We are given the following information
sin u = 5/13
cos v = -3/5
Where the angle u and v are in the 2nd quadrant.
[tex]\begin{gathered} \cos\theta=\frac{adjacent}{hypotenuse} \\ \sin\theta=\frac{opposite}{hypotenuse} \end{gathered}[/tex]Let us find cos u
Apply the Pythagorean theorem to find the 3rd side.
[tex]\begin{gathered} a^2+b^2=c^2 \\ a^2=c^2-b^2 \\ a^2=13^2-5^2 \\ a^2=169-25 \\ a^2=144 \\ a=\sqrt{144} \\ a=12 \end{gathered}[/tex]Cos u = 12/13
Now, let us find sin v
Apply the Pythagorean theorem to find the 3rd side.
[tex]\begin{gathered} a^2+b^2=c^2 \\ b^2=c^2-a^2 \\ b^2=5^2-(-3)^2 \\ b^2=25-9 \\ b^2=16 \\ b=\sqrt{16} \\ b=4 \end{gathered}[/tex]Sin v = 4/5
Recall the formula for sin (A - B)
[tex]\sin(A-B)=\sin A\cos B-\cos A\sin B[/tex]Let us apply the above formula to the given expression
[tex]\begin{gathered} \sin(u-v)=\sin u\cdot\cos v+\cos u\cdot\sin v \\ \sin(u-v)=\frac{5}{13}\cdot-\frac{3}{5}+\frac{12}{13}\cdot\frac{4}{5} \\ \sin(u-v)=\frac{33}{65} \end{gathered}[/tex]Therefore, sin (u - v) = 33/65
A cart weighing 200 pounds rests on an incline at an angle of 40°. What is the required force to keep the cart at rest? Round to the thousandths place.
Given:
There are given that the car weighed 200 pounds on an incline at an angle of 40 degrees.
Explanation:
To find the required force, first we need to draw the triangle.
So,
Now,
We need to find the value for x:
So,
To find the value for x, we need to use the sine function.
Then,
[tex]sin40=\frac{x}{200}[/tex]Then,
[tex]\begin{gathered} s\imaginaryI n40=\frac{x}{200} \\ x=sin40^{\circ}\times200 \\ x=128.5575 \\ x=128.558 \\ \end{gathered}[/tex]Final answer:
Henc
Answer:
128.558
Step-by-step explanation:
Graph the equation Y =7x
The graph of the equation y =7x is shown below.
To find the slope and y-intercept, use the slope-intercept form.
y = m x + b is the slope-intercept form, where m is the slope and b is the y-intercept.
We are given y = 7x.
Determine the values of m and b using the formula y = m x + b.
m = 7
b = 0
The value of m is the slope of the line, and the value of b is the y-intercept.
Slope: 7
y-intercept: (0, 0)
Also, other ordered pairs will be (1, 7), (-1, -7), etc.
Now let's draw the graph:
Thus, the graph of the equation y =7x is shown above.
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Suppose y varies directly with x, and y=6 when x=-2. Find x when y=9
The fact that y varies directly with x means that they have a relation like:
[tex]y=kx[/tex]Where k can be any number. We know that y=6 when x=-2 which means that k is given by:
[tex]\begin{gathered} y=kx \\ 6=-2k \\ \frac{6}{-2}=k \\ k=-3 \end{gathered}[/tex]Then if y=9 we get:
[tex]\begin{gathered} y=-3x \\ 9=-3x \\ \frac{9}{-3}=x \\ x=-3 \end{gathered}[/tex]So x=-3 when y=9.
Rationalize the denominator of the fraction below. What is the newdenominator?
To rationalize the denominator we have to multiply it by the conjugate, as follows:
[tex](3+\sqrt{6})(3-\sqrt{6})=3^2-(\sqrt{6}\rparen^2[/tex]The latter considering the property (a-b)(a+b)=a^2-b^2.
Finally we have:
[tex]3^2-6=9-6=3[/tex]The the answer is D. 3
Melissa and brain are at the base of a mountain.melissa hikes to a location 27 meters above sea level.brain hikes to a location 21 meters below sea level. what us the diffrence if the hikers altitudes?
The point at the base of the mountain is described as point zero, that is they are still at sea level. If Melissa now moves to a position 27 metres above sea level, that is positive 5, assuming we are now measuring along a vertical number line. Brian however moves to a location which is 21 metres below sea level, or negative 21 along the vertical number line. Since we are measuring distances, the distance from point zero to both hikers' new position will be measured in absolute values only, that is both distances will be measured as positive.
Hence the distance between Melissa and Brian is;
Distance = 27 + 21
Distance = 48
The difference in altitude between both hikers is 48 metres
Find the slope intercept equation of the line that has the given characteristics. Slope 1.3 and y intercept (0,-6)
We want to find the equation of the line in slope intercept form with the following values.
Slope = 1.3 and y-intercept ( 0, -6)
The equation of a line with slope m and y intercept (0,c) is;
[tex]y=mx+c[/tex]Thus, the equation of the line is;
[tex]y=1.3x-6[/tex]Select the correct answer from each drop-down menu.Given: and Prove:
Answer:
Given that,
[tex]GH\cong JH[/tex]GH and JH are congruent.
[tex]IG\cong IJ[/tex]IG and IJ are congruent.
The third side of the triangle GHI is HI and also for the triangle JHI is HI
HI is common for both the triangle GHI and triangle JHI.
we get,
[tex]HI\cong HI[/tex]By using SSS congrurnce criteria: SSS (Side – Side – Side) Congruence. If the three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.
we conclude that,
[tex]\Delta GHI\cong\Delta JHI[/tex]Hence proved.
Risky drivers: An automobile insurance company divides customers into three categories: good risks, medium risks, and poor risks. Assume that of a total of 11,210 customers, 7761 are good risks, 2499 are medium risks, and 950 are poor risks. As part of an audit, one customer is chosen at random. Round youranswers to four decimal places if necessary.Part 1 of 2(a) What is the probability that the customer is a good risk?The probability that the customer is a good risk isXŚPart: 1/2Part 2 of 2(b) What is the probability that the customer is not a poor risk?The probability that the customer is not a poor risk isXŚ
Given data:
Total: 11210
7761 good risk
2499 medium risk
950 poor risk
a) Probability of choose a customer with good risk (gr):
[tex]P(gr)=\frac{#customer\text{ }gr}{#total}=\frac{7761}{11210}=0.6923[/tex]Th eprobability that the customer is a good risk is 0.6923b) Probability that a customer is not a poor risk (pr):
[tex]P(no\text{ }pr)=1-P(pr)=1-\frac{#custormer\text{ }pr}{#total}=1-\frac{950}{11210}=\frac{11210-950}{11210}=\frac{10260}{11210}=0.9153[/tex]The probability that the customer is not a poor risk is 0.9153If y varies directly with x,and y is 14when x is 2,what is the value of x when y is 35
x=5
1) Since y varies directly with x, then we can write a table
x | y
2 14
35
2) Since y is 7 times the value of x, then we can state that
x | y
2 14
5 35
3) So this variation can be expressed as y=7x and x=5
I’m stuck I don’t know what I’m doing at all help me out??
Point: (x,y) = (-4,8)
We have to graph the point and set a vertical line.
Line equation:
x= -4
For any value of x, it always will be -4.
Graph the inequality.3x+4y>4
Given the inequality equation below:
[tex]3x+4y>4[/tex]Find the y-intercept
[tex]\begin{gathered} set\text{ x=0} \\ 3x+4y=4 \\ 3(0)+4y=4 \\ 4y=4 \\ y=\frac{4}{4}=1 \\ y-intercept\rightarrow(0,1) \end{gathered}[/tex]Find the x-intercept
[tex]\begin{gathered} set\text{ y=0} \\ 3x+4y=4 \\ 3x+4(0)=4 \\ 3x=4 \\ x=\frac{4}{3} \\ x-intercept\rightarrow(\frac{4}{3},0) \end{gathered}[/tex]Find the shaded area
[tex]\begin{gathered} set\text{ x=0, and y=0} \\ 3x+4y>4 \\ 3(0)+4(0)>4 \\ 0+0>4 \\ 0>4\rightarrow false \\ Shade\text{ the side of the line where \lparen0,0\rparen is not includedand use dot line} \end{gathered}[/tex]Hence, the graph is
The Lofoten Islands in Norway (one of Mr. Maier's favorite places) has a latitude of 68.4711 ° north of the equator. What is the linear speed as the earth rotates at that latitude? Use 3961.3 miles for the radius of the earth.
The equations are the linear velocity and angular moment respectively.
Since we have that the rotation of the Earth takes 24 hours, we transform it into seconds, that is:
[tex]24\cdot60\cdot60=86400[/tex]So, it has a period of 86400 seconds.
We now, transform the radius to the IS (from miles to meters), that is:
[tex]3961.3\text{miles}=6375.1\operatorname{km}[/tex]And, since the latitude is 68.4711° we solve in the function given at the start, that is:
[tex]w=\frac{2\pi}{86400}\Rightarrow w=7.272205217\cdot10^5[/tex]Then we divide this value by the time it takes to do a revolution of the Earth, the previously calculated 86400 seconds, that is:
[tex]v=wr\Rightarrow w=(7.272205217\cdot10^{-5})(6375.1)[/tex][tex]\Rightarrow v\approx0.464[/tex]So, the linear velocity at that latitude is approximately 0.464 Km/s.
Error Analysis A store is instructed by corporate headquarters to put a markup of 11% on all items. Anitem costing $18 is displayed by the store manager at a selling price of $2. As an employee, you noticethat this selling price is incorrect. Find the correct selling price. What was the manager's likely error?The correct selling price is $ ). (Round to the nearest dollar as needed)Enter your answer in the answer box and then click Check Answer
The item cost $18 and the selling prices must aim a markup os 11%
Therefore, the selling price of this item should be 1.11*18 = $19.98
Rounding to the nearest dollar, the price should be $20
Then, the manager's likely error was doesn't display the "0" algarism for the selling price.
Graph the function for the given domain.-2x - 10y = 10 , D: (-5, 0, 5, 10)
In order to graph the function, we need first to find the coordinates of the points. To do so, we need to apply the values of x given in the domain and calculate the corresponding values of y. So we have that:
[tex]\begin{gathered} x=-5\colon \\ -2\cdot(-5)-10y=10 \\ 10-10y=10 \\ -10y=0 \\ y=0 \\ \\ x=0\colon \\ -2\cdot(0)-10y=10 \\ -10y=10 \\ y=-1 \\ \\ x=5\colon \\ -2\cdot(5)-10y=10 \\ -10-10y=10 \\ -10y=20 \\ y=-2 \\ \\ x=10\colon \\ -2\cdot(10)-10y=10 \\ -20-10y=10 \\ -10y=30 \\ y=-3 \end{gathered}[/tex]So the points are (-5, 0), (0, -1), (5, -2) and (10, -3).
Graphing these points, we have that:
the following table represents the probability distribution of the number of vacations X taken last year for a randomly chosen family. compute the standard deviation
We have to use the formula for standard deviation of a probability distribution:
[tex]\sigma=\sqrt[]{\sum^{}_{i\mathop=0}(x_i-\mu)^2\cdot P(x_i)}[/tex]x P(x) x*P(x) (xi - μ)^2*P(x)
0 0.11 0 0.180
1 0.64 0.64 0.050
2 0.13 0.26 0.067
3 0.1 0.3 0.296
4 0.02 0.08 0.148
The expected value μ would be the sum of the values of the third column of the table.
Therefore μ = 1.28
The sum of the values of the fourth column would be: 0.7416
Taking the square root of the last value, we have: 0.861
The answer is option D
A car is traveling at a steady speed. It travels 1 1/2 miles in 2 1/4 minutes. How far will it travel in 47 Minutes ? In 1 hour ?The car will travel ( blank) miles in 47 minutes (Simplify your answer. Type an integer, proper fraction, or mixed number.)
1 1/2 miles ---> 2 1/4 minutes
x miles -------> 47 minutes
[tex]\begin{gathered} x\times2\frac{1}{4}=1\frac{1}{2}\times47 \\ x\times\frac{9}{4}=\frac{3}{2}\times47 \\ \frac{9}{4}x=70.5 \\ \frac{9}{4}x\times\frac{4}{9}=70.5\times\frac{4}{9} \\ x=\frac{94}{3}=31\frac{1}{3} \end{gathered}[/tex]answer: 31 1/3 miles in 47 minutes
for 1 hour = 60 minutes
[tex]\begin{gathered} \frac{9}{4}x=\frac{3}{2}\times60 \\ \frac{9}{4}x=90 \\ \frac{9}{4}x\times\frac{4}{9}=90\times\frac{4}{9} \\ x=40 \end{gathered}[/tex]answer: 40 miles in 1 hour
Answer:
1 1/2 miles ---> 2 1/4 minutes
x miles -------> 47 minutes
answer: 31 1/3 miles in 47 minutes
for 1 hour = 60 minutes
answer: 40 miles in 1 hour
Step-by-step explanation:
(a) Ivanna is driving on the freeway at a constant speed. She then speeds up to pass a truck. After passing the truck, she exits the freeway and slowsdown.SpeedSpeedSpeedSpeedTimeTimeTimeTimeOO
Ok, so
Ivanna is driving on the freeway at a constant speed. She then speeds up to pass a truck. After passing the truck, she exits the freeway and slows
down.
Notice that if the speed is constant, that means that the speed won't increase or decrease its value.
Then, the proper graph could be:
And the correct answer for (a) is c.
Now, the sight-seeing ship is stopped in the water for an hour. This means that it didn't change its distance. Then, the captain heads the ship back to the shore at a constant rate, which means that the distance to the shore is 0. The ship stays there for a while and then returns to the open sea.
Now, the correct graph will be:
The correct option is a.
Which undefined geometric term is described as an infinite set of points that has length but not width?distancelineplanesphere
A line (option B)
Explanation:
A line contains an infinite number of points. It has no width. It is one dimentional.
A plane has is two dimentional. Hence it has awidth and length.
The correct answer is a line
You spin the spinner twice.5243What is the probability of landing on a number less than 3 and then landing on a 5?Simplify your answer and write it as a fraction or whole number.Submit
To get the probability of an event, we need two things:
1. The total number of possibilities
2. The total number of possibilities considered favorable
For the first event A which is landing on a number less than 3, we only have one favorable possible which is landing on 2.
For the second event B which is landing on a 5, we also only have one favorable possible which is landing a 5 itself.
Now, for both events, the total number of possibilities is 4.
So, the probability of landing on a number less than 3 is 1/4 while the probability of landing on a 5 is also 1/4.
So, the probability of landing on a number lesser than 3 AND landing on a 5 is:
[tex]P(A\text{ }and\text{ }B)=P(A)\times P(B)[/tex][tex]P(A\text{ }and\text{ }B)=\frac{1}{4}\times\frac{1}{4}[/tex][tex]P(A\text{ }and\text{ }B)=\frac{1}{16}[/tex]Answer:
The probability of landing on a number lesser than 3 AND landing on a 5 on the next spin is 1/16.
6-4x=6x-8x-8. what does x =
Start by balancing it out.
First +4x to both sides:
6=6x-4x-8
Then +8 to both sides:
14=6x-4x
As 6x-4x=2x
14=2x
Finally, divide both sides by 2:
7=x
So, the answer is x = 7
Sam is paid $50 per room that he paint and he paint room in exactly two hours on sunday sam hopes to make at least $150 painting rooms and can work for exactly 10 hours which of the following sets represents the range of hours H that Sam can work without violating his monetary or restriction
Since Sam can paint 5 rooms in 10 hours, since:
[tex]\frac{10\text{hours}}{2\text{hours}}=5\text{ rooms}[/tex]then Sam would have to paint at least 3 rooms to make $150.
The range of hours would be from 6 to 10 hours, since 3 rooms takes 6 hours to paint.
Stephan owns a landscaping company. Today, he is mowing three lawns: one is of an acre, one is į of an acre, and oneis 14 acres. How many acres of lawn is Stephan going to mow today? Simplify your answer and write it as a mixedfraction if necessary.21 acres
The acres of lawn mowed by Stephen is the total of the fractions of each of the mowed lawns.
Thus, we have:
[tex]\frac{1}{4}+\frac{1}{2}+1\frac{1}{3}[/tex]Simplifying the fraction above, we have:
[tex]\begin{gathered} \frac{1}{4}+\frac{1}{2}+\frac{4}{3} \\ \text{The L.C.M of 4, 2 and 3 is 12} \\ \text{Thus, we have:} \\ \frac{3+6+16}{12}=\frac{25}{12} \\ 2\frac{1}{12} \end{gathered}[/tex]Hence, the correct option is Option A.
A projectile is launched upward with a velocity of 288 feet per second from the top of a 35-foot platform. What is the maximum height attained by the projectile?
The maximum height attained by the projectile is 403.79 meters = 1324.77 feet.
The height formula has the following formula:
h = h₀ + v₀t - gt²/2
In which h₀ is the initial height, v₀ is the initial speed and g = 9.8 m/s² is the gravity.
Given, We are working with the gravity in meters, so we must convert the feet measures to meters.
Each feet has 0.3048 meters.
So 288 feet per second = 87.78 meters per second.
35 foot = 10.66 meters.
This means that:
h₀ = 10.66, v = 87.78
so,
h(t) = 10.66 + 87.78 - 4.9t²
The maximum height is attained at the moment of time in which the velocity is 0. The velocity is the derivative of the height. So:
v(t) = h'(t) = -9.8t+87.78
v(t) = 0
9.8t = 87.78
t = 8.96
The maximum height is attained at 8.96s. This height is
h(t) = 10.66 + 87.78t - 4.9t²
h(8.96) = 10.66 + (87.78×8.96) - (4.9×(8.96)²)
= 10.66 + 786.50 - 393.37
= 403.79 m
The maximum height attained by the projectile is 403.79 meters = 1324.77 feet.
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John takes out a loan for $ 12 , 000 at a simple interest rate of 5% to be paid back in 36 monthly installments. What is the amount of the monthly payments?CORRECTION: The interest rate is 7.9%.
From the statement, we know that:
• John takes a loan for A₀ = $12,000,
,• at a simple interest rate of r = 7.9% = 0.079per year,
,• to be paid back in 36 monthly instalments.
1) The total amount to be paid is given by:
[tex]A=A_0\cdot(1+r\cdot n_{years})=\text{\$12,000}\cdot(1+0.079\cdot3)=\text{\$14,844.}[/tex]2) The monthly payments are given by:
[tex]m=\frac{A}{n_{months}}=\frac{\text{\$14,844}}{36}\cong\text{\$412.33.}[/tex]AnswerThe monthly payments are $412.33.
7. Quinn had 3 more than two times the number of marbles Rowan has. Together they have 77marbles. How many marbles does each child have?
Explanation:
Let the number of marbles Rowan has = x
Two times x = 2x
3 more than two times the number of marbles Rowan has = 2x + 3
Quinn = 2x + 3
Together they have = 77 marbles
Rowan marbles + Quinn marbles = 77
x + (2x + 3) = 77
x + 2x + 3 = 77
Collect like terms:
3x = 77-3
3x = 74
Divide through by 3:
x = 74/3
x = 24.7
sean is given a solution in which the population of a family of rabbits grows according to he equation....
No, the problem is not asking for
Here, we simply want to check if the method used is correct to find the number of months it will take for the population of Rabbits to be 500
The method used in this case is wrong
What should have been done is to substitute the value of 500 for y
Afterwards, we can proceed to find the value of t which is the number of months using technology
So the correct answer is the second option
and your while you have the following paper money 7 singles 352 tens + 620 is what is the probability of a fraction you would draw a 5 and then a 20
You have 7 ones
3 fives
2 tens
6 twenties
This is a total of 7+3+2+6 = 18 bills
First we want to know the probabilitity that you will draw a five
P(five dollar bill) = number of fives/ total = 3 / 18 = 1/6
Now we have 7 ones
2 fives
2 tens
6 twenties
This is a total of 7+2+2+6 = 17 bills left ( assuming you get to keep the bill)
Now we want to know the probability of getting a twenty dollar bill
P( twenty dollar bill) = number of twenties / total = 6/ 17
Multiply the probabilities together
1/6 * 6/17 = 1/17
The probability of getting a five and then a twenty is 1/17
The sale price S (in dollars) of an item is given by the formula S=L-rL, where L is the list price (in dollars) and r is the discount rate (in decimal form).Solve the equation for r.
ANSWER
[tex]r=1-(\frac{S}{L})[/tex]EXPLANATION
Given;
[tex]S=L-rL[/tex]To make r the subject of formula, flip the equation
[tex]rL=L-S[/tex]Divide both sides by L;
[tex]\begin{gathered} \frac{rL}{L}=\frac{L-S}{L} \\ r=\frac{L-S}{L} \\ =\frac{L}{L}-\frac{S}{L} \\ =1-\frac{S}{L} \end{gathered}[/tex]need help with geometry problem number 12 ( ignore my writing )
Given
Height of man = 6ft
Shadow of man = 9ft
Shadsw of building = 322.5ft
Find
Height of building
Explanation
At a particular time in the day the proportion of the shadow of man will be equal to that of the building
So triangle ABC will be similar to PQR
Hence the ratio of their corresponding sides will be equal
[tex]\begin{gathered} \frac{AB}{BC}=\frac{PQ}{QR} \\ \frac{6}{9}=\frac{PQ}{322.5} \\ PQ=322.5\times\frac{2}{3} \end{gathered}[/tex]Therefore,
PQ = 215ft
which is the required length
Final Answer
The height of the building is 215ft
Find the difference Colton of earth that is fine for the following function
GIven:
[tex]f(x)=-5x+7[/tex]Required:
To find the value of
[tex]\frac{f(x+h)-f(x)}{h},h\ne0[/tex]Explanation:
To find the value of f(x+h) we have to substitute (x+h) in the function f(x) instead of 'x'
The simplify with the given question.
[tex]\begin{gathered} f(x+h)=-5(x+h)+7_{} \\ =-5x-5h+7 \end{gathered}[/tex]Simplifying for the value,
[tex]\begin{gathered} \frac{f(x+h)-f(x)}{h}=\frac{-5x-5h+7-(-5x+7)}{h} \\ =\frac{-5x-5h+7+5x-7}{h} \\ =\frac{-5h}{h} \\ =-5 \end{gathered}[/tex]Final Answer:
[tex]\frac{f(x+h)-f(x)}{h}=-5[/tex]