The value of the integrand is -ln | cos(x) | + C
How to evaluate the integrandFrom the question, we have the following parameters that can be used in our computation:
Integral of tan(x) w.r.t x
The antiderivative (indefinite integral) of the tangent function, tan(x), with respect to x cannot be expressed in terms of elementary functions
However, it can be expressed in terms of special functions, such as the hyperbolic tangent and the dilogarithm.
One possible representation of the antiderivative of tan(x) is:
∫tan(x) dx = -ln | cos(x) | + C
where C is an arbitrary constant of integration.
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determine whether the angle vector v makes with vector u is acute, obtuse, straight, a right angle, or whether v is a vector in the same direction as u. uv
The angle that the vector "v = 9i + 8j - 4k" makes with the vector "u = 6i - 4j - k" is Acute Angle .
To determine the angle between two vectors, we need to find the dot product of the vectors and divide it by the product of their magnitudes.
If the result is positive, the angle between the vectors is acute, if it's negative the angle is obtuse, and if it's zero, the angle is a right angle.
In this case, the dot product of vectors "u" and "v" is:
⇒ (6i - 4j - k) . (9i + 8j - 4k) = 54 - 32 + 4 = 26 ;
The magnitude of vector "u" is = √(6² + (-4)² + (-1)²) = √(36 + 16 + 1) = √53
The magnitude of vector "v" is = √(9² + 8² + (-4)²) = √(81 + 64 + 16) = √161
So, the Cosine (Cos) of angle between two vectors "u" and "v" is:
⇒ Cos(θ) = 26/(√37 × √145) = 26/√5365 .
Since the value of Cos(θ) is positive, the angle between the vectors is acute. This means the vectors "u" and "v" are pointing in somewhat similar directions, but not exactly the same direction.
The given question is incomplete , the complete question is
Determine whether the angle vector "v" makes with vector "u" is acute, obtuse, straight, a right angle, or whether "v" is a vector in the same direction as "u" . u=6i-4j-k and v=9i+8j-4k .
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f(x)=x^2+2x g(x)=2x+1
There were 35 gallons of water in a tank and 4.5 gallons of water in a pail. An equal amount of water was poured into the tank and the pail. The ratio of the water in the tank to that pail became 7:2.
a. how much water was in the pail at the end?
b.how much water was poured into the pail?
please show work as well ty :)
Answer: A: 9 galloons and then
Step-by-step explanation:
Find the volume of each prism and match the volume to the correct prism. The units are understood to be square units, but are not included on the numeric answer.
Answer:
To find the volume of a prism, use the formula V = A * h, where A is the area of the base of the prism and h is its height. For example, for the first prism, the area of the base is 8 and the height is 4, so the volume is 8 * 4 = 32. For the second prism, the area of the base is 6 and the height is 9, so the volume is 6 * 9 = 54. The first prism has a volume of 32 and the second prism has a volume of 54.
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Shows the path of a beam of light through several layers with different indices of refraction. (a) If $\theta_{1}=30.0^{\circ}$, what is the angle $\theta_{2}$ of the cmerging beam? (b) What must the incident angle $\theta_{1}$ be to have total internal reflection at the surface between the medium with $n=1.20$ and the medium with $n=1.00 ?$
(a) If θ(1) = 26.0 degree, the angle θ(2) of the emerging beam is 41.3 degree.
(b) The smallest incident angle θ(1) to have total internal reflection at the surface between the medium with n(4) = 1.20 and the medium with n(4) = 1.06 is 62.01.
(a) The path of a beam of light through several layers with different indices of refraction.
Using the Snell's law
n(1) sinθ(i) = n(2) sinθ(r)
The two medium's refractive indices are n(1) and n(2), and the angles of incidence and refraction are θ(i) and θ(r).
The preceding can be revised as
sinθ(r) = sinθ(i)(n(1))/(n(2))
sinθ(r) = sin 26 × 1.60/1.40
sinθ(r) = 0.50
Going from n2 to n3 .
The above calculated will become angle of incidence made with the normal at n(2) and n(3) interface.
The angle of refraction at n(3) medium
sinθ(r3) = sinθ(r) × n(2)/n(3)
sinθ(r3) = 0.50 × 1.40/1.20
sinθ(r3) = 0.58
The angle of incidence for interfaces n(3) and n(4) is now θ(r3).
sinθ(2) = (sinθ(r3) × n(3))/n(4)
sinθ(2) = (0.58 × 1.2)/1.06
sinθ(2) = 0.66
Taking square root on both side, we get
θ(2) = [tex]\sin^{-1}[/tex](0.66)
θ(2) = 41.3 degree
(b) It is possible to calculate the critical angle at the n3 to n4 interface as
θ(c) = [tex]\sin^{-1}[/tex](n(4)/n(3))
θ(c) = [tex]\sin^{-1}[/tex](1.06/1.20)
θ(c) = 62.01
The angle at which 100% internal reflection takes place is known as the critical angle.
Total internal reflection will happen if the beam is incident at an angle of 62.01 at n(3).
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The complete question is:
The figure below shows the path of a beam of light through several layers with different indices of refraction. (Assume n(4) = 1.06.)
(a) If θ(1) = 26.0 degree, what is the angle θ(2) of the emerging beam?
(b) What is the smallest incident angle θ(1) to have total internal reflection at the surface between the medium with n(4) = 1.20 and the medium with n(4) = 1.06?
The perimeter of a rectangular restaurant kitchen is 56 meters. The area is 171 square meters. What are the dimensions of the kitchen?
answer: b = 9metres
l = 19metres
Answer:
Dimensions are L=19, w=9, or L=9, w=19
Step-by-step explanation:
Perimeter P=2(L+W)
So, 56=2(L+W)
28=L+W
L=28-W
Area A=L*W
Because A=171, so 171=L*W
Substituting the expressions: put L=28-w, to 171=L*W,
So, 171=(28-W)W
171=28w-w²
W²-28W+171=0
(W-9)(W-19)=0
W=9, or W=19
We got L=28-W before, so when w=9, put to L=28-W, so, L=19
Dimensions are L=19, w=9, or L=9, w=19
g a researcher is looking at the effect of drinking alcohol on the ability to play darts. he recruits 20 dart players from the nearby pub and has them come to a lab where he flips a coin for each player. if the coin comes up heads, he has the player drink a pint of beer. if the coin comes up tails, he has the player drink a pint of soda. each player then throws three darts at a dartboard and the score is recorded. the researcher calculates that the soda-drinkers score, on average, 2.5 points more than the beer-drinkers.
The paragraph above describes a/an c. controlled experiment.
The participants who drink beer are the b. control group, the participants who drink soda are the a. treatment group.
Flipping a coin to decide which player gets which drink is an example of g. randomization.
A controlled experiment is a type of study in which the researcher manipulates one or more independent variables to observe the effect on a dependent variable. In this case, the independent variable is the type of drink (beer or soda) and the dependent variable is the score achieved in a dart-throwing task.
The purpose of randomly assigning the players to drink either beer or soda is to control for any other factors that could affect the scores, such as the individual's dart-playing ability or the amount of alcohol consumed.
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Complete Question:
A researcher is looking at the effect of drinking alcohol on the ability to play darts. He recruits 20 dart players from the nearby pub and has them come to a lab where he flips a coin for each player. If the coin comes up heads, he has the player drink a pint of beer. If the coin comes up tails, he has the player drink a pint of soda. Each player then throws three darts at a dartboard and the score is recorded. The researcher calculates that the soda-drinkers score, on average, 2.5 points more than the beer-drinkers.
The paragraph above describes a/an _____________.The participants who drink beer are th_____________, the participants who drink soda are the _____________. Flipping a coin to decide which player gets which drink is an example of _____________.
Choose from the list below to fill in the blanks.
a. treatment group
b. control group
c. controlled experiment
d. observational study
e. placebo
f. confounding factor
g. randomization
Please help me with this question.
5x+4y is the objective function's value (10,0)
How to solve the the problem?The suggested LPP is: Maximize 6x+10y with restrictions 4x+6y =240, 2x+3y120
6x+3y≤240⇒2x+y≤80 x≥10 y≥0
Plot the graphs of x=10, 2x+3y=120, and x+y=80. The area of the solution that is viable is shown by the shading.
The viable region's corner points are (10, 0), (40, 0), (30, 20), and (10, 3 100).
When the objective function is examined at these values:
(x,y)
5x+4y is the objective function's value (10,0)
70 (40,0) 280 (30,20) 410 (10, 3 100 )
403.33
The figures show that 7x+10y is at its maximum when x=30 and y=20. The top number is 410.
max 5x_{1} + 4x_{2}
s.t. x_{1} + x_{2} <= 6 x_{1} - 2x_{2} <= 2 10x_{1} + 6x_{2} <= 45 x_{1} ,x 2 in mathbb Z
x_{1}, x_{2} >= 0
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Which of the following numbers is one-fifth of a given number if one-fourth of that same number is 20? Select the single best answer: A 10 B. 15 C. 20 D. 16 E. 25 usuan West >>
16 is the number which is one-fifth of a number when one-fourth of that same number is 20.
As per the given data:
One-fourth of the number is resulted to 20.
Here we have to determine the result of one-fifth of the same number from the given options.
An expression for a portion of a whole is a fraction.
For any real numbers, the fractional component of x is defined.
Let the number be X.
One-fourth of a number is 20 which means:
Multiply the one-fourth fraction with an unknown number which results in the number 20.
[tex]$\frac{1}{4}[/tex] (X) = 20
X = 20 × 4
X = 80
Now we have to determine that one-fifth of the same number.
Multiply the one-fifth fraction by 80.
We get:
= [tex]$\frac{1}{5}[/tex] (80)
= [tex]$\frac{1}{5}[/tex] × 5 × 16
= 16
One-fifth of the number 80 is 16
Therefore Option (D) - 16 is the correct answer.
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How would you find x?
Answer:
1/3
Step-by-step explanation:
You want to find x in a Venn diagram with regions labeled (x(x-5)), x, 2x, and 20, when the total is ε = 100. And you want to know the probability that a British stamp is from the 20th century.
Sum of the partsThe whole is the sum of the parts:
ε = x(x-5) +x +2x +20
100 = x² -2x +20 . . . . . . . . simplify
81 = x² -2x +1 . . . . . . . . . subtract 19 to make a complete square
81 = (x -1)²
9 = x -1 . . . . . . . positive square root
x = 10 . . . . . . . . add 1
ProbabilityNow we know ...
P(B) = (x +2x)/ε = 30/100 = 0.3
P(T&B) = x/ε = 10/100 = 0.1
The probability that a British stamp is from the 20th century is ...
P(T|B) = P(T&B)/P(B) = 0.1/0.3
P(T|B) = 1/3
[tex]\frac{x-4}{3}\leq 5[/tex]
Answer:
Hi, I'm Za'Riah! I will gladly assist you with your problem! (see explanation)
Step-by-step explanation:
Let's solve your inequality step-by-step.[tex]\frac{x-4}{3} \leq 5[/tex]
Step 1: Simplify both sides of the inequality.[tex]\frac{1}{3}x + \frac{-4}{3} \leq 5[/tex]
Step 2: Add 4/3 to both sides.[tex]\frac{1}{3}x+ \frac{-4}{3} + \frac{4}{3} \leq 5+ \frac{4}{3} \\\frac{1}{3}x\leq \frac{19}{3}[/tex]
Step 3: Multiply both sides by 3.[tex]3*\frac{1}{3}x\leq 3*( \frac{19}{3} )[/tex]
Answer:
x [tex]\leq[/tex] 19
(Hope this helped!)
(see image for number line graph)
The following are the scores of an algebra class of 20 students in a high school:
69 84 52 93 81 74 89 85 88 63 87 64 67 72 74 55 82 91 68 77
Find the interquartile range using R.
The interquartile range of the given data using R is 13.3
As per the given data,
The midterm scores of an algebra class of 20 students;
69, 84, 52, 93, 81, 74, 89, 85, 88, 63, 87, 64, 67, 72, 74, 55, 82, 91, 68, 77
We have to find the interquartile range using R.
Interquartile Range;-
The interquartile range includes the second and third quartiles or the middle half of your data set (IQR). The range gives the spread of the full data set, whereas the interquartile range gives the range of the middle half of the data set.
Interquartile range = [tex]Q_{3} -Q_{1}[/tex]
[tex]Q_{1}[/tex] is the lower quarter
[tex]Q_{3}[/tex] is the upper quarter
[tex]Q_{2}[/tex] is the median
Here,
[tex]Q_{2}[/tex] = 63 + [tex]$\frac{87}{2}[/tex]
[tex]Q_{2}[/tex] = [tex]$\frac{150}{2}[/tex]
[tex]Q_{2}[/tex] = 75
[tex]Q_{1}[/tex] = 81 + [tex]$\frac{74}{2}[/tex]
[tex]Q_{1}[/tex] = 77.5
[tex]Q_{3}[/tex] = 74 + [tex]$\frac{55}{2}[/tex]
[tex]Q_{3}[/tex] = 64.5
Then,
Interquartile range = [tex]Q_{3} -Q_{1}[/tex] = - (64 . 5 - 77.5) = 13.3
That is,
The interquartile range for the given data set is 13.3.
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In 1991, the moose population in a park was measured to be 3360. By 1996, the population was measured again to be 3560. If the population continues to change linearly:
Find a formula for the moose population, P, in terms of t, the
years since 1990. (I think my teacher meant for it to be 1991)
And what does your model predict for the moos population to be in 2007?
Answer: P=3360+40t; 4000
Step-by-step explanation: 3560-3360 = 200, 200/5=40, 3360+40t, substitute t=16 to find out 2007 and you get 4000.
if r(x) is a rational function in simplest form where the degree of the numerator is 2 and the degree of the denominator is 2, then
Here, the degree of the numerator, 2, is equal to the degree of the denominator, 2, so r(x) has a nonzero horizontal asymptote
Asymptote is a line taken in relation to curve. The line is always far apart from the curve irrespective of distance. Taking the definition in sense of curve, then the curve tries to reach this line while moving towards infinity. Horizontal asymptote indicates the behaviour of function at graph edge.
The equation to be considered for formation of horizontal asymptote is y = mx + b, where u is y-axis, m is slope, x is axis and b is constant. If the two values, that are numerator and Denominator are equal, then y = b.
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-4/5(y+x=
Simplify your answer
By multiplying the factors, y + x = -4/5 in y-intercept form is y = -1/5(x + 4).
What is the multiplication ?Multiplication is a mathematical operation that involves two numbers, known as factors, being multiplied together to produce a new number, known as the product. The equation is not in a form that can be simplified. The equation is an algebraic equation that needs to be solved using basic algebraic operations such as addition, subtraction, multiplication and division.
Generally, the factors are either whole numbers or fractions. The process of multiplication involves repeated addition of the same number multiple times, as for example, adding 5 three times results in 5 + 5 + 5 = 15.
y + x = -4/5
y = -4/5 - x
y = -1/5(4 +x)
y = -1/5(x + 4)
Thus, by multiplying the factors, y + x = -4/5 in y-intercept form is y = -1/5(x + 4).
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Complete question:
y + x = -4/5
Simplify your answer in y-intercept form
Last week, Alex took 90 selfies and Vic took 75 selfies. Today,
they each decided that some of these selfies were not very good
and deleted them. Alex deleted three times as many selfies
as Vic. Now, Alex has half as many selfies as Vic. How many
selfies did Alex delete?
PLEASE HELP ASAP
The number of selfies deleted by Alex is 52.5.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that Last week, Alex took 90 selfies and Vic took 75 selfies. Today, they each decided that some of these selfies were not very good and deleted them. Alex deleted three times as many selfies as Vic.
Alex= 90
Vic = 75
Deleted ( Alex = 3 Vic )
Alex = 1 / 2 Vic
Deleted selfies = 90 - 75 /2 = 52.5
Hence, the number of selfies deleted by Alex is 52.5.
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what is the approximate solution of the linear system represented by the graph below
The approximate solution of the linear system represented by the graph is, (5, 6)
What is the equation of line?The equation of a straight line is a relationship between x and y coordinates, The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.
Given that,
A graph in which two lines are intersecting each other,
basically solution of linear system means where both the lines will intersect,
So, in the graph it can be seen that lines are intersecting around x coordinate 5 and y coordinate 6,
Therefore, the solution is (5, 6)
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according to car and driver, an alfa romeo going 70 mph requires 177 feet to stop. assuming that the stopping distance is proportional to the square of the velocity, find the stopping distance required by an alfa romeo going at 25 mph and at 110 mph.At 25 mph, stopping distance =At 110 mph, stopping distance =
At 25 mph, stopping distance = 22.56 feet
At 110 mph, stopping distance = 436.81 feet
Now, According to the question:
Let d represents the stopping distance required by an alfa romeo.
The stopping distance is proportional to the square of velocity is equivalent to the equation,
[tex]d = kv^2[/tex]
Here, k is proportionality constant.
We have,
d = 177 feet and v = 70 mph.
So, proportionality constant
[tex]k =\frac{177}{(70mph)^2}[/tex] ≈ 0.0361
Thus, the stopping distances required by an alfa Romeo going at 25 mph and at 110 mph,
[tex]d_2_5=0.0361[/tex] × [tex](25mph)^2[/tex] = 22.56 feet
[tex]d_1_1_0[/tex] = 0.0361 × [tex](110mph)^2[/tex] = 436.81 feet
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If vector B is added to vector A, which two of the following choices must be true in order for the resultant vector to be equal to zero? and B are equal and opposite directions Aand B are perpendicular and B are equal and in the same direction and B are nJOt equal and in the sanie direction None of these'
If vector B is added to vector A and the resultant is a null vector then A and B are equal and have opposite directions
We are given two vectors, vector A and vector B.
Now, vector B is added to vector A and it is said that the resultant of this addition is a null vector. It can be written as
vector B + vector A = 0
It can also be written as
vector A = 0 - vector B
vector A = - vector B
We can see that the magnitude of both the vectors, vector A and vector B are equal. The minus sign here represents that the direction of vector B is opposite to vector A
Hence, we can conclude that if vector B is added to vector A and the resultant is a null vector then A and B are equal and have opposite directions
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Find the value of c for which the area enclosed by the curves y = −x^2 + c and y = x^2 − c is equal to 56.
Answer:
The area enclosed by two curves can be found by subtracting the area between one curve and the x-axis from the area between the other curve and the x-axis.
Let's call the x-value where the two curves intersect as X. At X, both y values are equal to 0. Hence, the equation for X is
-x^2 + c = x^2 - c
Solving for x, we get
2x^2 = 2c
x^2 = c
The area between y = -x^2 + c and the x-axis is equal to the area between y = x^2 - c and the x-axis, so the total area is double that, or 2c.
Setting 2c equal to 56, we have:
2c = 56
c = 28
So the value of c for which the area enclosed by the curves y = −x^2 + c and y = x^2 − c is equal to 56 is 28.
Type the correct answer in each box. If necessary, use / for the fraction bars,
Write the function for the parabola shown with its directrix in the graph.
f(x) =
4
3
2
→
&
تنا
2 3
(x-
y = -2.25
The equation of the parabola graphed is given as follows:
(x - 3)² = 5(y + 1)
How to obtain the equation of the parabola?The equation of a vertical parabola is given as follows:
(x - h)² = 4p(y - k)
In which:
(h,k) are the coordinates of the vertex.y = k - p are the coordinates of the directrix.(h, k + p) are the coordinates of the focus.The vertex is at the coordinate (3,-1), hence the parameters h and k are given as follows:
h = 3, k = -1.
The directrix is at the coordinate y = -2.25, hence the value of p is obtained as follows:
-1 - p = -2.25
p = 1.25.
Meaning that the equation of the parabola is given as follows:
(x - 3)² = 5(y + 1)
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Please find the answer to A B and C show work if possible please
Answer:um it dose not show the thing i downloded the file if u try again i will anser it for tho
Step-by-step explanation:
Janet unfolded a cardboard box. The figure of the unfolded box is shown below:
Which calculation will give the total surface area of the cardboard, in square inches, that was used to make the box? (1 point)
A. 5 × 6 × 6
B. 6 × 5 × 5
C. 10 × 6 × 6
D. 6 × 10 × 10
The total surface area of the cardboard in square inches is option B. 6 × 5 × 5.
What is Surface Area?The area of a three dimensional object on it's outer surface is called the surface area of the object.
From the given figure, there are 6 squares with each square having the side length equals 5 inches.
Area of a square = a × a, where a is the length of a side.
Area of a 5 inch square = 5 × 5
There are total of 6 squares.
Total surface area = 6 × 5 × 5
Hence the total surface area of the given figure is option B. 6 × 5 × 5.
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An electric pole was knocked over and is leaning at a 104 degree angle due to a recent storm. As a result, the power lines are hanging too low so some electricians were sent out to look in to the situation. One electrician is sitting 36 meters away from the base of the pole (on the obtuse angle side).
Although it is too dangerous to measure the length of the pole directly, the electricians can measure the angle of elevation from the ground to the top of the pole and then calculate the length based off of that. If the angle of elevation from the electrician to the top of the pole is 33.6 degrees, what is the length of the pole?
Round your answer to the nearest hundredth of a meter.
Answer:
29.54 m
Step-by-step explanation:
You want the side opposite the 33.6° angle in a triangle that is 36 m between its 33.6° angle and its 104° angle.
Law of sinesIn order to use the law of sines to find an unknown side opposite a given angle, we must have a known angle opposite a known side. The known side is opposite the third angle of the triangle, whose measure is ...
180° -104° -33.6° = 42.4°
Now, we can use the law of sines:
pole height/sin(33.6°) = (36 m)/sin(42.4°)
pole height = (36 m)·sin(33.6°)/sin(42.4°) ≈ 29.54475 m
pole height ≈ 29.54 m
A car rental agency has 20 cars. Of those cars, 4 are
luxury sedans and all the other cars are midsize sedans.
Each luxury sedan rents at a daily rate 50% greater
than the daily rate for the midsize sedans. If the luxury
sedans rent for $45 per day, what is the average daily
rental fee, to the nearest dollar, of all 20 cars at this
agency?
A. $27
B. $33
C. $38
D. $42
E. $56
Answer:
[tex]\Huge \boxed{\textbf{B. \$33}}[/tex]
Step-by-step explanation:
To solve this problem, we first need to find the daily rental rate for the midsize sedans. Since the luxury sedans rent for $45 per day and their daily rate is 50% greater than the midsize sedans, we can set up the following equation:
[tex]\Large \boxed{\texttt{45 = 1.5 $\times$ Midsize daily rate}}[/tex]
Now, we can solve for the midsize daily rate:
[tex]\texttt{Midsize daily rate} = \tt{\frac{45}{1.5}}[/tex][tex]\texttt{Midsize daily rate} = \tt{30}[/tex]So, the midsize sedans rent for $30 per day. There are 16 midsize sedans (20 total cars - 4 luxury sedans) and 4 luxury sedans. To find the average daily rental fee for all 20 cars, we can use the following formula:
[tex]\Large\boxed{\texttt{Average daily rental fee} = \frac{\texttt{Total rental fees}}{\texttt{Total number of cars}}}[/tex]
The total rental fees can be calculated as follows:
[tex]\texttt{Total rental fees} = \tt{(16 \times 30) + (4 \times 45) }\\[/tex][tex]\texttt{Total rental fees} = \tt{480 + 180}[/tex][tex]\texttt{Total rental fees} = \tt{660}[/tex]Now, we can find the average daily rental fee:
[tex]\texttt{Average daily rental fee} = \tt{\frac{660}{20}} \\[/tex][tex]\texttt{Average daily rental fee} = \tt{33}[/tex]So, the average daily rental fee for all 20 cars at this agency is $33, which corresponds to option B.
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________________________________________________________
c) Bhurashi can do part of a work in 1 day. She worked for 4 days and 20 left. If the remaining parts of the work was done by Rita, how much work did she do ?
Answer: the only clear answer i can think of would be, NO, the work she did was not clear i would say she did 4/10days she needed to work
Step-by-step explanation:
Can you please help me these math problems.
1. Find the slope of the line passing through the pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. (4,1) and (10,6)
2. Find the equation of a line in slope-intercept form that passes through a given point or has a slope of m. Parallel to y = 5; passing through (4,7)
3. Find the equation of a line in slope-intercept form that passes through a given point or has a slope of m. x-intercept = -3 and y-intercept = 4
4. Find the equation of a line in slope-intercept form that passes through a given point or has a slope of m. (0, 4); m = 12
5. What does it mean if the slope of a line is undefined?
The conclusions are listed below:
The slope of the line passing through points (4, 1) and (10, 6) is 5 / 6.The equation of the line parallel to line y = 5 is y = 7.The equation of the line is y = (4 / 3) · x + 4.The equation of the line is y = 12 · x + 4.Vertical lines has undefined slopes in accordance with secant line formula.How to analyze and interpret equations of the lineIn this question we find five cases related to lines, whose features can be inferred from following equation:
y = m · x + b
Where:
x - Independent variable.y - Dependent variable. m - Slopeb - InterceptPlease notice that line rises when m > 0, is horizontal when m = 0, falls when m < 0 and is vertical when m is undefined.
Slope can be determined by secant line formula:
m = Δy / Δx
In addition, two lines are parallel when they share the same slope.
Part 1 - The slope of the line passing through two points is:
m = (6 - 1) / (10 - 4)
m = 5 / 6
The slope of the line indicates that it rises.
Part 2 - First, write the slope of the parallel line:
m = 0
Second, calculate the y-intercept from equation of the line:
b = 7 - 0 · 4
b = 7
Third, write the equation of the parallel line:
y = 7
Part 3 - First, determine the slope of the line:
m = (4 - 0) / [0 - (-3)]
m = 4 / 3
Second, calculate the intercept of the line:
b = y - m · x
b = 4 - m · 0
b = 4
Third, write the equation of the line:
y = (4 / 3) · x + 4
Part 4 - First, write the slope of the line:
m = 12
Second, determine the y-intercept of the equation of the line:
b = y - m · x
b = 4 - 12 · 0
b = 4
Third, write the equation of the line:
y = 12 · x + 4
Part 5 - According to secant line formula, undefined slope indicates a vertical line, that is, a line parallel to y-axis.
To learn more on equations of the line: https://brainly.com/question/29774095
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Circle A has center of −2, −2 and a radius of 4, and circle B has a center of 3, 3 and a radius of 2. What steps will help show that circle A is similar to circle B
Dilate circle A by a scale factor of 0.5
Reflect circle A over the line y = x
Translate circle A using the rule (x − 5, y − 5)
Rotate circle A 90° clockwise about the origin
The required steps to show that circle A is similar to circle B are,
1. Dilate circle A by a scale factor of 0.5.
2. Translate circle A using the rule (x − 5, y − 5).
The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by
(x - h)² + (y - k)² = r²
where h, k is the coordinate of the center of the circle on the coordinate plane and r is the radius of the circle.
Here,
Circle A = Center of −2, −2 and a radius of 4,
Circle B = Center of 3, 3, and a radius of 2.
Steps to show circle A is similar to circle B
1. Dilate circle A by a scale factor of 0.5
2. Translate circle A using the rule (x − 5, y − 5)
Learn more about circle here:
brainly.com/question/11833983
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Alejandro Associates is an accounting firm that provides audit and tax services to its clients. Each tax return is considered a "job" for the firm, just like a manufacturing company considers a customer order as a "job."
Alejandro has direct costs related to Tax Return 8405 as follows:
7 hours of staff labor $96 per hour
4 hours of assembly labor $172 per hour
$62 of materials
In addition, Alejandro Associates estimates its overhead related to the manufacture of tax returns to be $57,230 for the year. The company expects to do 10,217 returns for the year. The company also expects to use 59,712 staff hours for the year. If Alejandro allocates overhead to jobs based on staff hours, what is the total cost of Tax Return 8405? *Hint, make a job order cost sheet for Job 454. It should include materials, labor, and overhead. *Round each step to the nearest 2 decimal places. For your final answer, round to the nearest dollar
can someone help mere please
Answer:
yes what do you need help with
