Answer:
The answer is d) 297000
Step-by-step explanation:
The stockholders' equity of a company represents the amount of money that will be returned to the accionists if all the assests will be liquidated and the compan'y debt will be paid. So to calculate the Swifty Corporation stockholders' equity at the end of the year you need to add all what enters to the company (assets and revenues) and substract all what goes out (liabilities, expenses and dividends).
- What enters?
The starting assets = $300.000Revenues = $633.000Total incomes = $300.000 + $633.000 = $933.000
- What goes out?
Liabilities = $240.000Expenses = $335.000Dividends = $ 61.000Total expenses = $240.000 + $335.000 + $61.000 = $636.000
Stockholders' equity = Total income - Total expenses
Stockholders' equity = $933.000 - $636.000 = $297.000
Amelia used 6 liters for gasoline to drive 48 kilometers How many kilometers did Amelia drive per liter? At that rate, how many liters does it take to drive 111 kilometer?
Amelia drive 8 kilometers per liter.
13.875 liters needs to drive 111 kilometers.
How many kilometers did amelia drive per liter ?Amelia used 6 liters for gasoline to drive 48 kilometers.
Here we have to find how many km she drive per liter.
Amelia used 6 liters to drive 48 kilometers
Amelia used 1 liter to drive 48/6 kilometers = 8 kilometers
Therefore, Amelia drive 8 kilometers per liter.
Now, to travel 8 kilometers, she needs 1 liter gasoline
To travel 1 kilometer, she needs 1/8 liter gasoline
To travel 111 kilometers, she needs 111/8 liters gasoline = 13.875 liters
Learn more about car problems here :
https://brainly.com/question/10658574
#SPJ2
find the are of the first one and the circumference of the second one :)
Answer:
area = π/16 in²circumference = (3/4)π inStep-by-step explanation:
The area formula is ...
A = πr²
When r = 1/4 in, the area is ...
A = π(1/4 in)² = π/16 in²
__
The circumference formula is ...
C = πd
When the diameter is 3/4 in, the circumference is ...
C = π(3/4 in) = (3/4)π in
Estimate the value of:
square root of 34
Answer:
d. √34 ≈ 5.82
Step-by-step explanation:
Both of choices B and D are valid calculations and should have resulted in the same estimate. Choice B, however, is incorrectly rounded, leaving choice D as the better answer.
___
The other answer choices do not result in a number between 5 and 6, so are clearly incorrect.
In an orienteering class, you have the goal of moving as far (straight-line distance) from base camp as possible by making three straight-line moves. You may use the following displacements in any order: (a) →a, 2.0 km due east (directly toward the east); (b) →b, 2.0 km 30° north of east (at an angle of 30° toward the north from due east); (c) →c, 1.0 km due west. Alternatively, you may substitute either −→b for →b or −→c for →c. What is the greatest distance you can be from base camp at the end of the third displacement? (We are not concerned about the direction.)
Answer:
The greatest distance we can be from the base camp at the end of the third displacement is 6.69 km
Step-by-step explanation:
We can think of each displacement as a vector, with a given magnitude and direction.
A vector can be written using its x and y coordinates like this
[tex]\vec{t}=(x, y)[/tex]
So, for the displacements a and c their vector coordinates would be:
[tex]\vec{a}=(2, 0)[/tex]
[tex]\vec{c}=(-1, 0)[/tex]
As the b displacement has an angle of 30° toward the north from due east, we can find its x and y coordinates using the following formulas:
[tex]x=(magnitude)*cos(angle)[/tex]
[tex]y=(magnitude)*sin(angle)[/tex]
Note: the angle in the formula is the one formed with the east measured counterclockwise.
So, the x and y coordinates for the b displacement will be:
[tex]\vec{b}=(2*cos(30), 2*sin(30))[/tex]
As the vector additon is commutative, the order won't affect the final position. Nevertheless, any change in the direction of any displacement will change the final position. So, in order to find the combination greatest distance we should calculate the following additions and find the one with the greatest magnitude:
[tex]\vec{R_{1}} =\vec{a}+\vec{b}+\vec{c}[/tex]
[tex]\vec{R_{2}} =\vec{a}-\vec{b}+\vec{c}[/tex]
[tex]\vec{R_{3}} =\vec{a}+\vec{b}-\vec{c}[/tex]
[tex]\vec{R_{4}} =\vec{a}-\vec{b}-\vec{c}[/tex]
Each resultant vector can be found adding each component. Afterwards, the magnitude can be found using the following formula:
[tex]|\vec{R}|=\sqrt[ ]{(R_{x})^2 +{(R_{y})^2}}[/tex]
Now, let's calculate!
[tex]\vec{R_{1}} =\vec{a}+\vec{b}+\vec{c}[/tex]
[tex]R_{1_x}} =2+2*cos(30)-1=2.73[/tex]
[tex]R_{1_y}} =0+2*sin(30)+0=1[/tex]
[tex]\vec{R_{1}}=(2.73,1)[/tex]
[tex]|\vec{R_{1}}|=\sqrt[ ]{(2.73)^2 +{(1)^2}}=3.86[/tex]
[tex]\vec{R_{2}} =\vec{a}-\vec{b}+\vec{c}[/tex]
[tex]R_{2_x}} =2-2*cos(30)-1=0.73[/tex]
[tex]R_{2_y}} =0-2*sin(30)+0=-1[/tex]
[tex]\vec{R_{2}}=(-0.73,-1)[/tex]}
[tex]|\vec{R_{2}}|=\sqrt[ ]{(-0.73)^2 +{(-1)^2}}=1.03[/tex]
[tex]\vec{R_{3}} =\vec{a}+\vec{b}-\vec{c}[/tex]
[tex]R_{3_x}} =2+2*cos(30)+1=4.73[/tex]
[tex]R_{3_y}} =0+2*sin(30)-0=1[/tex]
[tex]\vec{R_{3}}=(4.73,1)[/tex]
[tex]|\vec{R_{3}}|=\sqrt[ ]{(4.73)^2 +{(1)^2}}=6.69[/tex]
[tex]\vec{R_{4}} =\vec{a}-\vec{b}-\vec{c}[/tex]
[tex]R_{4_x}} =2-2*cos(30)+1=1.26[/tex]
[tex]R_{4_y}} =0-2*sin(30)-0=1[/tex]
[tex]\vec{R_{4}}=(1.26,-1)[/tex]
[tex]|\vec{R_{4}}|=\sqrt[ ]{(1.26)^2 +{(-1)^2}}=1.79[/tex]
So, after all the calculation, we can know for sure that the vector [tex]\vec{R_{3}}[/tex] has the biggest magnitude. Then, the greatest distance we can be from the base camp at the end of the third displacement is 6.69 km
Final answer:
To maximize your distance from base camp, move 2.0 km east, then 2.0 km 30° north of east, and finally 1.0 km west. The total distance achievable is around 3.732 km. The order of displacements does not affect the maximum distance reached.
Explanation:
The greatest distance you can be from base camp at the end of the third displacement is achieved when you move 2.0 km due east, then 2.0 km 30° north of east, and finally 1.0 km due west in any order.
This results in a total distance of approximately 3.732 km from base camp.
Regardless of the order in which you take the displacements, the resultant greatest distance achieved remains the same.
Laney walks one and two thirds of a mile to school from her house and rides the buss home. If she walked five days last week, how many miles did Laney walk in total?
Answer:
8 1/3
Step-by-step explanation:
The question is asking how many TOTAL (meaning it is increased so it could either be multiplication or addition) miles Loney walked in FIVE days. She walk 1 2/3 A DAY. This can be solved in two ways: multiplication AND addition. Addition: you just have tot turn the mixed fraction into improper fraction and then add the answer five times. But...wouldn’t multiplication be faster and easier..? Sure.
Step 1: Turn mixed fraction into improper.
1 2/3 as an improper fraction is 5/3. How? well multiply and denominator and the whole number and then add the numerator!
Step 2. Make an equation.
The equation should look like 5/3 x 5/1 (1 under 5 because remember there is ALWAYS an imaginary 1 under whole number while multiplying with fractions!)
Step 3. Multiply across
5x5=25
3x1=3 so it’s 25/3. There isn’t any LCM between 25 and 3 so we can only turn it into mixed number (you DEFINITELY can’t leave it like that! You MUST reduce to lowest terms for the correct answer!)
Step 4. Turn back into a mixed number.
there are several ways to do this.
1. Divided 25 by 3 and put the quotient as a whole number, remainder as a numerator and keep the same denominator.
OR
2. More faster way (if you know multiplication tables!)
How many times does 3 (denominato) goes into 25(numerator)? Well, read out the multiplication tables of 3!
3 times 8 equals 24! 3x9 will make it 27 so it doesn’t match with our numerator. So the answer is times 8! It becomes our whole number and it’s still 24 and our numerator is 25 so we have 1. Therefore, 1 is our numerator and we keep the same denominator :)
Hence, the answer is 8 1/3! Hope it helped! :D
The number of miles that Laney walked in total will be 25/3 miles.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
It is also known as the product. If the object n is given to m times then we just simply multiply them.
Laney walks one and two-thirds of a mile to school from her house and rides the bus home. If she walked five days last week.
Then the number of miles that Laney walked in total will be given by the product of the 1 2/3 and 5.
Number of miles = (1 2/3) x 5
Number of miles = (5/3) x 5
Number of miles = 25 / 3 miles
The number of miles that Laney walked in total will be 25/3 miles.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ2
Express the confidence interval 0.333 < p < 0.777 in the form p +/- E.
Answer:
p= 0.555 ; E= 0.222; then we have 0.555 +/- 0.222
Step-by-step explanation:
The confidence interval goes from 0.333 to 0.777.
To find the p, we need to locate the median of that series of numbers.
The median is 0.555 as is the middle value of that interval.
Now the E corresponds to the deviation or the Error that we can measure.
And since we know that our variance ranges between 0.333 and 0.777, we can sustract 0.333 to p and we can get 0.222. We can also check if we add 0.222 to p, and we can get 0.777.
ABC Designs, which produces rings, is developing direct material standards. Each ring requires 0.52 kilograms of a special metal. The allowance for waste is 0.03 kilograms per ring, while the allowance for rejects is 0.02 kilograms per ring. What is the standard quantity of metal per ring?
The standard quantity of metal per ring is 0.57 kilograms.
Step-by-step explanation:
Each ring requires 0.52 kilograms of a special metal.
The allowance for waste is 0.03 kilograms per ring, while the allowance for rejects is 0.02 kilograms per ring.
So, the standard quantity of metal per ring = 0.52 kg of metal required + 0.03 kg of allowance for waste + 0.02 kg of allowance for rejects)
= [tex]0.52+0.03+0.02=0.57[/tex] kilograms.
Hence, the standard quantity of metal per ring is 0.57 kilograms.
FAST HELp Which transformation carries the trapezoid onto itself?
Question 2 options:
reflect over the line x = –3
reflect over the line y = –3
reflect over the line y = 3
reflect over the line x = 3
Good morning ☕️
______
Answer:
reflect over the line y = –3
____________________
Step-by-step explanation:
Look at the photo below for more details.
:)
Answer: the answer is y=-3
Step-by-step explanation: I just answer this question and my quiz
And also -3 is what divided the trapezoid
Reasoning if you multiply two decimals that are less than 1,can you predict whether the product will be less thanor greater than either of the factors? Explain
Answer:
if both are positive, the result will be smaller than eitherif one is negative, the result is less than the positive number and greater than the negative number.if both are negative, the result is greater than eitherStep-by-step explanation:
The magnitude of a fraction of a fraction (their product) is always smaller than the magnitudes of either fraction. So, if both decimals are positive, the result is less than either factor.
___
Negative numbers are less than 1, so there can be several cases of interest when one or both numbers are negative.
Both numbers negative
The product will be positive, so will be greater than either negative factor.
__
One number negative, the other number positive
The product will be negative, so will be less than the positive factor and greater than the negative factor. (Multiplying a negative number by a positive fraction moves it closer to zero on the number line, hence to a value that is greater than the negative factor.)
Dear brainlys, i come to you in a time of need. My poor understanding of math has gotten the best of me once again. i am in need of assistance and i am offering a bounty for whomever can answer my question.
Ruby is visiting San Francisco. From her hotel she walks 2 blocks west and 3 blocks south to a coffee shop. Then she walks 7 blocks east and 4 blocks south to a museum. Where is the museum in relation to her hotel?
Answer:
Museum is at 7 blocks south and 5 blocks east to the Hotel
Step-by-step explanation:
| - - H
|
|_ _ _ _ _ _ _
|
|
|
|
Museum
Therefore, Museum is at 7 blocks south and 5 blocks east to the Hotel.
This is due tomorrow, so please help and show step by step
Answer:
slope = 3/2y-intercept = 3x-intercept = -2Step-by-step explanation:
The slope is the coefficient of x when the equation is of the form ...
y = (something).
Here, we can put the equation in that form by subtracting 12x and dividing by the coefficient of y:
12x -8y = -24 . . . . . given
-8y = -12x -24 . . . . .subtract 12x
y = 3/2x +3 . . . . . . . divide by -8
This is the "slope-intercept" form of the equation. Generically, it is written ...
y = mx + b . . . . . . where m is the slope and b is the y-intercept
So, the above equation answers two of your questions:
slope = 3/2
y-intercept = 3
__
The x-intercept is found fairly easily from the original equation by setting y=0:
12x = -24
x = -24/12 = -2 . . . . . the x-intercept
_____
A graph of the equation can also show you these things. The graph shows a rise of 3 units for a run of 2, so the slope is rise/run = 3/2. The line crosses the axes at x=-2 and y=3, the intercepts.
A space plane skims the edge of space at 4000 miles per hour. Neglecting altitude, if the circumference of the planet is approximately 25000 miles, how long will it take for the plane to travel around the planet?
A plane traveling at a speed of 4000 miles per hour would take approximately 6.25 hours to travel around a planet with a circumference of 25,000 miles.
Explanation:To solve this question, we will use the concept of time, speed, and distance. We know that the plane travels at a speed of 4000 miles per hour and the Earth's circumference is 25000 miles. Thus to compute the time it would take for the plane to travel around the planet, we can use the relation 'Time = Distance / Speed'.
The distance in this case is the circumference of the Earth, which is 25000 miles and the speed is the plane's speed, which is 4000 miles/hour. So, we simply divide 25000 miles by 4000 miles/hour:
Time = 25000 / 4000 = 6.25 hours
Learn more about Time, Speed and Distance here:https://brainly.com/question/35869086
#SPJ3
The population mean score for a particular exam is 74 and the standard deviation is 9. What are the mean and standard deviation of the class average score for classes composed of 36 students randomly drawn from the population?
Answer:
Step-by-step explanation:
!!!MARK AS BRAINLIEST!!!
Which inequality's solution is graphed here?
A)
x - 8 < 6
B)
x + 8 < 6
C)
x - 8 < 2
D)
x - 8 < -6
Answer:
c
Step-by-step explanation:
Answer:
Step-by-step explanation:
dapends on what x is but i think the answer is A or D
The angles of a triangle are 120 degrees. (x + 16) degrees, and X degrees.
What is the value of x?
Answer:
x = 22
Step-by-step explanation:
Adding all the degrees to a triangle must equal 180
120 + (x+16) + x = 180
2x + 136 = 180
-136. -136
2x = 44
[tex]\frac{2x}{2} = \frac{44}{2}[/tex]
x = 22
Final answer:
To find the value of x in the triangle with given angles, apply the rule that the sum of a triangle's interior angles is 180 degrees.
Explanation:
The value of x can be found by using the fact that the sum of the interior angles of a triangle is 180 degrees.
Angles of the triangle are given as 120 degrees, (x + 16) degrees, and x degrees.
Setting up the equation: 120 + (x + 16) + x = 180 and solving for x gives x = 22 degrees.
Nilda has $250 in her saving account. She plans to save $15 per week from her salary. Lona has only $200 in her account but can save $20 a week from her paycheck. How many weeks will it take before the amount in each savings account is the same?
Answer:
dang im late but its 10=x
Step-by-step explanation:
The number of weeks it would take before the amount in each savings account is the same is 10 weeks.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + b
Where:
m is the slope or rate of change.x and y are the points.b is the y-intercept or initial value.Let the variable x represent the number of weeks.
Based on the information provided above, a linear equation that models the situation can be written in slope-intercept form as follows;
250 + 15x = 200 + 20x
20x - 15x = 250 - 200
5x = 50
x = 50/5
x = 10 weeks.
Read more on slope-intercept here: brainly.com/question/7889446
#SPJ3
What single transformation rule would be the same as a reflection across the line y = 5 and then across the line y = –2 (Hint: The reflection is going down)? Group of answer choices (x, y) → (x – 14, y) (x, y) → (x +14, y) (x, y) → (x, y – 14) (x, y) → (x, y + 14)
Answer:
(x, y) → (x, y – 14)
Step-by-step explanation:
There is only one answer choice that translates downward, adding a negative number to the y-value:
(x, y) → (x, y – 14)
For some constants a and b let \[f(x) = \left\{ \begin{array}{cl} 9 - 2x & \text{if } x \le 3, \\ ax + b & \text{if } x > 3. \end{array} \right.\]The function f has the property that f(f(x)) = x for all x. What is a + b?
Answer:
The value of a+b is 4.
Step-by-step explanation:
The given function is
[tex]\[f(x) = \left\{ \begin{array}{cl} 9 - 2x & \text{if } x \le 3, \\ ax + b & \text{if } x > 3. \end{array} \right.\][/tex]
It is given that for some constants a and b the function f has the property that f(f(x))=x for all x.
For x≤3,
[tex]f(x)=9-2x[/tex]
For x>3,
[tex]f(x)=ax+b[/tex]
At x=0,
[tex]f(0)=9-2(0)=9[/tex]
[tex]f(f(0))=f(9)\Rightarrow a(9)+b=9a+b[/tex]
Using property f(f(x))=x,
[tex]f(f(0))=0[/tex]
[tex]9a+b=0[/tex] .... (1)
At x=1,
[tex]f(1)=9-2(1)=7[/tex]
[tex]f(f(1))=f(7)\Rightarrow a(7)+b=7a+b[/tex]
Using property f(f(x))=x,
[tex]f(f(1))=1[/tex]
[tex]7a+b=1[/tex] .... (2)
Subtract equation (2) from equation (1).
[tex]9a+b-(7a+b)=0-1[/tex]
[tex]2a=-1[/tex]
Divide both sides by 2.
[tex]a=-\frac{1}{2}[/tex]
Substitute this value in equation (1).
[tex]9(-\frac{1}{2})+b=0[/tex]
[tex]b=\frac{9}{2}[/tex]
The value of a is [tex]-\frac{1}{2}[/tex] and value of b is [tex]\frac{9}{2}[/tex]. The value of a+b is
[tex]a+b=-\frac{1}{2}+\frac{9}{2}[/tex]
[tex]a+b=4[/tex]
Therefore the value of a+b is 4.
Lola has $75 she buys a pair of shoes on sale for the one half and a pair of socks for $6 she has $32 left which equation can be use to find x the regular price of the shoesd find x the regular
Answer:
75 = 32 + 6 + x
Answer:
I believe it would be the first option on edge
Step-by-step explanation:
X + 6 + 32 = 75
What is an extraneous solution? a solution that was found due to an arithmetic error a solution that satisfies the original equation an apparent solution that is not a real number an apparent solution that does not satisfy the original equation
Answer:
an apparent solution that does not satisfy the original equation
Step-by-step explanation:
Usually, an extraneous solution is introduced by the solution process. Sometimes it takes the form of multiplying an equation by 0, often the result of eliminating the denominators of rational functions.
Other times, it takes the form of adding branches to a function that are unintended or undefined. (Squaring a square root will often introduce "solutions" that require the square root to be a negative value.) The attached graph shows that x=4 is an extraneous solution to ...
√x = x-6
It shows up when the equation is squared:
x = x² -12x +36 ⇒ (x -9)(x -4) = 0
The "solution" x=4 is extraneous because it does not satisfy the original equation.
As in this graphed example, using graphical methods to find solutions can often avoid extraneous solutions.
Answer:
an apparent solution that does not satisfy the original equation
Step-by-step explanation:
A choir director at your school wants to divide the choir into smaller groups there are 24 sooranos 60 altos and 36 tenors . Each group will have the same number of each type of voice what is the greast number of tje group that can be formed
Answer:
The question has a typo in it...so if you mean least: 2 groups......greatest: 12
Step-by-step explanation:
Least:
24, 60, and 36 are all even numbers, so they can divide by 2 so each group would have 12 Sopranos, 30 Altos, and 18 tenors.
Greatest:
24, 60, and 36 can all be divided by 12. So, each group would have 2 Sopranos, 5 altos, amd 4 tenors.
The greatest number of the group that can be formed is 12.
Based on the information given in the question, in order to solve the question, we'll have to find the factors of the numbers given and this will be:
24 = 1, 2, 3, 4, 6, 8, 12, and 24.
36 = 1, 2, 3, 4, 6, 9, 12, 18, and 36
60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
Therefore, from the numbers given above, we can see that the greatest number that's common to all is 12.
Read related link on:
https://brainly.com/question/12970676
Mona inherits her mother's personal residence, which she converts to a furnished rent house. These changes should affect the amount of ad valorem property taxes levied on the properties.
a) true
b) flase
Answer:
The answer is true.
Step-by-step explanation:
An ad valorem tax is based on the assessed value of a property. These include property taxes on real estate, sales tax on consumer goods etc,
When you are earning rent from a property, then you have to pay some tax for it, that will surely affect the amount of ad valorem property taxes levied on the properties.
Therefore, the answer is true.
(1 pt) A data set consists of the 11 data points shown below, plus one additional data point. When the additional point is included in the data set, the sample standard deviation of the 12 points is computed to be 12.091. If it is known that the additional data point is 25 or less, find the value of the twelfth data point. 25, 41, 49, 25, 30, 13, 31, 34, 27, 54, 38 Value of the additional data point
Answer:
12.83
Step-by-step explanation:
S = 12.091
N = 12
We must find the 12th point, X
The formula of S² (variance) as a function of µ (media) is as follows:
S² = (1/N Ʃ Xi²) - µ²
S² = 146.2
Multiplying both members by N,
N S² = Ʃ Xi² – N µ²
On the other hand,
µ = (25 + 41 + 49 + 25 + 30 + 13 + 31 + 34 + 27 + 54 + 38 + X) / 12
µ = (367 + X) / 12
Replacing,
12 x 146.2 = 13607 + X² – 12 (367 + X)² / 144
1754.4 = 13607 + X² – 0.0833 (134689 + 734 X + X²)
1754.4 = 13607 + X² – 11219.5 – 61.14 X – 0.0833 X²
0.92 X² – 61.14 X + 633.1 = 0
This is solved by finding the two values of X that satisfy the equation.
The solution requires solving the quadratic formula,
X12 = (-b ± √(b² - 4ac)) / 2a
The values are:
X1 = 12.83
X2 = 53.62
Since we know that the value is 25 or less, the answer is 12.83
The twelfth data point in the data set is x = 16.32
How to find the aditional point?
Let x be the value of the twelfth data point. We know that the sample standard deviation of the 12 points is 12.091. We can use the following formula to calculate the sample standard deviation:
s = √((Σ((xₙ - M)²) / (n - 1)))
where:
s is the sample standard deviationxₙ is the value of the n-th data pointM is the sample meann is the number of data pointsWe can plug in the given values to get the following equation:
if x is the missing data point then:
M = (25 + 41 + 49 + 25 + 30 + 13+ 31 + 34 + 27 + 54 + 38 + x)/12
M = 30.6+ x/12
And we know that:
s = 12.091
n = 12
Replacing these values we get:
12.091 = √((Σ((xₙ - 30.6 - x/12)²) / (12 - 1)))
Apply the square in both sides:
146.19 = (Σ((xₙ - 30.6 - x/12)²) / (11)
Multiply both sides by 11:
146.19*11 = Σ((xₙ - 30.6 - x/12)²
1,608.12 = Σ((xₙ - 30.6 - x/12)²
Now we can solve the right side:
1,608.12 = (-5.6 - x/12)² + (10.4 - x/12)² + (18.4- x/12)² + (-5.6 - x/12)² + (-0.6 - x/12)² + (-17.6 - x/12)² + (0.4 - x/12)² + (3.4 - x/12)² + (-3.6 - x/12)² + (23.4 - x/12)² + (7.4 - x/12)² + ( x - x/12)²
Now we can graph this, the positive solution is x = 16.32
Learn more about stardard deviation:
https://brainly.com/question/475676
#SPJ3
An explorer is caught in a whiteout (in which the snowfall is so thick that the ground cannot be distinguished from the sky) while returning to base camp. He was supposed to travel due north for 5.3 km, but when the snow clears, he discovers that he actually traveled 8.5 km at 54o north of due east. (a) How far and (b) in what direction (south of due west) must he now travel to reach base camp?
Answer:
(a) He must travel 5.25 km
(b) 17.7° south of west
Step-by-step explanation:
(Please see attached file)
1. He was supposed to travel 5.3 km due north to return to base camp
(vector S)
S = (Sx, Sy)
Sx= 0
Sy= 5.3
2. He discovers that he actually traveled 8.5 km at 54° north of due east (vector D)
D= (Dx, Dy)
Dx= Dcos Ф = 8.5cos54° = 5.0
Dy= Dsen Ф = 8.5sen54° = 6.9
3. He now needs to reach the base camp. Then, we need to find vector R.
From vectors addition/subtraction:
S = D + R
R = S - D
R= (Rx, Ry)
Rx = Dx - Sx = 0 - 5.0 = -5.0
Ry = Dy - Sy = 5.3 - 6.9 = -1.6
Magnitude of R = [tex]\sqrt{Rx^{2}+Ry^{2} }[/tex]
Magnitude of R = [tex]\sqrt{(-5.0)^{2}+(-1.6)^{2} }[/tex]
Magnitude of R = 5.25 km
Direction:
tanβ = [tex]\frac{Ry}{Rx}[/tex]
tanβ = [tex]\frac{1.6}{5.0}[/tex]
tanβ = 0.32
β = tan-1 (0.32)
β= 17.7° south of west
There is a 0.9986 probability that a randomly selected 33-year-old male lives through the year. A life insurance company charges $182 for insuring that the male will live through the year. If the male does not survive the year, the policy pays out $110 comma 000 as a death benefit. Complete parts (a) through (c) below.
Answer:
Expected Value = -$42 (loss of 42 dollars)
Step-by-step explanation:
Complete Question Below:
"There is a 0.9986 probability that a randomly selected 33-year-old male lives through the year. A life insurance company charges $182 for insuring that the male will live through the year. If the male does not survive the year, the policy pays out $110 comma 000 as a death benefit. If a 33-year-old male purchases the policy, what is his expected value?"
We can say P(survival) = 0.9986 and thus P(not survival) = 1 - P(survival) = 1-0.9986 = 0.0014
Also,
In case 33 year old doesn't live, the payment would be 100,000 - 182 = $99,818
And
In case 33 year old lives, the payment is
-$182
We know, the expected value is the sum of the product of each possibility with its probability.
[tex]ExpectedValue=\Sigma x*p(x)=(99818)(0.0014)+(-182)(0.9986)=-42[/tex]
This means a loss of $42 (or -$42)
A gardener is going to plant 2 red rosebushes and 2 white rosebushes. If the gardener is to select each of the bushes at random, one at a time, and plant them in a row, what is the probability that the 2 rosebushes in the middle of the row will be the red rosebushes?
a) 1/12
b) 1/6
c) 1/5
d) 1/3
e) ½
Answer: b) [tex]\dfrac{1}{6}[/tex]
Step-by-step explanation:
Sample space for the arrangement of red bushes :
[rrww , rwwr , wwrr , wrwr, rwrw , wrrw]
i.e. Total possible outcomes = 6
If the two rosebushes middle of the row are red , then the first and the last rosebushes must be white (wrrw).
i.e. the number of favorable outcomes for middle of the row are red =1
Now, the probability that the 2 rosebushes in the middle of the row will be the red rosebushes :
[tex]\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}\\\\=\dfrac{1}{6}[/tex]
Hence, the correct answer is option (b).
Sonya drops a marble while standing on a deck 7 7/8 feet above the ground. The marble falls 4 1/4 feta from Sonya's hand to the deck, and then rolls and falls to the ground. What is the total vertical distance that the marble falls?
Answer: just subtract 7 7/8 - 4 1/4 :)
Step-by-step explanation:
The distance that we can say that the marbel has fallen through is 3 5/8 feet
What is the distance of the fall?To subtract fractions, the denominators (the bottom numbers) of the fractions you're subtracting must be the same. If they're not already the same, you'll need to find a common denominator. If the fractions have different denominators, convert both fractions to an equivalent fraction
We have that;
Distance dropped = 7 7/8
Distance where the fall stopped = 4 1/4
Distance of the fall = 7 7/8 - 4 1/4
3 7 - 2/8
= 3 5/8 feet
Learn more about fractions:https://brainly.com/question/10354322
#SPJ3
Mr. Khans is buying staplers for his office. Each stapler costs $16.99. Part A: What does his final total cost depend upon? Part B: In this scenario, what is the input? What is the output?
Answer:
his cost depends on how many staplers he gets and the input is how much each stapler cost and output is how much he has to spend
Step-by-step explanation:
Answer:
A. Number of staplers.
B. Input is number of staplers and output is total cost.
Step-by-step explanation:
Part A : Let he bought x staplers,
∵ The cost of each stapler = $ 16.99
So, the cost of x staplers in dollars ( say y ) = price of each staplers × number of staplers
⇒ y = 16.99x
Which is the required equation that shows the given scenario,
∵ y ∝ x,
I.e. his final cost would depend upon the number of staplers.
Part B :
∵ in the equation y = 16.99x
x = input value, y = output value,
Thus, in this scenery, input is the number of staplers and output is total cost.
As a sales person you are paid $50 per week +2 per sale this week you want your pay to be at least $100 what's the minimum number of sales you can make turn at least $100
What is the measure of AngleDCF? Three lines extend from point C. The space between line C D and C E is 75 degrees. The space between lines C E and C F is 54 degrees.
Answer:
129°
Step-by-step explanation:
If CE is between CD and CF, then angle DCF is the sum of the given angles:
75° +54° = 129°
Answer:
129
Step-by-step explanation:
bc it just is right