So the marginal cost per mile for a one-day, 200-mile trip is $2/30 = $0.067 or approximately 6.7 cents per mile.
The cost of the car rental for one day is $50. The cost of gasoline for the 200-mile trip can be calculated as follows:
The car gets 30 miles per gallon, so it will use 200/30 = 6.67 gallons of gasoline for the trip.
The cost of 1 gallon of gasoline is $2, so the cost of 6.67 gallons is 6.67 x $2 = $13.34.
Therefore, the total cost of the trip is $50 + $13.34 = $63.34. The marginal cost per mile can be calculated by taking the derivative of the total cost with respect to the distance traveled:
d/dx ($50 + $2/30 x) = $2/30
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Which of the measurements of triangleBAC are correct
Answer:
yes
no
yes
Step-by-step explanation:
sin C = opp/hyp = 9/15 yes
tan B = opp/adj = 12/9 no
tan B = 12/9; B = tan^-1 12/9 = 53.13°
what should be added to 3x³-5x²+7x-4 to get 7x³+2x²-3x+9
Answer:
Let the number be a.
==: a + (5x³-2x²+3x+7) = (7x³+7x-5)
==: a = (7x³+7x-5) - (5x³-2x²+3x+7)
==: a = 7x³ + 7x - 5 - 5x³+ 2x² - 3x - 7
==: a = 2x³ + 2x² + 4x - 12
i guess this is the process if you don't understand i can explain more
In the 30-60-90 triangle below, side s has a length of
length of
30
90°
S
60
OA. 16√3, 5
B. 4√2, 4√2
OC. 4, 4√3
OD. 8.5, 16
OE. 16√3, 16√3
OF. 4, 8√3
and side q has a
Answer:
4, 4√3
Step-by-step explanation:
In a 30-60-90 triangle:
The leg opposite of the 30-degree angle is 1/2 of the hypotenuse: 8/2 = 4
The longer leg is √3 times the shorter leg: 4*√3 = 4√3
Check work: 4^2+(4√3)^2 = 8^2 --> 16+48 = 64 --> 64 = 64
Use trig to find the height of the hot air balloon. Write an equation and show work. Round answer to the nearest tenth
Answer:
x = 753.6 ft
Step-by-step explanation:
One leg is x.
The other leg is given.
The trig function that relates the two legs of a right triangle is the tangent.
tan A = opp/adj
tan 37° = x/1000ft
x = 1000 ft × tan 37°
x = 753.6 ft
Answer: 753.6 feet
Step-by-step explanation:
The angle, theta, is 37 degrees. However, we're not given the length of the hypotenuse in this case. So sine would be x by the hypotenuse and cosine would be 1,000 by the hypotenuse. In this case, we can use tangent, which is sine/cosine. In this case, tan 37 = x/1,000.
Hence,
tan 37 = x/1,000
x = tan 37 * 1000
x is approximately 753.6, rounded to the nearest tenth.
Nani needs to buy 8 cups of fresh pineapple for a fruit cocktail. the table shows the unit prices of pineapple at different stores. if nani only has $4, from which stores could she purchase her pineapple?
Nani could purchase her pineapple from stores A, D, and E.
Given Information
It is given that Nani needs to purchase 8 cups of pineapple.
The unit prices of pineapple at each store is as follows,
Store A : 0.49
Store B : 0.51
Store C : 0.55
Store D : 0.48
Store E : 0.45
Amount that Nani has = $4
Reason Behind Purchasing From Either A, D, or E
Since Nani has amount of $4, she can purchase pineapple only from the stores where the total cost of 8 pineapple cups adds up to less than $4. The purchase of 8 pineapple cups at each store would be given as,
Store A : 0.49(8) = $3.92
Store B : 0.51(8) = $4.08
Store C : 0.55(8) = $4.40
Store D : 0.48(8) = $3.84
Store E : 0.45(8) = $3.60
As it can be seen, Nani can purchase from the store A, D, and E as it falls within her budget of $4.
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Of the 17 students in a programming class, 6 own 1 computer, 3 own 2 computers, 3 own 3 computers, 2 own 4 computers, and 3 own 5 computers
The median number of computers owned by the 17 students is 2.
What is median in statistics?A dataset's median represents the midpoint; half of the data points are smaller and half are greater than the median.
Identifying the median: The data points should be arranged from smallest to largest. The median is the middle data point in the list if the number of data points is odd.
The total number of students are 17.
The data can be arranged in the following table
number of students number of computers
6 1
3 2
3 3
2 4
3 5
Arrange the given frequencies in the increasing order-
1 1 1 1 1 1 2 2 2 3 3 3 4 4 5 5 5
The middle term of the arrange frequencies is 17/2 = 8.5
Median = (8 term + 9 term)/2
= (2 + 2)/2
= 2
Therefore, the median number of computers owned by the 17 students is 2.
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The correct question is -
Of the 17 students in a programming class, 6 own 1 computer, 3 own 2 computers, 3 own 3 computers, 2 own 4
computers, and 3 own 5 computers. What is the median number of computers owned by the 17 students?
Express tan D as a fraction in simplest terms. 40 B 24 32 C
Answer:
[tex]\sf Tan \ D = \dfrac{4}{3}[/tex]
Step-by-step explanation:
Trigonometry ratios:
[tex]\sf \boxed{\bf \tan \ D =\dfrac{opposite \ side \ of \ \angle \ D}{adjacent \ side \ of \ \angle D}}[/tex]
[tex]\sf =\dfrac{BC}{DC}\\\\ =\dfrac{32}{24}\\\\=\dfrac{4}{3}[/tex]
The triangles are similar. Find the value of the variable.
Find the area of circle x that has a radius xy at coordinates x=(0,3) y=(-3,-1). use 3.14 for pi, and round your answer to the nearest tenth.
The area of the circle is 78.5 unit square.
What is circle?A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point.
The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.
The formula for area of circle is;
Area = [tex]\pi[/tex](radius)²
The distance between the two points are calculated by distance formula.
[tex]\begin{aligned}&d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}} \\&d=\text { distance } \\&\left(x_{1}, y_{1}\right)=\text { coordinates of the first point } \\&\left(x_{2}, y_{2}\right)=\text { coordinates of the second point }\end{aligned}[/tex]
Calculation for the area of the circle;
As, the radius of the circle is xy.
The distance between x and y points will be calculated by the distance formula.
x=(0,3) y=(-3,-1)
[tex]\begin{aligned}&d=\sqrt{\left(-3-0\right)^{2}+\left(-1-3\right)^{2}} \\\end{aligned}[/tex]
[tex]\begin{aligned}&d=\sqrt{\left(-3\right)^{2}+\left(-4\right)^{2}} \\\end{aligned}[/tex]
[tex]\begin{aligned}&d=\sqrt{25} \\\end{aligned}[/tex]
[tex]d=5[/tex]
As, distance between x and y point is 5 units which is the radius of the circle.
Area of circle = [tex]\pi[/tex](radius)²
= 3.14×(5)²
= 78.5
Therefore, the area of the circle is 78.5 unit square.
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BRANIEST + 15 POINT QUESTION
Let the missing number x
So, ATQ
[tex] \frac{3}{14} \times x = 6[/tex]
[tex] \frac{14}{3} \times \frac{3}{14} x = 6 \times \frac{14}{3} [/tex]
[tex] \frac{1}{3} \times 3x = \frac{14}{3} \times 6[/tex]
[tex]x = \frac{14}{3} \times 6[/tex]
[tex]x = 14 \times 2[/tex]
[tex]x = 28[/tex]
Therefore, 3/14 of 28 is 6...
Answer:
28
Step-by-step explanation:
Let the number we are looking for = [tex]x[/tex]
∴ [tex]\frac{3}{14}[/tex] of [tex]x[/tex] is 6
⇒ [tex]\frac{3}{14}[/tex] × [tex]x = 6[/tex]
• Divide both sides of equation by [tex]\frac{3}{14}[/tex] :
⇒ [tex]x = 6 \div \frac{3}{14}[/tex]
⇒ [tex]x = 28[/tex]
∴ The missing part is 28.
The document shows a 1040 form. a 1040 tax form. the 1040 form is used to collect state tax. local tax. federal tax. sales tax.
Answer:
Federal tax
Step-by-step explanation:
It is used for tax returns, given out by federal govt
Answer:
C. federal Tax.
Step-by-step explanation:
/ \
/ \
When figuring out the sign of a fraction as a
whole, you use the rules for dividing negatives.
Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 2 more than 5 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 110
Mark and Don have 18 and 92 marbles respectively.
What is the solution of the equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.
Let the number of marbles Mark has be x.
According to the question,
Don has (5x+2) marbles.
Total number of marbles=110
Thus, the required equation is:
x+5x+2=110
6x=108
x=108/6
x=18
Mark has 18 marbles.
Don has (5*18+2)=92 marbles.
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Explain why the following form linearly dependent sets of vectors. (solve this problem by inspection.)
u1 = (3, -l), u2 = (4, 5), u3 = (-4, 7) in r2
A set of vectors {v1,v2,...,vk} is linearly independent if the vector equation x1v1 + x2v2 + .......... + xkvk = 0 has only the trivial solution
x1 = x2 = .... = xk =0. Then the set {v1,v2,...,vk} is linearly dependent otherwise.
So putting in the formula we get
x1u1 + x2u2 + x3u3 = 0
x1u1 + x2u2 = -x3u3
au1 + bu2 = u3 ∵ (-x1/x3 = a & -x2/x3 = b)
On putting in the values
a(3,-1) + b(4,5) = (-4,7)
(3a+4b,-a+5b) = (-4,7)
On comparing we get
3a + 4b = -4 -(1)
-a + 5b = 7 -(2)
on solving these equations we get
b = 17/19 and a= -48/19
which is non trivial.
Thus the following form linearly dependent sets of vectors.
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ok more of a question not like a equation or anything but when do you know when there is a extraneous answer and how do you solve it (please provide an example equation)
One can know if an equation is extraneous if after plugging it in the original equation, it shows a false meaning or the value is undefined.
What is an extraneous equation?It should be noted that an extraneous equation means a root of a transformed equation that isn't the root of the original equation due to the fact that it's excluded from the domain of the original equation.
In this case, one can know if an equation is extraneous if after plugging it in the original equation, it shows a false meaning or the value is undefined.
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Please someone helpp
Due to length restrictions, we cannot summarize the results of the three parts about the quadratic equations of the form x² + b · x + c = 0. We kindly invite to check the explanation for further details.
How to apply algebra properties to solve quadratic equations of the form x² + b · x + c = 0In this question we have several exercises with quadratic equations of the form x² + b · x + c = 0 and, to be more exactly, quadratic equations with the following characteristics:
x² - (r₁ + r₂) · x + r₁ · r₂ = 0 (1)
Please notice that the first grade coefficient is equal to the inverse of the sum of the two roots and the zero grade coefficient is the product of the two coefficients.
Now we proceed to resolve all the points:
Part I
a) (x + 17) · (x + 1) = x² + 18 · x + 18, r₁ = - 17, r₂ = - 1
b) (x + 5) · (x + 4) = x² + 9 · x + 20, r₁ = - 5, r₂ = - 4
c) (x - 11) · (x - 1) = x² - 12 · x + 11, r₁ = 11, r₂ = 1
d) (x - 18) · (x - 2) = x² - 20 · x + 36, r₁ = 18, r₂ = 2
Part II
a) x² - 12 · x + 27
b) (x + 4) · (x + 8)
c) (x - 5) · (x - 7)
d) (x - 4) · (x - 5)
Part III
a) (x - 18) · (x + 3) = x² - 15 · x - 54
b) (x + 18) · (x + 3) = x² + 21 · x + 54
c) (x + 18) · (x - 3) = x² + 15 · x - 54
d) (x - 18) · (x - 3) = x² - 21 · x + 54
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A company makes rubber rafts. 12% of them develop cracks within the first month of operation. 27 new rafts are randomly sampled and tested, by being used for one month, under standardized conditions that mimic typical operating conditions. Calculate the probability that the number of tested rafts that develop cracks is no more than 3. Round your answer to four decimal places.
The probability that the number of tested rafts that develop cracks is no more than 3 is .00006.
The true proportion, p for the population is given to 0.12.
Thus, the mean, μ, for the sample = np = 27*0.12 = 3.24.
The sample size, n, given to us is 27.
Thus, the standard deviation, s, for the sample can be calculated using the formula, s = √{p(1 - p)}/n.
s = √{0.12(1 - 0.12)}/27 = √0.003911 = 0.0625389.
We are asked to calculate the probability that the number of tested rafts that develop cracks is no more than 3, that is, we need to calculate P(X ≤3).
P(X ≤ 3)
= P(Z ≤ {(3 - 3.24)/0.0625389) {Using the formula z = (x - μ)/s}
= P(Z ≤ -3.8376114706)
= .00006 {From table}.
Thus, the probability that the number of tested rafts that develop cracks is no more than 3 is .00006.
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Rewrite each equation without absolute value for the given conditions.
[tex]y=/x-5/+/x+5/ if -5\ \textless \ x\ \textless \ 5[/tex]
Answer: 10
Step-by-step explanation:
If [tex]-5 < x < 5[/tex], then [tex]|x-5|=5-x[/tex] and [tex]|x+5|=x+5[/tex].
So, the expression is equal to 10.
The points (-3,2) (5,2) and (5,1) are three vertices of a rectangle what is the fourth vortex?
help me please 10 points
Answer:160ft^3
Step-by-step explanation:
Volume=(bh/2)h
V=(5ftx8ft/2)8ft
V=20x8=160
Volume=160ft^3
HOPE YOU GET IT RIGHT:)!
suppose cos(A) = 4/5. use the trig identity sin^2(A)+cos^2(A)=1 to find sin(A) in quadrant IV. round to the ten-thousandth.
a. -0.3954
b. -0.6000
c. 0.6485
d. 0.4500
In quadrant IV, [tex]\sin(A)[/tex] is negative. So
[tex]\sin^2(A) + \cos^2(A) = 1 \implies \sin(A) = -\sqrt{1-\cos^2(A)} = -\dfrac35 = \boxed{-0.6000}[/tex]
In ΔPQR, find the measure of ∡P. Hypotenuse is 57.6 and the opposite side is 33.8.
Step-by-step explanation:
pythogoras theorem = Q²=P²+R²
P=P
Q= 57.6
R=33.8 =
(57.8)²=(P)²+(33.8)²
=3,340.84=(P)²+1142.44
=3340.84-1142.44=P²
=2,198.4=P²
[tex] = \sqrt{2198.4} = p \\ = 46.8 = p[/tex]
Help please, will give brainliest
Answer: The answer is D
Step-by-step explanation:
find the vertical asymptote(s) of f(x)=x2+3x+6/x2-4
Answer:
x=-2, 2
Step-by-step explanation:
Aighty check this out
[tex]f(x) = \frac{ {x}^{2} + 3x + 6 }{ {x}^{2} - 4 } = = = > \\(x + 2)(x - 2) \\ so \: x = - 2 \: and \: x = 2 \: are \: not \: defined \: \\ and \: are \: the \: candidates [/tex]
if non of the root give out 0/0 both can be the asymptotes:
[tex]f(2) = \frac{{2}^{2} + 3(2) + 6 }{ { - 2}^{2} + 4 } = = = > \\ f(2) = \frac{16}{0} [/tex]
this one is OK
[tex]f( - 2) = \frac{ { - 2}^{2} + 3( - 2) + 6}{ { - 2}^{2} + 4 } = = = > \\ f( - 2) = \frac{4}{0} [/tex]
so is this one
so the asymptotes are x=-2, 2
______×(457+35)=79×457+79×______
Answer:
a(b+c) = a into b + a*c
So, 79(457+35) = 79*457 + 79*35
Step-by-step explanation:
The weight of football players is normally distributed with a mean of 180 pounds and a standard deviation of 20 pounds. what is the probability of a player weighing less than 215 pounds?
Answer:
Given:
mu = 200 lb, the mean sigma = 25 the standard deviation
For the random variable x = 250 lb, the
z-score is z = (x - mu) / sigma = (250 - 200) / 25 = 2
From standard tables for the normal distribution, obtain
P(x < 250) = 0.977
Answer: 0.977
What's the exact value of sin 7/12?
Answer:
C
Step-by-step explanation:
using the addition formula for sine
sin(A + B) = sinAcosB + cosAsinB
note that [tex]\frac{7\pi }{12}[/tex] = [tex]\frac{\pi }{3}[/tex] + [tex]\frac{\pi }{4}[/tex] , then
sin [tex]\frac{7\pi }{12}[/tex]
= sin([tex]\frac{\pi }{3}[/tex] + [tex]\frac{\pi }{4}[/tex] )
= sin[tex]\frac{\pi }{3}[/tex]cos[tex]\frac{\pi }{4}[/tex] + cos[tex]\frac{\pi }{3}[/tex]sin[tex]\frac{\pi }{4}[/tex]
= ( [tex]\frac{\sqrt{3} }{2}[/tex] × [tex]\frac{\sqrt{2} }{2}[/tex] ) + ([tex]\frac{1}{2}[/tex] × [tex]\frac{\sqrt{2} }{2}[/tex] )
= [tex]\frac{\sqrt{6} }{4}[/tex] + [tex]\frac{\sqrt{2} }{4}[/tex]
= [tex]\frac{\sqrt{2}+\sqrt{6} }{4}[/tex]
Please help me
better be worth my 57 points
Answer: a
Step-by-step explanation:
The slope is the rate at which a line goes up or down (i.e., how steep it is). It is measured by the slope formula, which is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where (x1, y1) and (x2, y2) are two points on the line.
Below, (x1, y1) are (c, d) and (x2, y2) are (a, b).
When all variables are plugged in, the slope is
[tex]\frac{b-d}{a-c}[/tex]
Solve the system of equations 4x+5y=-1 and -5x-8y=10 by combining the equations.
The solutions to the given system of equations are x = 6 and y = -5
Simultaneous linear equationsFrom the question, we are to solve the given system of equations
The given system of equation is
4x+5y=-1
-5x-8y=10
Multiply the first equation by 5 and the second equation by 4
5× (4x+5y=-1)
4× (-5x-8y=10)
20x + 25y = -5
-20x - 32y = 40
------------------------
0x + (-7y) = 35
-7y = 35
y = 35/-7
y = -5
Substitute the value of y into the first equation to find x
4x + 5y = -1
4x + 5(-5) = -1
4x -25 = -1
4x = -1 +25
4x = 24
x = 24/4
x = 6
Hence, the solutions to the given system of equations are x = 6 and y = -5
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Levi rented a movie for $3.20 and bought a package of candy for $2.55. How much money did Levi spend in total?
$5.25
$5.50
$5.75
$6.00
The total amount of money Levi spent on renting movie and buying candy is $5.75
EquationAmount Levi rented movie = $3.20A package of candy = $2.55Total = Amount Levi rented movie + A package of candy
= $3.20 + $2.55
= $5.75
Therefore, the total money spent by Levi is $5.75
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