable with parameter λ, which are:
Theoretical mean: E(X) = 1/λ
Theoretical variance: Var(X) = 1/λ^2
To perform this test, we can generate n exponential random variables with parameter λ using a random number generator, and then calculate the empirical mean and variance using the formulas above. We repeat this process for 10,000 simulations and compare the results with the theoretical mean and variance.
If the results of the calculations are in line with what we expect, the empirical mean and variance should be close to the theoretical mean and variance, respectively. This is because the law of large numbers states that as the sample size increases, the sample mean and variance approach the population mean and variance.
If the results are not in line with what we expect, it could be due to a number of factors such as a faulty random number generator, an insufficient number of simulations, or a mistake in the calculation of the empirical mean and variance.
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Someone pls help???????????????????????
Answers
Answer: the answer is:
(9,0)
(11,2)
(15,6)
(18,9)
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Use the formula for the area of a trapezoid A=h(b1+b22), where A is area, b1 and b2 are the length of the bases, and h is the height, to answer the question.
How many square feet of grass are there on a trapezoidal field with a height of 75 ft and bases of 125 ft and 81 ft?
50 POINTSSSS
Answers
Answer:
Step-by-step explanation:
area = h (base1 + base2)
area = 75 (125 + 81)
area = 75 ( 206)
area = 15450 sq ft
Help please....I’m desperate
Answers
Answer:
6
Step-by-step explanation:
8×4=32/2=16
2×5=10
16-10=6
get the area of the entire large triangle, then subtract the are of the rectangle
Answer:
44
Step-by-step explanation:
I got 44
Gl
Select all the pairs of numbers that have the same greatest common factor.
Answers
Pairs of numbers that have the same greatest common factor are: (12, 18) and (12, 30) and (18, 30) with a greatest common factor of 6.
Define the term greatest common factor?The largest positive integer that divides two or more numbers without producing a remainder is known as the greatest common factor (GCF).
To find the greatest common factor (GCF) of two numbers, we need to find the largest number that divides both of them.
Let's start by listing the factors of each number:
12: 1, 2, 3, 4, 6, 12
18: 1, 2, 3, 6, 9, 18
20: 1, 2, 4, 5, 10, 20
30: 1, 2, 3, 5, 6, 10, 15, 30
Now we can compare the pairs of numbers and see which ones have the same GCF:
GCF(12, 18) = 6
GCF(12, 20) = 4
GCF(12, 30) = 6
GCF(18, 20) = 2
GCF(18, 30) = 6
GCF(20, 30) = 10
So the pairs that have the same GCF are:
12 and 18, with a GCF of 6
12 and 30, with a GCF of 6
18 and 30, with a GCF of 6
Therefore, Pairs of numbers that have the same greatest common factor are: (12, 18) and (12, 30) and (18, 30) with a GCF of 6.
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a certain type of storage battery lasts, on average, 3.0 years with a standard deviation of 0.5 year. the battery lives are assumed normally distributed. a. what is the probability that a given battery will last between 2.3 and 3.6 years? b. what is the probability that a given battery will last longer than 24 months?
Answers
Part a: The probability that a given battery will last between 2.3 and 3.6 years is 80.41%.
Part b: The probability that a given battery will last longer than 24 months is 97.72%.
What is meant by the normal distribution?A normal distribution is a data set arrangement in which the majority of values cluster inside the center of the range and the remainder slacken off symmetrically toward any extreme.For the given question,
The data for the storage battery are-
Mean μ = 3.0 years.Standard deviation σ = 0.5 years.Part a: The probability that a given battery will last between 2.3 and 3.6 years.
Find z score for x = 2.3 years.
z(2.3) = (x - μ )/σ
Put the values,
z(2.3) = (2.3 - 3.0)/0.5
z(2.3) = -1.4
Use negative z score table;
P(z = -1.4) = 0.0808
Similarly, for x = 3.6
z = (3.6 - 3)/0.5
z = 1.2
Use positive z table;
z = 0.8849
P(2.3<x<3.6) = 0.8849 - 0.0808
P(2.3<x<3.6) = 0.8041
Thus, the probability that a given battery will last between 2.3 and 3.6 years is 80.41%.
Part b: The probability that a given battery will last longer than 24 months = 2 years.
x = 2 years
z (2) = ( 2 - 3.0 )/ 0.5
z = 2
P(x > 2) = 0.9772
Thus, the probability that a given battery will last longer than 24 months is 97.72%.
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Item 2
Which expression is equivalent to 24y^2+6y?
6y(4y+1)
−6y(4y−1)
−6y(4y+1)
6y(4y−1)
Answers
Answer:
first option
Step-by-step explanation:
6y(4y + 1)
distribute the 6y: 6y(4y) + 1(6y)
24\(y^{2}\) + 6y
Use the diagram to find m∠2
if m∠1=105°
.
Answers
The required measure of angle ∠2 in the figure is given as 75°.
What is the angle?Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
Here,
∠1 and ∠2 are supplementary angles,
The definition of the supplementary angles, states that the sum of the angle is 180°.
So,
∠1 + ∠2 = 180
From the figure,
∠1 = 105°
105 + ∠2 = 180°
∠2 = 75°
Thus, the required measure of angle ∠2 in the figure is given as 75°.
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please help!! i have no idea!
Answers
Answer:
θ = 60.34
Step-by-step explanation:
\(\frac{\left(12.8\cdot \:sin\left(90\right)\right)}{sin\left(52.3\right)}\) = 16.177
\(\frac{\left(16.177\cdot \:sin\left(90\right)\right)}{18.6}\) = θ = .869
\(arcsin\left(.869\right)\) = 60.34
Answer:
60.4°
Step-by-step explanation:
There are two right triangles.
One right triangle (on the left side) has an acute angle measuring 52.3°.
Its opposite leg measures 12.8 cm.
We can find the length of its hypotenuse, x.
sin 52.3° = opp/hyp
sin 52.3° = 12.8 cm/x
x * sin 52.3° = 12.8 cm
x = 12.8 cm/sin 52.3°
x = 16.2 cm
Now we use the hypotenuse of the left side triangle which is a leg of the right side triangle.
For the right side triangle, we are looking for angle Θ. We know the opposite leg, 16.2 cm and the hypotenuse, 18.6 cm.
sin Θ = opp/hyp
sin Θ = 16.2/18.6
sin Θ = 0.8698
Θ = sin^-1 0.8698
Θ = 60.4°
How do you step by step solve the equation n(n+2) = 0
Answers
Answer: n = 0 and -2
Step-by-step explanation:
Equate the expressions to zero
n(n+2) = 0
n = 0 and n+2 = 0
n = 0 and n = -2
The figure below is divided into 100 squares of equal size.
What percent of the figure is shaded?
Answers
Answer:
36%
Step-by-step explanation:
If there are 100 squares of equal size
There are 36 squares that are shaded
36 out of 100 as a percentage is 36%
Answer:
36%
Step-by-step explanation:
First, count how many squares there are. There are 36 shaded squares according to my count.
Then, since we are trying to find what percent 36 is out of 100, we divide the part (P) by the total (T).
36/100= 0.36
Multiply that number by 100 and you have your percentage!
use trigonometric identities to find general solutions of the equation.
y'' + 9y = sin^4x
The general solution is y(x) = ....
Answers
The general solution to the given differential equation y'' + 9y = sin^4x can be expressed as y(x) = Asin(3x) + Bcos(3x) - (1/192)*(3x + sin(6x)), where A and B are arbitrary constants.
Explanation:
To find the general solution, we can start by considering the homogeneous equation y'' + 9y = 0, which has the characteristic equation r^2 + 9 = 0. Solving this equation, we get the roots r = 3i and -3i. Therefore, the homogeneous solution is y_h(x) = Asin(3x) + Bcos(3x), where A and B are constants.
Next, we need to find a particular solution to the non-homogeneous equation y'' + 9y = sin^4x. Since the right-hand side contains a trigonometric function, we can use the method of undetermined coefficients and assume a particular solution of the form y_p(x) = C*(3x + sin(6x)), where C is a constant to be determined.
Taking the derivatives and substituting into the differential equation, we find that C = -1/192. Therefore, the particular solution is y_p(x) = -(1/192)*(3x + sin(6x)).
Finally, the general solution is obtained by combining the homogeneous and particular solutions: y(x) = y_h(x) + y_p(x) = Asin(3x) + Bcos(3x) - (1/192)*(3x + sin(6x)), where A and B are arbitrary constants.
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