Answer:
3/4-1/2=1/4 4/5-3/15
Step-by-step explanation:
3/4-1/2
=3/4-2/4
=1/4
4/5-3/15
=4/5-1/5
=3/5
xp-q+1×xq-r+1×xr-p+1
Answer:
Look into the picture
Step-by-step explanation:
Let me know if there's something wrong to my answer
La señora Alcántara realiza una compra en el supermercado fortuna, ella solo tiene 12,400 pesos ,compra varios artículos y su compra es equivalente a 13,600 pesos. ¿Cuánto tiene que pagar si le realizan un descuento de un 15%? ¿Cuántos le quedaron de lo que tenía en efectivo?
Answer:
She spent = 11560 pesos
Amount left = 840 pesos
Step-by-step explanation:
Mrs. Alcántara makes a purchase at the fortuna supermarket, she only has 12,400 pesos, she buys several items and her purchase is equivalent to 13,600 pesos. How much do you have to pay if they give you a 15% discount? How many was left of what he had in cash?
Amount she has = 12400pesos
Item purchased = 13600 pesos
discount = 15 %
So, the total discount on the item purchased is
= 15 % of 13600
= 0.15 x 13600
= 2040 pesos
So, the amount spent = 13600 - 2040 = 11560 pesos
Amount she left = 12400 - 11560 = 840 pesos
Please answer for me ! And if you do answer Tysm please show your work also! ❤️
A paddleboat can move at a speed of 4 km/h in still water. The boat is paddled 12 km downstream in a river in the same time it takes to go 6 km upstream. What is the speed of the river?
Answer:
Speed of the river = [tex]\frac{4}{3}[/tex] km per hour
Step-by-step explanation:
Speed of the boat in still water = 4 km per hour
Let the speed of the river = v km per hour
Speed of the boat upstream = (4 - v) km per hour
Time taken to cover 6 km = [tex]\frac{\text{Distance}}{\text{Speed}}[/tex]
= [tex]\frac{6}{4-v}[/tex] hours
Speed of the boat downstream = (4 + v) km per hour
Time taken to cover 12 km = [tex]\frac{12}{4+v}[/tex] hours
Since, time taken by the boat in both the cases is same,
[tex]\frac{6}{4-v}= \frac{12}{4+v}[/tex]
6(4 + v) = 12(4 - v)
24 + 6v = 48 - 12v
12v + 6v = 48 - 24
18v = 24
v = [tex]\frac{24}{18}[/tex]
v = [tex]\frac{4}{3}[/tex] km per hour
Given that Q(x)=2x^2 +5x-3 find and simplify Q(a+h)-Q(a-h)
Answer:
[tex]Q(a+h)-Q(a-h)=8ah+10h[/tex]
Step-by-step explanation:
We are given the function:
[tex]Q(x)=2x^2+5x-3[/tex]
And we want to find and simplify:
[tex]Q(a+h)-Q(a-h)[/tex]
Substitute:
[tex]=[2(a+h)^2+5(a+h)-3]-[2(a-h)^2+5(a-h)-3][/tex]
Expand:
[tex]\displaystyle =[2(a^2+2ah+h^2)+5a+5h-3]-[2(a^2-2ah+h^2)+5a-5h-3][/tex]
Distribute:
[tex]=[2a^2+4ah+2h^2+5a+5h-3]-[2a^2-4ah+h^2+5a-5h-3][/tex]
Distribute:
[tex]=(2a^2+4ah+2h^2+5a+5h-3)+(-2a^2+4ah-2h^2-5a+5h+3)[/tex]
Rewrite:
[tex]=(2a^2-2a^2)+(4ah+4ah)+(2h^2-2h^2)+(5a-5a)+(5h+5h)+(-3+3)[/tex]
Combine like terms:
[tex]=8ah+10h[/tex]
Hence:
[tex]Q(a+h)-Q(a-h)=8ah+10h[/tex]
The height and base radius of a cone are increased by a factor of 2 to create a similar cone. How is the slant height of the cone affected? The slant height of the larger cone is equal to the slant height of the smaller cone. The slant height of the larger cone is double the slant height of the smaller cone. The slant height of the larger cone is 4 times the slant height of the smaller cone. The slant height of the larger cone is 8 times the slant height of the smaller cone.
Answer:
The slant height of the cone affected is two times the slant height of original cone
Step-by-step explanation:
we know that
If the height and base radius of a cone are increased by a factor of to create a similar cone
then
the scale factor is equal to
therefore
the slant height of the cone affected is equal to the slant height of the original cone multiplied by the scale factor
Find the slant height of the original cone
Let
l-----> slant height of original cone
la-----> slant height of the cone affected
Applying the Pythagoras theorem
so
The slant height of the cone affected is two times the slant height of original cone
(I GOT THIS FROM SOMEONE ELSES ANSWER IN 2017 SO I HOPE THIS HELPS)
The slant height of the larger cone is double the slant height of the smaller cone.
Option B is the correct answer.
What is a cone?It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.
The volume of a cone is 1/3 πr²h
We have,
The slant height of the cone is affected by a factor of 2.
When the height and base radius of a cone are multiplied by 2, the dimensions of the new cone are doubled.
Therefore,
The slant height of the larger cone is double the slant height of the smaller cone.
Learn more about cones here:
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Assume that $4,000 I deposited into an investment account doubled in value over a six year period. What annual interest rate must I have earned over this period? Is the initial amount of the deposit relevant to the calculation of the annual interest rate? Why or why not?
Answer:
Interest rate is about 12.246%
The initial deposit doesn't matter because when you divide both sides by the initial deposit you're always left with (1+i)ⁿ=2
Step-by-step explanation:
[tex]4000(1+i)^6=8000\\(1+i)^6=2\\1+i=\sqrt[6]{2} \\1+i=1.122462048\\i=.12246[/tex]
Your EZ Pass account begins with $80. It costs you $4/day. Write an equation
for the amount in your account (A) in terms of the number of days (D).
Answer:
The equation is [tex]A(d) = 80 - 4d[/tex]
Step-by-step explanation:
Linear function:
A linear function for the amount of money in an account after t days is given by:
[tex]A(d) = A(0) - md[/tex]
In which A(0) is the initial value and m is the daily cost.
Your EZ Pass account begins with $80. It costs you $4/day.
This means that [tex]A(0) = 80, m = 4[/tex]
So
[tex]A(d) = A(0) - md[/tex]
[tex]A(d) = 80 - 4d[/tex]
A car originally costs $20,000. Its price went up by 20% and then by another $8,000. How much did the price go up as a percentage of the original price?
Answer:
60%
Step-by-step explanation:
20,000
we can move the decimal place one to the left to find 10 percent
2,000
multiply 10 x 2 to find twenty percent or 4,000
we add this to the original total. 24,000
then add the 8,000
32,000
we know find one percent of the original total
200
and find the difference between the two totals
32000-20000 = 12,000
12000 divided by 200 which is 6
multiply six by ten to get
60 percent
How Do I do this equation
Answer:
Part A 12 ≤ 6x ≤ 36
Part B 2 ≤ x ≤ 6
Step-by-step explanation:
The following formula gives the area A of a trapezoid with base lengths b1 and b2, and height h.
A=12(b1+b2)h
Find the area of a trapezoid with base lengths 3 and 6 and a height of 8.
The point-slope form of the equation of a line that passes through points (8, 4) and (0, 2) is y -4 = %(x -8). What is
the slope-intercept form of the equation for this line?
O y = ÷x-12
O y= x-4
O y= =x+2
O y= =x +6
Answer:
y= x-4
Step-by-step explanation:
It has a time to failure distribution which is normal with a mean of 35,000 vehicle miles and a standard deviation of 7,000 vehicle miles. Find its designed life if a .97 reliability is desired.
Answer:
The designed life should be of 21,840 vehicle miles.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 35,000 vehicle miles and a standard deviation of 7,000 vehicle miles.
This means that [tex]\mu = 35000, \sigma = 7000[/tex]
Find its designed life if a .97 reliability is desired.
The designed life should be the 100 - 97 = 3rd percentile(we want only 3% of the vehicles to fail within this time), which is X when Z has a p-value of 0.03, so X when Z = -1.88.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.88 = \frac{X - 35000}{7000}[/tex]
[tex]X - 35000 = -1.88*7000[/tex]
[tex]X = 21840[/tex]
The designed life should be of 21,840 vehicle miles.
In any triangle ABC,Prove by vector method c^2=a^2+b^2-2abcosC
Answer:
Let be [tex]\vec A[/tex], [tex]\vec B[/tex] and [tex]\vec C[/tex] the vector of a triangle so that [tex]\vec C = \vec A + \vec B[/tex]. By definition of Dot Product:
[tex]\vec C \,\bullet\,\vec C = (\vec A + \vec B) \,\bullet \vec C[/tex]
[tex]\vec C \,\bullet \,\vec C = (\vec A\,\bullet \,\vec C) + (\vec B \,\bullet \,\vec C)[/tex]
[tex]\|\vec C\|^{2} = [\vec A \,\bullet \,(\vec A + \vec B)] + [\vec B\,\bullet \,(\vec A + \vec B)][/tex]
[tex]\|\vec C\|^{2} = \vec A \,\bullet \, \vec A + \vec B\,\bullet \vec B + 2\cdot (\vec A \,\bullet \, \vec B)[/tex]
[tex]\|\vec C\|^{2} = \|\vec A\|^{2} + \|\vec B\|^{2} + 2\cdot \|\vec A\|\cdot \|\vec B\|\cdot \cos\theta_{C}[/tex]
Step-by-step explanation:
Let be [tex]\vec A[/tex], [tex]\vec B[/tex] and [tex]\vec C[/tex] the vector of a triangle so that [tex]\vec C = \vec A + \vec B[/tex]. By definition of Dot Product:
[tex]\vec C \,\bullet\,\vec C = (\vec A + \vec B) \,\bullet \vec C[/tex]
[tex]\vec C \,\bullet \,\vec C = (\vec A\,\bullet \,\vec C) + (\vec B \,\bullet \,\vec C)[/tex]
[tex]\|\vec C\|^{2} = [\vec A \,\bullet \,(\vec A + \vec B)] + [\vec B\,\bullet \,(\vec A + \vec B)][/tex]
[tex]\|\vec C\|^{2} = \vec A \,\bullet \, \vec A + \vec B\,\bullet \vec B + 2\cdot (\vec A \,\bullet \, \vec B)[/tex]
[tex]\|\vec C\|^{2} = \|\vec A\|^{2} + \|\vec B\|^{2} + 2\cdot \|\vec A\|\cdot \|\vec B\|\cdot \cos\theta_{C}[/tex]
Seth and Ted can paint a room in 5 hours if they work together. If Ted were to work by himself, it would take him 2 hours longer than it would take Seth working by himself. How long would it take Seth to paint the room by himself if Ted calls in sick?
Answer:
9 hours
Step-by-step explanation:
Let
x = number of hours it would take Seth to work by himself
He would paint 1/x in 1 hour
x + 2 = number of hours it would take Ted to work by himself
He would paint 1/(x + 2) in 1 hour
Seth and Ted = 5 hours
They would paint 1/5 in 1 hour
The equation is this:
1/x + 1/(x + 2) = 1/5
(x + 2)+x/x(x+2) = 1/5
x+2+x / x(x+2) = 1/5
2x + 2 / x(x+2) = 1/5
2x + 2 = x(x + 2)1/5
2x + 2 = (x² + 2x)1/5
5(2x + 2) = x² + 2x
10x + 10 = x² + 2x
x² + 2x - 10x - 10 = 0
x² - 8x - 10 = 0
x = -b ± √b² - 4ac/2a
= -(-8) ± √(-8)² - 4(1)(-10) / 2(1)
= 8 ± √64 - (-40) / 2
= 8 ± √64 + 40) / 2
= 8 ± √104 / 2
= 8 ± 2√26 / 2
= 8/2 ± 2√26/2
= 4 ± √26
= 4 ± 5.0990195135927
= 4 + 5.0990195135927 or 4 - 5.0990195135927
= 9.0990195135927 or -1.Answer:
Step-by-step explanation:
Let
x = number of hours it would take Seth to work by himself
He would paint 1/x in 1 hour
x + 2 = number of hours it would take Ted to work by himself
He would paint 1/(x + 2) in 1 hour
Seth and Ted = 5 hours
They would paint 1/5 in 1 hour
The equation is this:
1/x + 1/(x + 2) = 1/5
(x + 2)+x / x(x+2) = 1/5
x+2+x / x(x+2) = 1/5
2x + 2 / x(x+2) = 1/5
Cross product
2x + 2 = x(x + 2)1/5
2x + 2 = (x² + 2x)1/5
Cross product
5(2x + 2) = x² + 2x
10x + 10 = x² + 2x
x² + 2x - 10x - 10 = 0
x² - 8x - 10 = 0
x = -b ± √b² - 4ac/2a
= -(-8) ± √(-8)² - 4(1)(-10) / 2(1)
= 8 ± √64 - (-40) / 2
= 8 ± √64 + 40) / 2
= 8 ± √104 / 2
= 8 ± 2√26 / 2
= 8/2 ± 2√26/2
= 4 ± √26
= 4 ± 5.0990195135927
= 4 + 5.0990195135927 or 4 - 5.0990195135927
= 9.0990195135927 or -1.0990195135927
Approximately,
x = 9 hours or -1 hour
It can't take Seth negative hours to work
Therefore,
x = number of hours it would take Seth to work by himself = 9 hours
The data represent the results for a test for a certain disease. Assume one individual from the group is randomly selected. Find the probability of getting someone who tests negative, given that he or she did not have the disease.
The individual actually had the disease
Yes No
Positive 135 11
Negative 99 145
Answer:
0.9295 = 92.95% probability of getting someone who tests negative, given that he or she did not have the disease.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question:
11 + 145 = 156 people did not have the disease.
Out of those, 145 tested positive. So
[tex]p = \frac{145}{156} = 0.9295[/tex]
0.9295 = 92.95% probability of getting someone who tests negative, given that he or she did not have the disease.
Determine the mean and variance of the random variable with the following probability mass function. f(x)=(216/43)(1/6)x, x=1,2,3 Round your answers to three decimal places (e.g. 98.765).
Mean:
E[X] = ∑ x f(x) = 1 × f (1) + 2 × f (2) + 3 × f (3) = 51/43 ≈ 1.186
Variance:
Recall that for a random variable X, its variance is defined as
Var[X] = E[(X - E[X])²] = E[X ²] - E[X]²
Now,
E[X ²] = ∑ x ² f(x) = 1² × f (1) + 2² × f (2) + 3² × f (3) = 69/43
Then
Var[X] = 69/43 - (51/43)² = 366/1849 ≈ 0.198
(each sum is taken over x in the set {1, 2, 3})
Find the volume (in cubic yards) of a cylinder with radius 1.2 yards and height 2.9 yards. (Round your answer to one decimal place.)
Answer:
11.8 yd³
Step-by-step explanation:
Ray is constructing a flower bed
Answer:
41 feet
Step-by-step explanation:
12 +12 + [tex]\sqrt{144+144}[/tex]
Answer:
Perfilar. Comienza por delimitar la forma y dimensión del macizo. ...
Cavar y abonar. ...
Enmarcar y rastrillar. ...
Distribuir y plantar.
Step-by-step explanation:
find the value of...
Answer:
1
Step-by-step explanation:
tan(1)tan(2)....tan(89)=?
Recall tan(90-x)=cot(x) and cot(x)tan(x)=1.
tan(89)=tan(90-1)=cot(1)
tan(88)=tan(90-2)=cot(2)
tan(87)=tan(90-3)=cot(3)
...
tan(46)=tan(90-44)=cot(44)
tan(45)=tan(90-45)=cot(45)
So we can replace the last half of the factors with cotangent of the angles in the first half.
The only one that doesn't get a partner is the exact middle factor which is tan(45).
So this is whar we have:
tan(1)tan(2)tan(3)....tan(45)....cot(3)cot(2)cot(1)
So you should see that cot(1)tan(1)=1 and cot(2)tan(2)=1 and so on....
So the product equals tan(45) and tan(45)=1 using unit circle.
Which proportion resulted in the equation 3a = 7b?
StartFraction 3 over a EndFraction = StartFraction 7 over b EndFraction
StartFraction 3 over b EndFraction = StartFraction 7 over a EndFraction
StartFraction a over b EndFraction = StartFraction 3 over 7 EndFraction
StartFraction 3 over 7 EndFraction = StartFraction 3 over b EndFraction
Answer:
The correct one is 3 over b equals 7 over a
Answer:
3/b = 7/a
Step-by-step explanation:
I took it on Edge
Determine the value of z in the figure
5z
130°
A.Z = 30°
B.Z = 45°
C.z = 50°
D.Z = 10°
Hi!
180° - 130° = 50°
5z = 50° || : 5
z = 10°
Answer:
10
Step-by-step explanation:
since 130 and the 5z are complementary angles, by subtracting 130 from 180, you get 50. then you equal in 50 to 5z. 50=5z. to solve, you divide 5 from 50 and your answer is 10.
What is the solution to the system of equations below
Answer:
A
Step-by-step explanation:
1/2x-4=-2x-9...u vil get the ans
A Line passes through the .4 -6 and has a slope of -3 and four which is the equation of the line
Answer:
(in the image)
Step-by-step explanation:
I'm not sure I understood your question completely but I hope this helps.
Marla scored 70% on her last unit exam in her statistics class. When Marla took the SAT exam, she scored at the 70th percentile in mathematics. Explain the difference in these two scores.
Answer:
The difference is that Marla's exam in her statistics class was graded by percent of correct answers, in her case 70%, while the SAT is graded into a curve, taking other students' grades also into account, and since she scored in the 70th percentile, Marla scored better than 70% of the students.
Step-by-step explanation:
Marla scored 70% on her last unit exam in her statistics class.
This means that in her statistics class, Marla got 70% of her test correct.
When Marla took the SAT exam, she scored at the 70th percentile in mathematics.
This means that on the SAT exam, graded on a curve, Marla scored better than 70% of the students.
Explain the difference in these two scores.
The difference is that Marla's exam in her statistics class was graded by percent of correct answers, in her case 70%, while the SAT is graded into a curve, taking other students' grades also into account, and since she scored in the 70th percentile, Marla scored better than 70% of the students.
A ball is thrown vertically upward with an initial velocity of 19 m/s. Its height, h(t)metres after t seconds, is given by the equation h(t) = -3t2 + 20t + 2.0.
The time taken by the ball to reach the maximum height is ________ seconds. Round your answer to the nearest tenth.
Answer:
Step-by-step explanation:
There are 2 different ways to do this: calculus and by completing the square. In this particular instance, calculus is WAY easier, and since I don't know for what class you are doing this, I'll do both ways. First the calculus way. We know the position equation, and the first derivative of the position is velocity. We also know that when the velocity is equal to 0 is when the object is at its max height. So we'll find the derivative first, then solve it for t:
If [tex]s(t)=-3t^2+20t+2[/tex] then the first derivative is
v(t) = -6t + 20 Solving for t requires that we set the velocity equal to 0 (again, this is where the object is at its max height), so
0 = -6t + 20 and
-20 = -6t so
t = 3.3 seconds. Now that we know that at 3.3 seconds the object is at its highest point, we sub that time into the position function to see where it is at that time:
s(3.3) = [tex]-3(3.3)^2+20(3.3)+2[/tex] and
s(3.3) = 35.3 meters.
Now onto the more difficult way...completing the square. Begin by setting the position function equal to 0 and then move over the constant to get:
[tex]-3t^2+20t=-2[/tex] Since the leading coefficient is not a 1 (it's a 3), we have to factor out the 3, leaving us with:
[tex]-3(t^2-\frac{20}{3}t)=-2[/tex] Now the rule is to take half the linear term, square it, and add it to both sides. Our linear term is [tex]\frac{20}{3}[/tex] and half of that is [tex]\frac{20}{6}[/tex]. Squaring that:
[tex](\frac{20}{6})^2=\frac{400}{36}=\frac{100}{9}[/tex]. We will add that in to both sides. On the left it's easy, but on the right we have to take into account that we still have that -3 sitting out front, refusing to be ignored. So we have to multiply it in when we add it to the right. Doing that gives us:
[tex]-3(t^2-\frac{20}{3}t+\frac{100}{9})=-2-\frac{100}{3}[/tex] We will clean this up a bit now. The reason we do this is because on the left we have created a perfect square binomial which will give us the time we are looking for to answer this question. Simplifying the right and at the same time writing the perfect square binomial gives us:
[tex]-3(t-\frac{20}{6})^2=-\frac{106}{3}[/tex] Now the last step is to move the constant back over and set the quadratic back equal to y:
[tex]y=-3(t-\frac{20}{6})^2+\frac{106}{3}[/tex]. The vertex of this quadratic is
[tex](\frac{20}{6},\frac{106}{3})[/tex] where
[tex]\frac{20}{6}=3.3[/tex] as the time it takes for the ball to reach its max height of
[tex]\frac{106}{3}=35.3[/tex] meters.
I'd say if you plan on taking calculus cuz you're not there yet, you'll see that many of these types of problems become much simpler when you know it!
What is the rate of change of the line on the graph
Answer:
A. ¼
Step-by-step explanation:
Rate of change (m) = [tex] \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Using two points on the line, (4, 1) and (-4, -1), find the rate of change using the formula stated above:
Where,
[tex] (4, 1) = (x_1, y_1) [/tex]
[tex] (-4, -1) = (x_2, y_2) [/tex]
Plug in the values
Rate of change (m) = [tex] \frac{-1 - 1}{-4 - 4} [/tex]
= [tex] \frac{-2}{-8} [/tex]
= [tex] \frac{1}{4} [/tex]
Rate of change = ¼
what is the range of the funcion y=x^2
Answer:
Range = [0, infinity)
Step-by-step explanation:
Minimum point of the graph is at (0,0) and it is a u shaped graph. Hence, range is 0 inclusive to infinity
PLEASE HELP WILL MARK BRAINLIEST!
9514 1404 393
Answer:
7.5
Step-by-step explanation:
Corresponding sides are proportional, so ...
UV/VW = LM/MN
x/6 = 15/12
x = 6(15/12) = 15/2
x = 7.5
What type of line is PQ⎯⎯⎯⎯⎯⎯⎯⎯?
Answer:
median
Step-by-step explanation:
Q is at the midpoint of RS and so PQ is a median
A median is a segment from a vertex to the midpoint of the opposite side.
We want to define what type of line is PQ (the line that passes through points P and Q) by looking at the given image, one can easily see that the line PQ is a median, now let's explain why.
First, let's analyze the image:
In the image, we can see that P is one vertex of the triangle, and Q is the midpoint of the segment RS (you can see that RQ = 4 and QS = 4) , where R and S are the other two vertexes of the triangle.
Particularly, we can define a median of a triangle as the line that passes through the midpoint of one side of the triangle and by the vertex that does not belong to that side.
With that definition, we can see that PQ is a median because Q is the midpoint of one side of the triangle and P is the vertex that does not belong to that side.
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