The magnitude of the resultant vector is 27 miles
How to determine the vector magnitudeResultant vector = Distance of A - Distance of B
This is so because of the opposite direction of the car's movement
A = 87 miles
B = 114 miles
Resultant vector = 114 - 87
Resultant vector = 27 miles
Thus, the magnitude of the resultant vector is 27 miles
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On april 1 of the current year, a company purchased and placed in service a machine with a cost of $240,000. the company estimated the machine's useful life to be four years or 60,000 units of output with an estimated salvage value of $60,000. during the current year, 12,000 units were produced. prepare the necessary december 31 adjusting journal entry to record depreciation for the current year assuming the company uses: a. the straight-line method of depreciation b. the units-of-production method of depreciation c. the double-declining balance method of depreciation
The answers to the questions are:
a. $33,750b. $36000c. $90000a. the straight-line method of depreciation
[tex]\frac{cost of machine - salvage}{useful life} * period[/tex]
= (240000 - 60000) / 4 * (9 / 12)
= $33,750
The debit is 33750 as well as the credit
b. the units-of-production method of depreciation
(240000 - 60000) / 60000 * 12000
= $36000
c. the double-declining balance method of depreciation
(24000 *2 /4) * (9/12)
= $90000
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Avery solves the equation below by first squaring both sides of the equation.
√z^2+8 = 1 -2z
What extraneous solution does Avery obtain?
z= ?
[tex]\left(\sqrt{z^{2}+8} \right)^{2}=(1-2z)^{2}\\\\z^{2}+8=4z^{2}-4z+1\\\\0=3z^{2}-4z-7\\\\0=(z+1)(3z-7)\\\\z=-1, z=\frac{7}{3}[/tex]
We know that if z=7/3, the right-hand side will be negative, which means it is an extraneous solution as square roots cannot be negative.
The __________ states that as a procedure is repeated again and again and again and again, the probability tends to approach the actual probability.
Answer:
Law of large Numbers
Step-by-step explanation:
The Law of large numbers.
What is the Law of natural numbers?The law of large numbers plays the main role in probability and statistics. It means that if you repeat an experiment independently so many times and average the result, what you get has to be close to the expected value.
An example of the Law of Large Numbers:
Let's assume that you rolled the dice three times and the outcomes were 6, 6, and 3. Then the average result is 5.
So, according to the law of the large numbers, if we roll the dice a large no. of times, then the average result should be closer to the expected value.
It also states that probability and statistics set a sample size that grows, and the mean of the sample size gets closer to the average of the entire population.
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is translation a and b?
Really short Question; Please help and Show your Work! I would rate you 5 stars or anything you like
Answer:
about 94.41°
Step-by-step explanation:
The Law of Cosines can be used to find an angle in a triangle with three sides given.
SetupThe law of cosines relation generally relates the side opposite the angle to the other measures in the triangle:
r² = p² +q² -2pq·cos(R)
SolutionWe want to find the measure of angle R, so we solve the equation for that:
2pq·cos(R) = p² +q² -r² . . . . . . add 2pq·cos(R)-r²
cos(R) = (p² +q² -r²)/(2pq) . . . . divide by the coefficient of the cosine
We can fill in the given side lengths at this point:
cos(R) = (13² +10² -17²)/(2·13·10) = -20/260 = -1/13
Then the angle can be found using the arccos function:
R = arccos(-1/13) ≈ 94.41°
The measure of angle R is about 94.41°.
__
Additional comment
When you have done a few of these, you recognize that the angle opposite side 'c' is ...
C = arccos((a² +b² -c²)/(2ab))
A calculator can make short work of this. The second attachment shows the evaluation of this expression with a=10, b=13, c=17. The calculator angle mode is set to degrees. The arccos function is the 2ND function of the Cos key.
What is slope-intercept form
Answer:
y=mx+b
Step-by-step explanation:
Slope intercept form is y=mx+b where "m" should be substituted with the slope and "b" stands for the y-intercept value. "x" and "y" are your input and output values respectively.
Given that OA = 2x + 9y , OB = 4x + 8y and CD = 4x - 2y , explain the geometrical relationships between the straight line AB and CD.
It’s a 3 mark question sooo if someone could help then thanks.
The geometrical relationships between the straight lines AB and CD is that they are parallel to each other
How to determine the relationshipIt is important to note the following;
A drawn from the origin and passes through point A (a , b), then the equation of OA = ax + byIf a line is drawn from the origin and passes through point B (c , d), then the equation of OB = cx + dyWe find the equation of AB by subtracting OB from OA, thus AB = (c - a)x + (d - b)y
The slope of line AB =
⇒ OA= 2 x + 9 y
⇒ OA = 4 x + 8 y
⇒AB = OB - OA
⇒AB = (4 x + 8 y) - (2 x + 9 y)
⇒ AB = 4 x + 8 y - 2 x - 9 y
Collect like terms
⇒ AB = (4 x - 2 x) + (8 y - 9 y)
⇒AB = 2 x + -y
⇒ AB = 2 x - y
⇒ Coefficient of x = 2
⇒ Coefficient of y = -1
⇒ The slope of ab = [tex]\frac{-2}{-1}[/tex] = 2
For CD
⇒ CD = 4 x - 2 y
⇒Coefficient of x = -4
⇒ Coefficient of y = -2
⇒The slope of cd = [tex]\frac{-4}{-2}[/tex] = 2
Note that Parallel lines have same slopes
And Slope of ab = slope of cd
AB // CD
Therefore, the geometrical relationships between the straight lines AB and CD is that they are parallel to each other
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What is the probability that , in a group of 200 random people , at least two of them have the same triple of initials (such as JTK for James Tiberius Kirk)
The probability is P(X >= 2).
200 random people, n = 200
Let us consider the Binomial expression
i.e.,
P(X = r) = nCr*p^r*q^(n-r)
Here we have to assume that the 3 initials are equally likely events.
i.e.,
p = 1/3
q = 1 - 1/3
= 2/3
Required probability = P(X >= 2)
= 1 - [P(X = 0) + P(X = 1)]
= 1 - [200C0*(1/3)^0*(2/3)^200 + 200C1*(1/3)^1*(2/3)^199]
= 1 - [1*1*(2/3)^200 + 200*(1/3)*(2/3)^199]
= 1 - [(2/3)^200 + 200*(1/3)*(2/3)^199]
= 1 - (2/3)^200 - 200*(1/3)*(2/3)^199
Probability is truly how possibly something is to happen. every time we're unsure about the final results of an event, we will talk about the possibilities of certain consequences and how probably they are. The evaluation of events ruled by means of possibility is called records.
3 styles of probability
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math!! please please helppp!!!
What is the slope of the line below?
(i attached an image)
a) (0,4)
b) -1/3
c) (-1.5,0)
d) 3
e) 4
f) (0,4)
g) -3
h) 1/3
Answer:
The slope is 3
Step-by-step explanation:
it is 3 up and 1 across, which is 3/1 = 3
Answer:
3
Step-by-step explanation:
Look at the two lower dots shown on the line.
slope = rise/run
The vertical distance from the lower point to the higher point is 3. That is the rise.
The horizontal distance from the lower point to the higher point is 1. That is the run.
slope = 3/1 = 3
Answer: 3
Select the correct answer from each drop-down menu. ∆ABC has vertices at A(11, 6), B(5, 6), and C(5, 17). ∆XYZ has vertices at X(-10, 5), Y(-12, -2), and Z(-4, 15). ∆MNO has vertices at M(-9, -4), N(-3, -4), and O(-3, -15). ∆JKL has vertices at J(17, -2), K(12, -2), and L(12, 7). ∆PQR has vertices at P(12, 3), Q(12, -2), and R(3, -2). can be shown to be congruent by a sequence of reflections and translations. can be shown to be congruent by a single rotation.
The option that is shown to be congruent by a sequence of reflections and translations is Option B: Triangle ABC and Triangle MNO
Option C: Triangle JKL and Triangle PQR can be shown to be congruent by a single rotation.How are they congruent?Note that:
If ∆MNO can be gotten from ∆ABC then ∆MNO ≅ ∆ABC
To solve for Reflection (x axis), it will be:
The coordinate note for the reflection is (x, y) will be: (x,-y)
Since ∆MNO M(-9, -4), N(-3, -4), and O(-3, -15).
Then the reflections will be:
M(-9, -4)- M1(-9,4)
N(-3, -4)- N1(-3,4)
O(-3,-15)-O1(-3,15)
To solve for Reflection (y axis), it will be:
The coordinate note for the Reflection is (x,y) will be (-x,y)
Since ∆M1N1O1 = M1(-9, 4), N1(-3, 4), and O1(-3, 15).
Then M1(-9, -4) - M2(9,4)
N1(-3, -4) - N2(3,4)
O1(-3,-15)- O2(3,15)
To solve for Translation
The coordinate note for the Translation is (x,y) will be (x+2,y+2)
Since ∆M2N2O2 = M2(9,4), N2(3,4), and O2(3, 15).
Then M2(9, 4) - M3(11,6)=A
N2(3,4) - N3(5,6)=B
O2(3,15) - O3(5,17)=C
Hence ∆MNO ≅ ∆ABC
To know the congruent by a single rotation.
If ∆JKL can be gotten from ∆PQR
Then ∆JKL ≅ ∆PQR
For Rotation of 90 degree in an anticlockwise position, then:
The coordinate note for the Rotation is (x,y) will be (-y, x)
So, ∆JKL = J(17, -2), K(12, -2), and L(12, 7).
J(17, -2)- J1(2,17)
K(12, -2) - K1(2,12)
L(12,7) - L1(-7,12)
To solve for translation
The coordinate note for the translation is (x,y) will be (x+10,y-14)
Then ∆J1K1L1 = J1(2, 17), K1(2, 12), and L1(-7, 12).
Hence J1(2, 17) - J2(12,3) = P
K1(2, 12)- K2(12,-2) = Q
L1(-7, 12)- L2(3,-2) = R
So, ∆JKL ≅ ∆PQR.
So therefore, The option that is shown to be congruent by a sequence of reflections and translations is Option B: Triangle ABC and Triangle MNO
Option C: Triangle JKL and Triangle PQR can be shown to be congruent by a single rotation.See options below
___ can be shown to be congruent by a sequence of reflections and translations.
1)Pick one to go with the sentence.
a Triangle ABC and Triangle XYZ
b Triangle ABC and Triangle MNO
c Triangle JKL and Triangle ABC
d Triangle PQR and Triangle XYZ
___ can be shown to be congruent by a single rotation.
Pick one to go with the sentence.
a Triangle ABC and Triangle XYZ
b Triangle PQR and Triangle XYZ
c Triangle JKL and Triangle PQR
d Triangle JKL and Triangle XYZ
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If a linear function contains the pairs (5,7) and (9,11), which pairs should have the reciprocal function to this one?
Please choose an answer.
a.
(7.5) and (11.9)
b.
(5.7) and (11.9)
c.
(5.7) and (9.11)
d.
(7.5) and (9.11)
The pair of the reciprocal function will be (7, 5) and (11, 9). Then the correct option is A.
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space.
If a linear function contains the pairs (5, 7) and (9, 11).
If the pairs should have the reciprocal function to this one. Then the coordinate gets swapped.
The pair of the reciprocal function will be (7, 5) and (11, 9).
Then the correct option is A.
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Please Answer Asap!!! Write the equation based on the graph of the following base 2 logarithmic function:
The graph of the logarithmic function that passes through (-2,-2) and (1,0) is [tex]\log_2(x+3)-2[/tex].
Suppose that the function is
[tex]f(x)=\log_2(x+c)+d[/tex]
Then there are two observations that we must consider from the figure
The graph must pass through (-2,-2) and (1,0)So,
[tex]-2=\log_2(-2+c)+d[/tex]
[tex]\implies -2+c=e^{-2-d} ...~...~(1)[/tex]
And,
[tex]0=\log_2(1+c)+d\\\implies 1+c=e^{-d} ~...~...~(2)[/tex]
Observe the figure given below we see that the graph of
[tex]\log_2(x)[/tex] passes through (1,0) but does not pass through (-2,-2) and the graph is to the right of (-2,-2) hence, we need the graph to move left.
When we increase c the graph [tex]\log_2(x+c)+d[/tex] moves left and
When we decrease d then the graph [tex]\log_2(x+c)+d[/tex] moves down.
That makes the graph required to be [tex]\log_2(x+3)-2[/tex].
Hence, the graph of the logarithmic function that passes through (-2,-2) and (1,0) is [tex]\log_2(x+3)-2[/tex].
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There are 210 rabbits at the farm. For every 5 gray rabbits, there are 2 white rabbits. How many white rabbits are at the farm
The number of white rabbits that are at the farm is 60
Calculating quantityFrom the question, we are to determine the number of white rabbits that are at the farm
From the given information,
There are 210 rabbits at the farm
and
For every 5 gray rabbits, there are 2 white rabbits
Then, we can write that
5x + 2x = 210
Where x is the number of groups of 5 gray rabbits and 2 white rabbits
Then,
7x = 210
x = 210/7
x = 30
The number of white rabbits is 2x
∴ Number of white rabbits = 2×30
Number of white rabbits = 60
Hence, the number of white rabbits that are at the farm is 60
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Necesito saber
El cuádruplo de su anterior es igual al cubo de menos cuatro
Y tambien un ejercio aparte que dice
La tercera parte de su siguiente es igual al anterior de menos diez
Las expresiones matemáticas descritas son: (x-1)4=-4³ y 1/3(x+1)=(-10)-1.
¿Cómo identificar las expresiones matemáticas?Para identificar las expresiones matemáticas debemos organizar los datos proporcionados en el fragmento de la siguiente manera:
El cuádruplo de su anterior es igual al cubo de menos cuatro: (x-1)4=-4³La tercera parte de su siguiente es igual al anterior de menos diez: 1/3(x+1)=(-10)-1Luego debemos solucionar las expresiones matemáticas para encontrar el resultado final:
A. (x-1)4 = -4³
4x-4 = -64
4x = -64+4
4x = -60
x = -60/4
x = -15
B. 1/3(x+1) = (-10)-1
1/3x+1/3 = -11
1/3x = -11-1/3
1/3x = -32/3
x = -32/3•3
x = -32
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pls help on algebra homework!! will mark brainliest!
Answer:
32
Step-by-step explanation:
YZ = ⅗XY.
XY = 20
20 / 5 x 3 = 12
YZ = 12
XZ = YZ + XY
XZ = 20 + 12
XZ = 32
Work is attached. Hope it helps!
la suma de dos ángulos internos es siempre mayor que la medida del tercer ángulo
verdadero o falso y por que
Utilizando el triangulo rectangulo como contraejemplo, veremos que esto es falso.
¿Es la propicición verdadera o falsa?Primero, sabemos que para todo triangulo la suma de sus angulos internos es igual que 180°.
Ahora, vamos a el triangulo más comun. El triangulo rectangulo.
Este es el triangulo que tiene uno de sus angulos internos igual a 90°.
Digamos que los otros dos angulos internos son A y B, entonces tendriamos:
A + B + 90° = 180°
Despejando A + B obtenemos:
A + B = 180° - 90° = 90°
A + B = 90°
Entonces vemos que la suma de estos dos angulos internos es igual que el tercer angulo.
Encontramos un contraejemplo de la proposición, asi, concluimos que la proposición es falsa.
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Question 6 The volumes of two similar solids are 729m3 and 125m3 The surface area of the larger solid is 324m2. What is the surface area of the smaller solid
Answer:
100 m²
Step-by-step explanation:
The scale factor for volume of similar figures is the cube of the scale factor for linear dimensions. The scale factor for area is the square of that linear dimension scale factor.
Scale factorIf the ratio of volumes is the cube of the scale factor, then the scale factor for the smaller figure in terms of the larger is ...
[tex]k=\sqrt[3]{\dfrac{125\text{ m}^3}{729\text{ m}^3}}=\sqrt[3]{\dfrac{5^3}{9^3}}=\dfrac{5}{9}[/tex]
Smaller areaThe area of the smaller figure is found from ...
[tex]\dfrac{A}{324\text{ m}^2}=\left(\dfrac{5}{9}\right)^2=\dfrac{25}{81}\\\\A=(324\text{ m}^2)\cdot\dfrac{25}{81}=\boxed{100\text{ m}^2}[/tex]
The surface area of the smaller solid is 100 square meters.
__
Additional comment
The least surface area for a given volume is that of a sphere. The larger volume given corresponds to a sphere with a radius of about 5.583 meters. Such a sphere will have an area of about 391.7 square meters. There is no known physical object with a volume of 729 m³ that can have a surface area as little as 324 m².
Therea re 8 kids at a birthday party. If there are 6 girls and 2 boys at the party, what draction of the kids are girls?
Answer:
3/4
Step-by-step explanation:
The total number of children is 8 and the number of girls is 6. This can be represented as 6/8.
You would then need to simplify...
6/2=3
8/2=4
which which lead you to 3/4!
Please help 15 points
Since in each option, each input is mapped to only one output, all the options are correct.
When a relationship represents a function?A relationship represents a function when each input is mapped to only one output.
In this problem:
For the Venn sets, only one line departs each value of x, hence it is a function.For the ordered pairs, each value of x(2, 5 and -4), is mapped to only one value of y, hence it is a function.The graph has no vertically aligned points, hence it is a function.Thus all the options are correct.
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a textbook company ships its books in boxes that can hold 30 pounds. one particular order calls for a shipment of 800 books. if each book weighs 1.4 kilograms, how many boxes will be required to fulfill this order
83 boxes are required to carry 800 books.
According to the question:
One Box can hold weight = 30 pounds
We know that , 1 pound= 0.45 kg
hence, 30 pounds = 30 x 0.45 = 13.5kg
hence, one box can carry 13.5 kg of weight.
Now,
Weight of 1 book = 1.4 kg
So, Total Weight of 800 books= 1.4 x 800 kg
And , No. of boxes required to carry 800 books = (1.4 x 800)/13.5 = 82.96
or approximately 83 boxes
Hence, 83 boxes are required to carry 800 books.
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Someone help, I need answers ASAP pls it’s urgent pls
Which table or graph shows the value of y going up as the value of x goes up?
O A. x y
16
OB.
2
3
4
9896SHSN1
4
← PREVIOUS
12
18
24
The value of y is increasing for x values in Graph C, the correct option is C.
What is a Linear Graph?A Linear Graph is the graphical representation of a Straight line equation.
From the graph attached with the answer, The x-y values for all the graphs are observed to determine the graph in which the y value goes up as the x value increases.
For the x value increasing, the value of y is decreasing in Graph A, B, and D.
The y value is rising only for Graph C.
Therefore, the correct option is C.
The complete question is attached with the answer.
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What are the four steps for multiply rational expressions as seen in the lesson
question on the image
Answer:
232.28°
Step-by-step explanation:
Using N = 0 degrees
Arctan ( 12.8 / 9.9) = 52.28 degrees ( this A to C )
C to A would be 232.28 ° ( just add 180 degrees)
Answer:
16.2
pls give brainlest
explanation:
lets use pythagorean theorem
12.8^2+9.9^2
which is 163.84+98.01=261.85
261.85 square root = 16.181177
round 16.18=16.2
answer 16.2
Identify the line with an undefined slope
Answer:
d. vertical line
Step-by-step explanation:
A line with an undefined slope is a vertical line
Slope is the change in y over the change in x
When the slope is undefined, it means that the x does not change, which is a vertical line
Answer:
Line D
Step-by-step explanation:
Slope is defined as rise/run. Since a vertical line has zero run and infinite rise the equation is infinity/0 and anything divided by zero is undefined.
A door delivery florist wishes to estimate the proportion of people in his city that will purchase his flowers. Suppose the true proportion is 0.07. If 289 are sampled, what is the probability that the sample proportion will differ from the population proportion by more than 0.03
The probability that the sample proportion will differ from the population proportion by more than 0.03 is 0.99968.
Given the true proportion is 0.07, sample size 289.
We have to calculate the probability that the sample proportion will differ from the population proportion by more than 0.03.
Probability is the likeliness or chance of happening an event among all the events possible. The probability lies between 0 and 1.
Probability=number of items/ total items.
True proportion=0.07
n=289
sample population mean=0.07
Sample proportion standard error=[tex]\sqrt{pq/n}[/tex]
=[tex]\sqrt{0.07*0.93)/289}[/tex]
=[tex]\sqrt{0.0651/289}[/tex]
=[tex]\sqrt{0.00022}[/tex]
=0.015
Probability that the sample proportion will differ from the population proportion by more than 0.03=P(I P-p I>0.03)
=P( I Z I>0.03*0.015)
=P ( I z I >0.0045)
=0.99968.
Hence the probability that the sample proportion will differ from the population proportion by more than 0.03 is 0.99968.
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the sum of lengths of two legs of a right angle triangle is 14 cm and its area is 24 cm square find the perimeter of the triangle
A particular brand of cell phone case is available in four different styles and each style comes in three colors. How many different cases are available
Answer:
12
Step-by-step explanation:
the number of the available cases is :
3 × 4 = 12
which statement accurately describes how to reflect point A (3,-1) over the y axis
The reflection over the y-axis only changes the sign of the x-component so the reflected point is A' (-3, -1)
How to reflect point A over the y-axis?Here we can't see the options, so I will teach you how to reflect any point over the y-axis.
Any point on the X-Y plane is defined by its coordinates (x, y).
If we reflect this point over the y-plane, we only change the sign of the x-component of the point.
So after the reflection, we get the point (-x, y).
Then if we apply that reflection to point A (3, -1). We will get the reflected point:
A' (-3, -1)
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A rectangular plot is to be fenced off and divided into three parts/plots on land that borders a barn. If you do not fence the side along the barn, find the length and width of the plot that will maximize the area if you have 200 feet of fence. What is the largest area that can be enclosed
5000 square feet is the largest area that can be enclosed
It is given that a rectangular plot is to be fenced off and divided into three parts/plots on land that borders a barn there are and there is 200 feet of fence that is available.
One-fourth of the perimeter = 50
The other width also equals 50.
So the length of fencing = 200 - 50 - 50 = 100
So the area = 50 x 100 = 5000 square feet.
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