The speed in miles per hour is 111.2 and the direction angle in degrees is 260.2.
We are given the speed of a plane on a bearing of N [tex]75^\circ[/tex] E and its ground speed. We have to find its speed in miles per hour and the direction angle in degrees. We will apply the formula of projection for both the x-axis and y-axis.
As we know, projection, R = V + W
Now, the x-axis projection will be R cos[tex]15^\circ[/tex] according to the angle given to us. Therefore, R cos [tex]15^\circ[/tex] = V cos[tex]30^\circ[/tex] + [tex]W_{x}[/tex]
The y-axis projection,
R sin [tex]15^\circ[/tex] = V sin [tex]30^\circ[/tex] + [tex]W_{y}[/tex]
From here, now we will find [tex]W_{x}{[/tex] and [tex]W_{y}[/tex]
[tex]W_{x}{[/tex] = 330 cos[tex]15^\circ[/tex] - 390 cos[tex]30^\circ[/tex]
[tex]W_{x}[/tex] = -19 miles/hour
[tex]W_{y}[/tex] = 330 sin[tex]15^\circ[/tex] - 390 sin[tex]30^\circ[/tex]
[tex]W_{y}{[/tex] = -109.6 miles per hour
Now, W = [tex]\sqrt{(W_{x})^{2} + (W_{y})^{2{}}[/tex]
W = [tex]\sqrt{(-19.0)^{2} + (-109.6})^{2{}}[/tex]
W = 111.2 miles/hour
Now, we will find the angle with the help of tan θ.
tan θ = [tex]\frac{W_{y}}{W_{x}}[/tex]
tan θ = [tex]\frac{-109.6}{-19.0}[/tex]
θ = [tex]tan ^{-1} (\frac{109.6}{19.0})[/tex]
θ = 260.[tex]2^\circ[/tex]
Therefore, the speed in miles per hour is 111.2 and the direction angle in degrees is 260.2.
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help this assignment is already past due
The decimals as a power of 10 are given as follows:
Decimal: [tex]1 x 10^{-1}[/tex]Centimeter: [tex]1 x 10^{-2}[/tex]Millimeter: [tex]1 x 10^{-3}[/tex]Micrometer: [tex]1 x 10^{-6}[/tex]What is scientific notation?A number in scientific notation is given by the notation presented as follows:
[tex]a \times 10^b[/tex]
With the base being [tex]a \in [1, 10)[/tex], meaning that it can assume values from 1 to 10, with an open interval at 10 meaning that for 10 the number is written as 10 = 1 x 10¹, meaning that the base is 1, justifying the open interval at 10.
Hence the numbers are represented as follows:
Decimal: [tex]1 x 10^{-1}[/tex] -> the one is the first decimal digit.Centimeter: [tex]1 x 10^{-2}[/tex] -> the one is the second decimal digit.Millimeter: [tex]1 x 10^{-3}[/tex] -> the one is the third decimal digit.Micrometer: [tex]1 x 10^{-6}[/tex] -> the one is the sixth decimal digit.More can be learned about scientific notation at https://brainly.com/question/5756316
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An angle measures 132 . What is the measure of its supplement
Answer: 48
Step-by-step explanation:
180-132=48
Answer:
48
Step-by-step explanation:
angle = 132
supplementary angle = 180
measure of supplementary angle = 180 - 132 = 48
thus the measure of the supplement is 48
hope you got your answer.
HELP PLEASE
at big 5, the percent of sales tax is 6 percent. you want to buy a skateboard that costs 98 dollars. you have 100 dollars to spend. do you have enough money? if you don't, how much more money would you need in order to buy the skateboard.
You would need an additional $3.88 to buy the skateboard.
To find out if you have enough money to buy the skateboardWe need to calculate the total cost, including sales tax.
The sales tax rate is 6%, so the tax on a skateboard costing $98 would be as follows:
tax = 0.06 x $98 = $5.88
Consequently, the skateboard would have a total cost of:
total cost = $98 + $5.88 = $103.88
Since you have $100 to spend, you do not have enough money to buy the skateboard. You would need:
additional money = $103.88 - $100 = $3.88
Therefore, you would need an additional $3.88 to buy the skateboard.
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please guys i need help
[tex][D]= \begin{bmatrix} 5&0&-8\\ 10&-2&7\\ -3&-9&6 \end{bmatrix}\implies 2[D] \stackrel{ \textit{scalar multiplication} }{\begin{bmatrix} (2)5&(2)0&(2)-8\\ (2)10&(2)-2&(2)7\\ (2)-3&(2)-9&(2)6 \end{bmatrix}} \\\\\\ ~\hspace{12.5em} 2[D]= \begin{bmatrix} 10&0&-16\\ 20&-4&14\\ -6&-18&12 \end{bmatrix}[/tex]
will mark as brainlist is answer correct. which meauser of center is the most appropriate answer for table two. pls give a reason. 25 points.
The meauser of center is the most appropriate answer for table two is the mean.
How to explain the meanMean, in terms of math, is the total added values of all the data in a set divided by the number of data in the set.
Each mean serves to summarize a given group of data, often to better understand the overall value of a given data set. Pythagorean means consist of arithmetic mean, geometric mean, and harmonic mean
It is the mean because all of the data points are fairly close and there aren't any outliers (extreme values).
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Which linear equation is represented in the graph?
A. y = 2x – 1
B. y = –2x – 1
C. y = –2x + 1
D. y = 2x + 1
Help me with this question please
Answer:
[tex]c. 1/5[/tex]
Step-by-step explanation:
You have the points (-5, 0) and (0, 1).
To find the slope, b, of the original line, you can use the formula [tex](y_{1}-y_2) /(x_1-x_2)[/tex].
[tex]b = (0-1)/(-5-0) = -1/-5 = 1/5.[/tex]
The slope of a line parallel to the original line would have the same slope as the original line, therefore [tex]1/5.[/tex]
A list contains the names of six anthropology students, two sociology students, and four psychology students. If one name is selected at random to assist in the professor's new study, find the probability that the chosen student is
P(anthropology)=
help pls I don't understand it bc I'm not smart
Answer: the answer to be smart is to learn
Step-by-step explanation:
if you learn then you can understand the u are not smart
100 Points!!! Algebra question. Use synthetic substitution to find f(-3) and f(4) for 3x^4-4x^3+3x^2-5x-3. Please show as much work as possible. Photo attached. Thank you!
The mapping of the function f(x) given as 3x⁴ - 4x³ + 3x² - 5x - 3 is define at;
-3, f(-3) = 390 and at 4, f(4) = 537
What is a functionA function is a rule that defines a relationship between one variable. It is the mapping whose codomain is the set of real numbers
By substitution:
For x = -3;
f(-3) = 3(-3)⁴ - 4(-3)³ + 3(-3)² - 5(-3) - 3
f(-3) = 3(81) + 4(27) + 3(9) + 15 - 3
f(-3) = 243 + 108 + 27 + 15 - 3
f(-3) = 390
For x = 4;
f(4) = 3(4)⁴ - 4(4)³ + 3(4)² - 5(4) - 3
f(4) = 3(256) - 4(64) + 3(16) - 20 - 3
f(4) = 768 - 256 + 48 - 20 - 3
f(4) = 537
Therefore, the mapping of the function f(x) = 3x⁴ - 4x³ + 3x² - 5x - 3 for the values of x: -3 and 4 we have the results 390 and 537 respectively.
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Help please Jared uses two theorems together to make a conjecture about the sum of the interior angles of pentagons. What kind of reasoning is Jared using?
A)Inductive Reasoning
B)Deductive Reasoning
If Jared uses two theorems together to make a conjecture about the sum of the interior angles of pentagons, Jared is using deductive reasoning. Correct option is B.
Deductive reasoning is a logical process in which a conclusion is reached by applying general principles or known information to specific situations. In this case, Jared is using two theorems, which are general principles that have been proven to be true, to make a conclusion about a specific situation, the sum of interior angles of pentagons.
The conclusion that Jared makes is a conjecture, which is a hypothesis or a tentative conclusion that is based on limited evidence or observation.
In contrast, inductive reasoning is a logical process in which a conclusion is reached based on a series of observations or specific instances. Inductive reasoning involves making generalizations based on specific observations, which can lead to a hypothesis or a theory.
Therefore, Jared's use of two theorems to make a conclusion is an example of deductive reasoning. Correct option is B.
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Help me please man, I’m stuck
The value of function g (5) is,
⇒ g (5) = 30/13
We have to given that;
Function is,
g (x) = {(x² + 5) / (x + 8) if x ≠ - 8
= { x - 1 ; if x = - 8
Hence, The value of function g (5) is,
⇒ g (5) = (x² + 5) / (x + 8)
⇒ g (5) = (5² + 5) / (5 + 8)
⇒ g (5) = (30) / (13)
Thus, The value of function g (5) is,
⇒ g (5) = 30/13
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Help please Given the diagram below, what statement could you make about the relationship between angles 1 and 4?
A) ∠1 is congruent to ∠4.
B) m∠1 is greater than m∠4.
C) m∠1 is less than m∠4.
D) ∠1 and ∠4 cannot be determined.
Answer:
A) angle 1 is congruent (equal size) to angle 4.
Step-by-step explanation:
when 2 lines intersect, then the intersection angles are the same on both sides of any of the lines. they are only left-right mirrored.
Answer:
A) angle 1 is congruent (equal size) to angle 4.
Step-by-step explanation:
please help me quick on this math work, here is the screenshot what answer should I put? please help quick and right answers only!!
The functions that have a range of all real numbers include the following:
Option 1; f(x) = -x + 2
Option 3; [tex]h(x) = 2^x +1[/tex]
What is a range?In Mathematics and Geometry, a range can be defined as the set of all real numbers that connects with the elements of a domain.
Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following range for f(x) and h(x):
Range = {-∞, ∞}, y|y ∈ R, or all real numbers.
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Choose as many answers as apply. Which are stated goals for this class? Explain the basics of home mortgages. Increase your knowledge of consumer applications and personal financial management. O Help students develop their ability to apply math concepts to real-world problems. Provide students with the tools to plan for retirement.
The following are stated goals for this class:
1. Help students develop their ability to apply math concepts to real-world problems.
2. Increase your knowledge of consumer applications and personal financial management.
3. Explain the basics of home mortgages.
These goals are aimed at providing students with practical skills and knowledge that can be applied to their everyday lives, such as managing personal finances, understanding the mortgage process, and planning for retirement.
By learning math concepts in the context of real-world situations, students are better equipped to make informed decisions and solve problems that they may encounter in their personal and professional lives.
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Patrick spent last summer working in construction with his dad, and he put of his earnings into a new high-yield savings account. The money in this savings account will increase by each . Write an exponential equation in the form Patrick's account, , after starting the account. that can model the amount of money in Use whole numbers, decimals, or simplified fractions for the values of and . □ \frac {\square }{\square } (\square ) If Patrick makes no other deposits or withdrawals, after how many will his account have more than ? Submit
a) An exponential equation in the form of y = a(b)ˣ that can model the amount of money (future value) in Patrick's account, y, x years after starting the account is y = 894(1.02)ˣ.
b) If Patrick makes no other deposits or withdrawals, after 5 years or approximately 6 years his account will have more than $1,000 (future value).
What is an exponential equation?An exponential equation is a mathematical function, written in the form of y = a(b)ˣ, where y is the ending value, a is the initial value, b is the growth or decay rate, and x is the exponent or number of years.
Thus, there are two types of exponential functions: exponential growth and exponential decay functions.
y = 894(1.02)^6
1,000 ≤ 894(1.02)ˣ
I/Y (Interest per year) = 2%
Present Value = $894
FV (Future Value) ≥ $-1,000
Results:
x = 5.658
x ≈ 6 years
= $1,006.79
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Complete Question:Patrick spent last summer working in construction with his dad, and he put $894 of his earnings into a new high-yield savings account. The money in this savings account will increase by 2% each year.
a) Write an exponential equation in the form of y = a(b)ˣ that can model the amount of money in Patrick's account, y, x years after starting the account. Use whole numbers, decimals, or simplified fractions for the values of a and b.
y =
b) If Patrick makes no other deposits or withdrawals, after how many years will his account have more than $1,000?
does a number being squared with x and being negative make it so it has to be multiplied by 2 like the first number in the third part of the question? I'm unsure where it came from
Squaring a number implies increasing it by itself. In case the number being squared is negative, the result will continuously be positive. Increasing a number by 2 implies multiplying it, which is not linked to squaring a number.
What is the number about?To square a number, one must raise it to the power of two, that is different from carrying out its multiplication with itself. One way of squaring a value is shown by taking the number 3 and raising it to the power of 2.
3² = 3 x 3 = 9
By the same way , if we raise -2 to the power of 2, the result will be a positive value of four.
Raising numbers to the power of two is a frequent mathematical procedure use in numerous academic fields such as algebra, geometry, physics, and statistics.
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Solve the inequality then list 5 numbers that fit in the solution set_,_,_,_,_ 4 - 5g > 39
The values that fit in the solution are -4, -3, -2, -1 , 0
g > - 5
How to solve the inequalityInequalities are described as expressions that are used to represent an unequal relationship between numbers or variables.
They are represented with the symbols;
< is less than> represents the greater than≥ represents the greater than or equal≤ represents the less than or equal toFrom the information given, we have that;
4 - 5g > 39
collect the like terms, we get;
-5g > 39 - 4
subtract the values
-5g > 35
Divide by the coefficient of g, we get;
g > -5
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how many miles is 60,000 inches
Answer:
it is 0.94 miles
Step-by-step explanation:
that is because to make a mile you need 63,360 but since you have 60,000 it is not technically a mile
q
5cm
X =
X
8cm
4cm
cm
Answer:
2.5 cm
Step-by-step explanation:
The small arrow is 1/2 the side of the large arrow. 1/2 of 5 is 2.5 or 2 1/2.
Helping in the name of Jesus.
18. Name a pair of complementary angles in this figure.
Answer:
Step-by-step explanation:
Angle KEF and JEK
Answer:
∠DEH and ∠HEJ or∠JEK and ∠KEF----------------------------
Complementary angles are the angles that together form a right angle.
In the picture we see two right angles:
∠DEJ and ∠JEFThe first one, ∠DEJ has a pair of complementary angles:
∠DEH and ∠HEJThe second one, ∠JEF has a pair of complementary angles:
∠JEK and ∠KEF9. What is the volume of a rectangular prism with a length of 11 meters, width of 26 meters, and height of 38 meters?
Answer:
10868
Step-by-step explanation:
11x26=286
286x38=10868
PLEASE HELP WITH THE IMAGE!! ITS DUE TOMORROW
Answer:no image
Step-by-step explanation:
Step-by-step explanation:
No image is overe there please add the image
What is the probability that a random sample of 20 second grade students from the city results in a mean reading rate of more than 96 words per minute?
Answer:
Step-by-step explanation:
We can calculate the t-statistic and the p-value as follows:
If we assume that the null hypothesis is true, then the t-statistic will follow a t-distribution with 19 degrees of freedom. We can compare the calculated t-statistic with the critical t-value at the 0.05 level of significance using a t-distribution table or statistical software.
If the calculated t-statistic is greater than the critical t-value, then we can reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis that the population mean reading rate is greater than 96 words per minute.
The p-value is the probability of obtaining a t-statistic as extreme or more extreme than the calculated t-statistic, assuming the null hypothesis is true. We can use the t-distribution table or statistical software to find the corresponding p-value.
If the p-value is less than the significance level of 0.05, then we can reject the null hypothesis at the 0.05 level of significance and conclude that the probability of obtaining a random sample of 20 second grade students with a mean reading rate of more than 96 words per minute is statistically significant.
The same item is on sale at two stores. Which one is the better price? 60% off $60 or 55% off %50
Answer:
The item when it is costs $50 and there is a 55% item, as the cost would be $22.50
Step-by-step explanation:
Whenever a discount is offered on a certain item, we can find the new price of the item using the formula.
[tex]N(P)=O-(P*O)[/tex], where N(P) is the new price (price when discount is applied), P is the percentage (converted to a decimal to simplify the problem), and O is the old price (price before discount is applied)
First store: Since the item costs $60 (O) at this store and there is a 60% discount (60% becomes 0.60 and is our P value), we can find the new price aka N(P):
[tex]N(0.60)=60-(0.60*60)\\N(0.60)=60-36\\N(0.60)=24[/tex]
Second store: For this store, our O value is $50, and our P value is 0.55 (55% becomes 0.55):
[tex]N(0.55)=50-(0.55*50)\\N(0.55)=50-27.50\\N(0.55)=22.50[/tex]
Thus, the second store has the better price
At Atlas Auto Sales, 51 of the 204 cars for sale are minivans. What percent of the cars are
minivans?
Answer: 25%
Step-by-step explanation:
51/204=0.25
0.25 x 100 = 25
Answer:25%
Step-by-step explanation:
Alice purchased a car for $24,000. The value of the car depreciates at a rate of 5.5% each year.
Which function equation represents the value of the car after t years?
ANSWER IS: f(t)=24,000(0.945)t
just took the test
According to the given question, Alice should use this equation f(t) = [tex]24,000(0.945)^t[/tex] to represent the value of the car after t years.
Depreciation is defined by who?Depreciation is the expected decrease in the value of fixed assets over the course of a fiscal year. For physical assets like real estate, machinery, vehicles, and other items, large lump sum acquisitions are made.
The equation[tex]f(t) = 24,000(0.945)^t[/tex] represents the value of the car after t years, where 0.945 represents the remaining value of the car after one year of depreciation at a rate of 5.5%.
To calculate the value of the car after two years, for example, we would substitute t = 2 into the equation:
f(2) = [tex]24,000(0.945)^2[/tex]
f(2) = 24,000(0.893025)
f(2) ≈ 21,433.80
Therefore, the value of the car after two years would be approximately $21,433.80.
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Rewrite the cylinder volume formula to solve for r.
Answer:
[tex]v = \pi {r}^{2} h[/tex]
[tex] {r}^{2} = \frac{v}{\pi \times h} [/tex]
[tex]r = \sqrt{ \frac{v}{\pi \times h} } [/tex]
D is the correct answer.
If f(5)=-1 , write a corresponding ordered pair solution
Answer: (5, -1)
Step-by-step explanation:
format: f(x)
in f(5)=-1 x=5
also sometimes f(x) is called y so y= -1
put into ordered pair format
(5, -1)
A college student takes the same number of credits each semester. They had 19 credits when they started, and after 6 semesters, they had 67 credits. Which of these expresses the rate at which they is earning credits?
As per the given variables, the rate at which they earn credits is 8 credits per semester
Total number of credits = 19
Total number of semesters = 6
Credits after six semesters = 67
Calculating the change in credits -
Change in credits -
Credits after six semesters - Inital credits
= 67 - 19
= 48 credits
Total time = 6 semesters
Calculating the change in credits over the six semesters and dividing by the total time to get the pace at which the college student is acquiring credits.
Therefore, the rate at which the college student is earning credits is:
Rate = Change in credits / Total time
= 48 credits / 6 semesters
= 8 credits per semester
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