Answer:
13.75 dollars
Step-by-step explanation:
n=4
3n+7/n =3(4) + 7/4
=12 + 1.75
=$13.75
Answer: A) 4.75
Step-by-step explanation:
average age of 15 students of iub 11years if teacher is also included average age becomes 13 years how old is teachers
Answer: the teacher is 43
Step-by-step explanation: if you take 11 and multiply it by 15 you get 165 if you take 208 and divide it by 16 you get 13.
so basically you subtract 208 from 165 to get 43
A mail truck traveled 82 miles in 4 1/2 hours. The distance is the product of the rate and the time. To the nearest tenth, what was the average speed of the mail truck?
Answer:
= 18.2 miles per hour
Step-by-step explanation:
Speed = distance / time
=82 miles / 4.5 hours
=18.22222222 miles per hour
Rounding
= 18.2 miles per hour
Answer:
Given that
Distance = rate × time
82 = r × 4½
r = 18.2 mph
what is the number if 4 is subtracted from the sum of one fourth of 5 times of 8 and 10
Answer:18.5
Step-by-step explanation:
10+8=18
18*5=90
90/4
22.5-4=18.5
Find the sum of all solutions to this equation : ((2x-4)/x+1)) * ((2x+8)/2) * ((2x-70)/(x+2)) =0
Answer:
x=0 or x=2 or x=−4 or x= (7)(2)
Step-by-step explanation:
You have 9kg of oats and cup scales that gears of 50g and 200g. How − in three weighings− can you measure 2kg of the oats?
Answer: You will need 8 cup scales
Step-by-step explanation:
kg=1000 grams
2000/250=8
Answer:
8
Step-by-step explanation:
2000/250=8
A bus company has contracted with a local high school to carry 450 students on a field trip. The company has 18 large buses which can carry up to 30 students and 19 small buses which can carry up to 15 students. There are only 20 drivers available on the day of the field trip.
The total cost of operating one large bus is $225 a day, and the total cost of operating one small bus is $100 per day.
Determine the minimum cost of transporting all 450 students.
Answer:
Step-by-step explanation:
From the given information;
Let consider p to be the number of large buses and q to be the number of small buses.
The company has 18 large buses which can carry up to 30 students and 19 small buses which can carry up to 15 students.
The linear inequality represent the students with respect to the total students s:
30p + 15q ≥ 450 -----(1)
They are only 20 drivers available on the day of the field trip, therefore only 20 buses can be used. So,
p + q ≤ 20 ----- (2)
Also , There are only 19 small buses and 18 large buses:
∴
0 ≤ p ≤ 18
0 ≤ q ≤ 19
The total cost of operating one large bus is $225 a day, and the total cost of operating one small bus is $100 per day
In order to minimize the cost of transporting all 450 students, let z be the minimal cost. i.e
z = 225p + 100q
From equation 1 and 2 ; if we plot them graphically on the graph, the following points of intersection were obtained as shown in the sketch below, in which the shaded region lies the answer.
The point of intersection between equation (1) and (2) is (p,q) = (10,10)
From the critical point in the sketch of our graph attached below, the following values of z can be determined.
Point(s) Value for Z
(15,0) 15 × 225 = 3375
(18,0) 18 × 225 = 4050
(18,2) (18 × 225 )+ (2 × 100 ) = 4250
(10,10) (10 × 225) + (10 × 100) = 3250
Thus ; the minimum cost of transporting all 450 students = $3250
The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 220 grams of a radioactive isotope, how much will be left after 5 half-lives?
Answer:
[tex]\boxed{6.875 \text{\: grams}}[/tex]
Step-by-step explanation:
Half-lives are how long it takes for half of a substance to decay. If you start with a certain amount and it decays for a certain amount of half-lives, you are dividing by [tex]2^{x}[/tex], where x is equal to the amount of half-lives.
In order to solve this question, simply divide the starting value by 2 raised to the value of half-lives.
[tex]\large\boxed{\frac{220}{2^{5}}=6.875\text{\: grams}}[/tex]
If In (x) = 3.53, what is the value of x ?
Rosa is trying to copy an angle. She reads and understands all of the steps, but insists on drawing circles instead of arcs. Which of the following is the best response to tell Rosa?
A. It is acceptable to draw circles instead of arcs, but because they are bigger and take up more space, your drawing may become messy, increasing the chance for errors. <-- MY ANSWER
B. You have to use arcs because a compass cannot make a full circle.
C. You have to draw arcs because arcs and circles are not interchangeable.
D. She is right because it is better to draw circles than arcs. Circles are clearer and easier to draw than arcs so you are less likely to make a mistake.
Thanks!
You have the correct answer. It is choice A. Nice work.
I prefer using full circles because sometimes the arcs could be too small in measure to not go where you want them to. If you're worried about things getting too cluttered (a legitimate concern), then I recommend drawing everything in pencil and only doing the circles as faint lines you can erase later. Once the construction is complete, you would go over the stuff you want to keep with a darker pencil, pen or marker. You can also use the circle as a way to trace over an arc if needed.
Choice B is false as a full circle can be constructed with a compass. Simply rotate the compass a full 360 degrees. Any arc is a fractional portion of a circle.
Choice C is false for similar reasoning as choice B, and what I mentioned in the paragraph above.
Choice D contradicts choice A, so we can rule it out. Arcs are easier to draw since it takes less time/energy to rotate only a portion of 360 degrees. Also, as mentioned earlier, having many full circles tend to clutter things up.
Use DeMoivre's Theorem to find the indicated power of the complex number. Write the answer in rectangular form.
2(cos20∘+isin20∘))3=__________
Answer:
After solving the power:
[tex]\bold{2(cos60^\circ+isin60^\circ)}[/tex]
Rectangular form:
[tex]\bold{1+i\sqrt3}[/tex]
Step-by-step explanation:
Given the complex number:
[tex]2(cos20^\circ+isin20^\circ)^3[/tex]
To find:
The indicated power by using De Moivre's theorem.
The complex number in rectangular form.
Rectangular form of a complex number is given as [tex]a+ib[/tex] where a and b are real numbers.
Solution:
First of all, let us have a look at the De Moivre's theorem:
[tex](cos\theta+isin\theta )^n=cos(n\theta)+isin(n\theta )[/tex]
First of all, let us solve:
[tex](cos20^\circ+isin20^\circ)^3[/tex]
Let us apply the De Moivre's Theorem:
Here, n = 3
[tex](cos20^\circ+isin20^\circ)^3 = cos(3 \times 20)^\circ+isin(3 \times 20)^\circ\\\Rightarrow cos60^\circ+isin60^\circ[/tex]
Now, the given complex number becomes:
[tex]2(cos60^\circ+isin60^\circ)[/tex]
Let us put the values of [tex]cos60^\circ = \frac{1}{2}[/tex] and [tex]sin60^\circ = \frac{\sqrt3}{2}[/tex]
[tex]2(\dfrac{1}{2}+i\dfrac{\sqrt3}2)\\\Rightarrow (2 \times \dfrac{1}{2}+i\dfrac{\sqrt3}2\times 2)\\\Rightarrow \bold{1 +i\sqrt3 }[/tex]
So, the rectangular form of the given complex number is:
[tex]\bold{1+i\sqrt3}[/tex]
A right triangle has vertices (−7,9),(3,9),(−7,−15). Find the perimeter of the triangle. please help. a simple formula will due. and an explanation
Answer:
60
Step-by-step explanation:
If the sides of the triangle have lengths a, b, c, the perimeter is their sum:
P = a + b + c
Any of the side lengths can be found using the distance formula. However, since two of the sides are aligned with the axes, their lengths are easily found by subtracting coordinates.
If the points are labeled A, B, C, in order, then the two right-angle sides are ...
c = AB = 3 -(-7) = 10
b = AC = 9 -(-15) = 24
The Pythagorean theorem tells you that you can find the third side from the relation ...
a² = b² +c²
a² = 10² +24² = 676
a = √676 = 26
Now, we can use these values in the formula for the perimeter:
P = a + b + c = 26 + 24 + 10
P = 60
The perimeter of the triangle is 60 units.
What two rational expressions sum to [tex]\frac{4x+2}{x^{2}-9+8 }[/tex] Enter your answer by filling in the boxes. Enter your answer so that each rational expression is in simplified form.
Answer:
[tex]\frac{4x+2}{x^2 - 9x + 8} = \frac{4x}{(x-8)(x-1)} + \frac{2}{(x-8)(x-1)}[/tex]
Step-by-step explanation:
Given
[tex]\frac{4x+2}{x^{2}-9+8 } = \frac{A}{()(x-1)} + \frac{B}{()(x-8)}[/tex]
Required
Fill in the gaps
Going by the given parameters, we have that
[tex]\frac{4x+2}{x^{2}-9+8 } = \frac{A}{()(x-1)} + \frac{B}{()(x-8)}[/tex]
[tex]x^2 - 9x + 8[/tex], when factorized is [tex](x-1)(x-8)[/tex]
Hence; the expression becomes
[tex]\frac{4x+2}{(x-1)(x-8)} = \frac{A}{(x-8)(x-1)} + \frac{B}{(x-1)(x-8)}[/tex]
Combine Fractions
[tex]\frac{4x+2}{(x-1)(x-8)} = \frac{A + B}{(x-8)(x-1)}[/tex]
Simplify the denominators
[tex]4x + 2 = A + B[/tex]
By direct comparison
[tex]A = 4x[/tex]
[tex]B = 2[/tex]
Hence, the complete expression is
[tex]\frac{4x+2}{x^2 - 9x + 8} = \frac{4x}{(x-8)(x-1)} + \frac{2}{(x-8)(x-1)}[/tex]
Answer:4x+2/x2−9x+8 = −6/7(x−1) + 34/7(x−8)
find the derivative by using product rule and distribution
pls help quickly and show work
Answer:
Below
Step-by-step explanation:
First method:
● f(x)= (x^3-2x+1)×(x-3)
● f'(x)= (x^3-2x+1)' ×(x-3) + (x^3-2x+1)×(x-3)'
●f'(x)= (3x^2-2)×(x-3) + (x^3-2x+1) × 1
●f'(x) = 3x^3-9x^2-2x+6 + x^3-2x+1
● f'(x)= 4x^3-9x^2-4x+7
■■■■■■■■■■■■■■■■■■■■■■■■■■
Second method:
●f(x) = (x^3-2x+1)×(x-3)
●f(x) = x^4-3x^3 -2x^2+6x+x-3
●f(x) = x^4-3x^3-2x^2+7x-3
●f'(x) = 4x^3-9x^2-4x+7
We got the same result using both methods.
An equation for the depreciation of a car is given by y=A(1-r)t where y=current value of the car.A=original cost r=rate of depreciation and t=time in years. The value of a car is half what it originally cost. The rate of depreciation is 10%. Approximately how old is the car?
The more accurate value is 6.57881347896059, which you can round however you need. I picked two decimal places.
==================================================
Explanation:
Let's pick a starting value of the car. It doesn't matter what the starting value, but it might help make the problem easier. Let's say A = 1000. Half of that is 1000/2 = 500.
So we want to find out how long it takes for the car's value to go from $1000 to $500 if it depreciates 10% per year.
The value of r is r = 0.10 as its the decimal form of 10%
t is the unknown number of years we want to solve for
---------------------------
y = A(1 - r)^t
500 = 1000(1 - 0.1)^t
500 = 1000(0.9)^t
1000(0.9)^t = 500
0.9^t = 500/1000
0.9^t = 0.5
log( 0.9^t ) = log( 0.5 )
t*log( 0.9 ) = log( 0.5 )
t = log( 0.5 )/log( 0.9 )
t = 6.57881347896059
Note the use of logs to help us isolate the exponent.
I will mark u brainleiest if u help me and 5 stars
Answer:
[tex]\boxed{50}[/tex]
Step-by-step explanation:
Because the initial temperature is 40 degrees and it increases by 10, add the two values together to get the final temperature.
40 + 10 = 50
Therefore, the final answer is 50 degrees.
Answer:
50
Step-by-step explanation:
If it starts at 40 degrees and increases 10 degrees, it is going to be 50 degrees. Increases means adding, so it is asking you to add 10 to 40 which is 50. If it asks decreases in the future you will have to subtract.
While walking from the car into your dormitory you dropped your engagement ring somewhere in the snow. The path is 30 feet long. You are distraught because the density of its location seems to be constant along this 30-foot route. a) What is the probability that the ring is within 12 feet of your car
Answer:
0.4
Step-by-step explanation:
we are required to find the probability that the ring is within 12 meters from nthe car.
we start by defining a random variable x to be the distance from the car. the car is the starting point.
x follows a normal distribution (0,30)
[tex]f(x)=\frac{1}{30}[/tex]
[tex]0<x<30[/tex]
probabilty of x ≤ 12
= [tex]\int\limits^a_ b{\frac{1}{30} } \, dx[/tex]
a = 12
b = 0
[tex]\frac{1}{30} *(12-0)[/tex]
[tex]\frac{12}{30} = 0.4[/tex]
therefore 0.4 is the probability that the ring is within 12 feet of your car.
Determine the point estimate of the population proportion and the margin of error for the following confidence interval.Lower boundequals0.212,upper boundequals0.758,nequals1200The point estimate of the population proportion is . 485.(Round to the nearest thousandth as needed.)The margin of error is 0.273.(Round to the nearest thousandth as needed.)
Answer: The point estimate of the population proportion is . 485.
The margin of error is 0.273.
Step-by-step explanation:
Confidence interval for population proportion(p):
sample proportion ± Margin of error
Given: Lower bound of confidence interval = 0.212
Upper bound = 0.758
⇒sample proportion - Margin of error=0.212 (i)
sample proportion + Margin of error= 0.758 (ii)
Adding (i) and (ii) , we get
2(sample proportion) =0.970
⇒ sample proportion = 0.970÷2= 0.485
Since sample proportion is the point estimate of the population proportion.
So, the point estimate of the population proportion= 0.485
Now put sample proportion =0.485 in (ii), we get
0.485+ Margin of error= 0.758
⇒ Margin of error= 0.758 - 0.485 =0.273
i.e. The margin of error is 0.273.
4. Solve the system of equations. (6 points) Part I: Explain the steps you would take to solve the system by eliminating the x-terms. (1 point) Part II: Explain the steps you would take to solve the system by eliminating the y-terms. (2 points) Part III: Choose either of the methods described in parts I or II to solve the system of equations. Write your answer as an ordered pair. Show your work. (3 points)
Answer:
The system of equations you want to be solved is not given. I would however give an example with which the method of elimination will be shown, and can be used in solving problems of the nature.
Step-by-step explanation:
Consider the system of equations:
x + y = 7 ................................(1)
2x - y = 8 ..............................(2)
To eliminate x:
First multiply (1) by 2 to have
2x + 2y = 14 ...........................(3)
Next, subtract (2) from (3) to have
3y = 6
y = 6/3 = 2
To eliminate y:
Add (1) and (2) to have
3x = 15
x = 15/3 = 5
Therefore, (x, y) = (5, 2).
How do I solve these equations:
sin(2θ) + sin θ = 0
sin(2θ) = sqrt 3 cos θ
for intervals 0=< θ < 2pi
Answer:
Step-by-step explanation:
Given that
sin(2θ)+sinθ=0
We know that
sin(2θ)=2 sinθ x cosθ
Therefore
2 sinθ x cosθ + sinθ=0
sinθ(2 cosθ+1)=0
sinθ= 0
θ=0
2 cosθ+1=0
cosθ= - 1/2
θ=120°
_______________________________________________________
[tex]sin 2\theta=\sqrt{3cos\theta}[/tex]
By squaring both sides
[tex]sin^2 2\theta={3cos\theta}[/tex]
4 sin²θ x cos²θ=3 cosθ
4 sin²θ x cos²θ - 3 cosθ=0
cos θ = 0
θ= 90°
4 sin²θ=3
θ=60°
You are starting a sock company. You must determine your costs to manufacture your product. The start-up cost is $2000 (which helps you purchase sewing machines). Material and labor is $2.50 per pair of socks.
a. Write an equation to model your company’s cost for manufacturing the socks. (i.e. y=mx+b)
b. Which variable represents the domain? Explain your answer.
c. What is the domain for this situation?
d. Which variable represents the range? Explain your answer.
e. What is the range for this situation?
f. Using your equation, what would be the cost of manufacturing 25 pairs of socks?
g. How many socks could you make with $2500?
h. Create a coordinate graph on a sheet of paper to represent this situation. Describe the graph. Include the dimensions you would use for the x and y axes.
PLS HELP ASAP!
a. y = 2.5x + 2000
b. The variable x represents the domain because the domain is the range of the possible x values.
c. x ≥ 0
d. The variable y represents the range because the range is the range of the possible y values.
e. y ≥ 2000
f. y = 2.5(25) + 2000
y = 62.5 + 2000
y = $2062.50
g. 2500 = 2.5x + 2000
2.5x = 500
x = 200
h. I am sorry I cannot make the graph but hopefully you can figure out how to make it using the info I have given in the above parts of the problem :)
Which point slope form equations could be produced with the points (3,2) and (4,6)
Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation of a line given two points first find the slope of the line and use the formula
y - y1 = m( x - x1) to find the Equation of the line using any of the points given
Slope of the line using points
(3,2) and (4,6) is
[tex]m = \frac{6 - 2}{4 - 3} = \frac{4}{1} = 4[/tex]
So the equation of the line using point
( 3 , 2 ) and slope 4 is
y - 2 = 4( x - 3)Hope this helps you
simplify 4x+3y please
Answer:
[tex]\boxed{4x + 3y}[/tex]
Step-by-step explanation:
Hey there!
Well 4x + 3y cannot be added together because they are 2 different variables.
4x + 3y = 4x + 3y
So 4x + 3y simplified is,
4x + 3yHope this helps :)
Which expression is equal to 7 times the sum of a number and 4
Answer:
7(n + 4)
Step-by-step explanation:
Represent the number by n. Then the verbal expression becomes
7(n + 4).
Which equation demonstrates the additive identity property?
Answer:
See Explanation
Step-by-step explanation:
The options are not given; however, you can take a clue from my explanation to answer your question
Let x be a real number;
Additive identity property implies that; adding x to 0 or 0 to x gives x;
In other words;
[tex]x + 0 = x[/tex]
[tex]0 + x = x[/tex]
Note that x can be replaced with any real number; Take for instance
[tex]1 + 0 = 1[/tex]
[tex]0 + 2.5 = 2.5[/tex]
[tex]3 + 0 = 3[/tex]
There are uncountable number of examples;
However, take note that adding 0 to a given digit results in the exact digit and that's the implication of addition identity property
Answer:
(7+4i)+0=7+4i
Step-by-step explanation:
To find ∫ (x − y) dx + (x + y) dy directly, we must parameterize C. Since C is a circle with radius 2 centered at the origin, then a parameterization is the following. (Use t as the independent variable.)
x = 2 cos(t)
y = 2 sin(t)
0 ≤ t ≤ 2π
With this parameterization, find the followings
dy=_____
dx=_____
Answer:
Step-by-step explanation:
Hello, please consider the following.
[tex]x=x(t)=2cos(t)\\\\dx=\dfrac{dx}{dt}dt=x'(t)dt=-2sin(t)dt[/tex]
and
[tex]y=y(t)=2sin(t)\\\\dy=\dfrac{dy}{dt}dt=y'(t)dt=2cos(t)dt[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
The values of dx and dy are give as -2sin(t)dt and 2cos(t)dt respectively. The answer to the given problem can be stated as,
dy = 2cos(t)dt
And, dx = -2sin(t)dt.
What is the integration of a function?The integration can be defined as the inverse operation of differentiation. If a function is the integration of some function f(x) , then differentiation of that function is f(x).
The given integral over C is ∫ (x − y) dx + (x + y) dy.
And, the parameters for C are as follows,
x = 2cos(t)
y = 2sin(t)
0 ≤ t ≤ 2π
Now, on the basis of these parameters dx and dy can be found as follows,
x = 2cos(t)
Differentiate both sides with respect to t as follows,
dx/dt = 2d(cos(t))/dt
=> dx/dt = -2sin(t)
=> dx = -2sin(t)dt
And, y = 2sin(t)
Differentiate both sides with respect to t as follows,
dy/dt = 2d(sin(t))/dt
=> dy/dt = 2cos(t)
=> dy = 2cos(t)dt
Hence, the value of dx and dy as per the given parameters is -2sin(t)dt and 2cos(t)dt respectively.
To know more about integration click on,
https://brainly.com/question/18125359
#SPJ2
Which equation will solve the following word problem? Jared has 13 cases of soda. He has 468 cans of soda. How many cans of soda are in each case? 13(468) = c 468c = 13 468/13 = c 13 = c/468
Answer:
c = 468 / 13
Step-by-step explanation:
If c is the number of cans of soda in each case, we know that the number of cans in 13 cases is 13 * c = 13c, and since the number of cans in 13 cases is 468 and we know that "is" denotes that we need to use the "=" sign, the equation is 13c = 468. To get rid of the 13, we need to divide both sides of the equation by 13 because division is the opposite of multiplication, therefore the answer is c = 468 / 13.
Answer:
468/13 = c
Step-by-step explanation: Further explanation :
[tex]13 \:cases = 468\:cans\\1 \:case\:\:\:\:= c\: cans\\Cross\:Multiply \\\\13x = 468\\\\\frac{13x}{13} = \frac{468}{13} \\\\c = 36\: cans[/tex]
Matrices and determinants What is 4c?
Answer:
Answer is D.
Step-by-step explanation:
do 4 times every value in the ( )
Answer:
[tex]\boxed{\sf D}[/tex]
Step-by-step explanation:
0 = -12 + 4y - 3x whats the slope
Answer:
3/4 is the slope
Step-by-step explanation:
We want to put this in slope intercept form
y = mx+b where m is the slope and b is the y intercept
0 = -12 + 4y - 3x
Subtract 4y from each side
-4y = -3x-12
Divide each side by -4
-4y/-4 = -3x/-4 -12/-4
y = 3/4 x +3
Answer:
Slope=3/4
Step-by-step explanation:
0=-12+4y-3x (Add 12 on the other side)
12=4y-3x (Add 3x on the other side)
3x+12=4y (Divide by 4)
y=3/4+3
Find the slope of the line that passes through the points (1, -4) and (3,-1)
Hi there! :)
Answer:
[tex]\huge\boxed{m = \frac{3}{2}}[/tex]
Find the slope using the slope formula:
[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Plug in the coordinates of each point:
[tex]m = \frac{-1 - (-4)}{3 - 1}[/tex]
Simplify:
[tex]m = \frac{3}{2}[/tex]
Therefore, the slope of the line is 3/2.
Answer:
3/2
Step-by-step explanation:
The slope is given by
m = (y2-y1)/(x2-x1)
= ( -1 - -4)/(3-1)
= ( -1+4)/(2)
= ( 3/2)
The grade appeal process at a university requires that a jury be structured by selecting individuals randomly from a pool of students and faculty. (a) What is the probability of selecting a jury of all students? (b) What is the probability of selecting a jury of all faculty? (c) What is the probability of selecting a jury of students and faculty
Correct question is ;
The grade appeal process at a university requires that a jury be structured by selecting eight individuals randomly from a pool of nine students and eleven faculty. (a) What is the probability of selecting a jury of all students? (b) What is the probability of selecting a jury of all faculty? (c) What is the probability of selecting a jury of six students and two faculty?
Answer:
A) 7.144 × 10^(-5)
B) 0.00131
C) 0.0367
Step-by-step explanation:
We are given;
Number of students = 9
Number of faculty members = 11
A) Now, the number of ways we can select eight students from 9 =
C(9, 8) = 9!/(8! × 1!) = 9
Also, number of ways of selecting 8 individuals out of the total of 20 = C(20,8) = 20!/(8! × 12!) = 125970
Thus, probability of selecting a jury of all students = 9/125970 = 7.144 × 10^(-5)
B) P(selecting a jury of all faculty) = (number of ways to choose 8 faculty out of 11 faculty)/(Total number of ways to choose 8 individuals out of 20 individuals) = [C(11,8)]/[C(20,8)] = (11!/(8! × 3!))/125970 = 0.00131
C) P(selecting a jury of six students and two faculty) = ((number of ways to choose 6 students out of 9 students) × (number of ways to choose 2 faculty out of 11 faculty))/(Total number of ways to choose 8 individuals out of 20 individuals) = [(C(9,6) × C(11,2)]/125970
This gives;
(84 × 55)/125970 = 0.0367
