x = Edna's age
x + 1 = Ellie's age
x + 2 = Elsa's age
the sum of their ages = 114
Let's set all of their ages equal to 114
x + x + 1 + x + 2 = 114
Combine like terms
3x + 3 = 114
Subtract 3 from both sides
3x = 111
Divide both sides by 3
x = 37
Edna's age = x = 37 years old
Ellie's age = x + 1 = 37 + 1 = 38 years old
Elsa's age = x + 2 = 37 + 2 = 39 years old
Find the first partial derivatives of the function f(x,y,z)=4xsin(y−z)
Answer:
[tex]f_x(x,y,z)=4\sin (y-z)[/tex]
[tex]f_x(x,y,z)=4x\cos (y-z)[/tex]
[tex]f_z(x,y,z)=-4x\cos (y-z)[/tex]
Step-by-step explanation:
The given function is
[tex]f(x,y,z)=4x\sin (y-z)[/tex]
We need to find first partial derivatives of the function.
Differentiate partially w.r.t. x and y, z are constants.
[tex]f_x(x,y,z)=4(1)\sin (y-z)[/tex]
[tex]f_x(x,y,z)=4\sin (y-z)[/tex]
Differentiate partially w.r.t. y and x, z are constants.
[tex]f_y(x,y,z)=4x\cos (y-z)\dfrac{\partial}{\partial y}(y-z)[/tex]
[tex]f_y(x,y,z)=4x\cos (y-z)[/tex]
Differentiate partially w.r.t. z and x, y are constants.
[tex]f_z(x,y,z)=4x\cos (y-z)\dfrac{\partial}{\partial z}(y-z)[/tex]
[tex]f_z(x,y,z)=4x\cos (y-z)(-1)[/tex]
[tex]f_z(x,y,z)=-4x\cos (y-z)[/tex]
Therefore, the first partial derivatives of the function are [tex]f_x(x,y,z)=4\sin (y-z), f_x(x,y,z)=4x\cos (y-z)\text{ and }f_z(x,y,z)=-4x\cos (y-z)[/tex].
A store offers customers a 40% discount on the price of x of selected items. Then, the store takes off an additional 16% at the cash register. Write a price function P(x) that computes the final price of the item in terms of the original price x.
P(x) = ?
Answer:
x-40%-16%
Step-by-step explanation:
Aaron is a high school graduate working as a retail clerk. He earns a median salary for a high school graduate. Aaron is thinking about going to college to get an associate's degree. If he completes his degree in 2 years and college costs total $30,000, how long will it take Aaron to recover his investment, assuming that he earns the median salary and continues to work full time while he is attending school? A graph titled Median Annual Household Income by Educational Attainment of Householder, 1997. Professional degree, 92,228 dollars; doctorate degree, 87,232 dollars; master's degree, 68,115 dollars; Bachelor's degree or more, 63,292 dollars; Bachelor's degree, 59,048 dollars; associate degree, 45,258 dollars; some college, no degree, 40,015 dollars; high school graduate, 33,779 dollars; ninth to twelfth grade, 19,851 dollars; than twelfth grade, 15,541 dollars. a. about 2.5 years b. about 5.5 years c. about 8.5 years d. about 11.5 years
Answer:
i would say c
Step-by-step explanation:
evaluate each expression. (1/3)^4
Answer:
1/81
Step-by-step explanation:
[tex] \huge \bigg( \frac{1}{3} \bigg)^{4} = \frac{1}{ {3}^{4} } = \frac{1}{81} \\ [/tex]
( 5 - 2i)2 Write answer in standard form a +bi. Remember you can not have i2 in your answer it is a number.
(5 - 2i)^2
Simplify.
25 - 20i + 4i^2
Remember that i^2 = -1.
25 - 20i - 4
Combine like terms
21 - 20i
5445,568
Step-by-step explanation:
5.1436 rounded to the nearest tenth
Answer:
5.1
Step-by-step explanation:
we have
5.1436
since 4 is less than five we cannot pass the 1 to 2
so it stays like
5.1
Solve the equation t+ 25 =26
Answer:
t = 1
Step-by-step explanation:
t + 25 = 26
Subtract 25 from each side
t = 1
In the diagram of circle A, what is the measure of
ZXYZ?
35°
70°
75°
140°
Using the intersecting secant theorem:
Angle xyz = 1/2( wz- XX)
Xyz = 1/2(175-105)
Xyz = 1/2(70)
Xyz= 35
The answer is 35 degrees
The measure of <XYZ is 35 degrees
Circle geometryTo find the measure of<XYZ, we will use the expression as shown below:
The angle at the vertex is half the difference of the intercepted arcs
<XYZ = 1/2(175 - 105)
<XYZ = 1/2(70)
<XYZ = 35 degrees
Hence the measure of <XYZ is 35 degrees
Learn more on geometry here: https://brainly.com/question/24375372
What is one equivalent ratio for 1/3
Answer: 2/6
Step-by-step explanation:
Answer:
[tex]\frac{2}{6}[/tex]
Step-by-step explanation:
In order to create an equal ratio to [tex]\frac{1}{3}[/tex], we need to find a constant to multiply both the numerator and the denominator by.
Let's do 2.
[tex]1\cdot 2 = 2\\\\3\cdot 2 = 6\\\\[/tex]
So:
[tex]\frac{2}{6}[/tex]
Hope this helped!
help please i’ll thank you
So first, we must figure out how many dollars = pesos
1 United States Dollar equals
22.38 Mexican Peso
With this, we convert the Dollars from the math problem, to the pesos in the math problem, which is done for us. So we have to figure out how much pesos equal a dollar.
510 Mexican Peso equals
22.80 United States Dollar
What is the value of -3.5
Answer:
[tex]3.5[/tex]
Step-by-step explanation:
The value of [tex]|-3.5|[/tex] is [tex]3.5[/tex], because you have [tex]|-3.5|[/tex] and it will change to [tex]3.5[/tex] by the absolute value, which it turned from negative to a positive.
Point G ia on line segment FH Given FG = 5x + 2 GH = 3x -1 and FH = 9 determine the numerical length of FG
Answer:
Step-by-step explanation:
FG=7
The table shown below displays the distance that students on a track team walked during after-school practice.
Student
Distance (Miles)
John
2.75
Paul
2
Sierra
1.4
Anastasia
31
What was the total distance, in miles, that the students walked during after-school practice?
What is the translation for this graph? O (X-4, Y-3)
O (X-3. y - 4)
O (X-3. y. 4)
O (X- 4. y-3)
Answer:
wow dis might take a while to solve
Peter leaves Mitchell's house traveling 30 mph. Mitchell leaves 15 min later, trying to catch up to peter, going 40 mph. if they drive along the same route, how long will it take Mitchell to catch Peter?
Answer:
45 minutes
Step-by-step explanation:
At 30 mph for 1/4 hour, Peter has a 7.5 mile head start. After he leaves, Mitchell closes that gap at the rate of 40-30 = 10 miles per hour. It will take him ...
t = d/s
t = (7.5 mi)/(10 mi/h) = 0.75 h
to catch Peter.
Mitchell will catch Peter in 45 minutes.
__
Alternate Solution
Another way to look at it is that Mitchell's 10 mph advantage is 1/3 of Peter's speed, so it will take 1/(1/3) = 3 times the period of Peter's head start:
3 × 15 minutes = 45 minutes . . . for Mitchell to catch Peter
_____
You can write equations involving time and distance and see where the distances traveled become the same. You need to be careful choosing the time reference, since you're concerned with Mitchell's travel time. I personally prefer to work "head start" problems by considering the differences in time and speed, as above. This is where you end up using the equations approach, anyway.
12x+12=13x−12 how many sultions
.....................................................................................................................................................................................................................................................................
Solve 5x - (2x - 1) = 2, Answer is a decimal round to the hundredth (2 digits) or use / for fraction bar.
5x - (2x - 1) = 2
Distribute the - sign.
5x - 2x + 1 = 2
Combine like terms.
3x + 1 = 2
Subtract 1 from both sides.
3x = 1
Divide both sides by 3
x = 1/3 or 0.33
Given f(x)=3x-1 find f(-1)
Answer:
f( - 1) = - 4Step-by-step explanation:
f(x) = 3x - 1
To find f(-1) substitute the value of x that's
- 1 into f(x). That's for every x in f(x) replace it with - 1 and solve
That's
f( - 1) = 3(-1) - 1
= - 3 - 1
We have the final answer as
f(-1) = - 4Hope this helps you
compare these numbers
Answer:
[tex]-3.97621,\ -2.5,\ 2\frac{1}{4},\ \sqrt{11},\ 3.\overline{6}[/tex]
Step-by-step explanation:
√11 is about 3.32.
Smallest-to-largest, the numbers are ...
[tex]-3.97621,\ -2.5,\ 2\frac{1}{4},\ \sqrt{11},\ 3.\overline{6}[/tex]
NASA launches a rocket at t = 0 seconds. Its height, in meters above sea-level, as a function of time is given by h(t) = -4.9t^2 + 148 t + 227. Assuming that the rocket will splash down into the ocean, at what time does splashdown occur? The rocket splashes down after 32 seconds. How high above sea-level does the rocket get at its peak? The rocket peaks at meters above sea-level.
Answer:
A.) 24.08 seconds
B.) 825.42 metres
Step-by-step explanation:
function of time is given as
h ( t ) = − 4.9 t 2 + 118 t + 115 .
Where a = -4.9, b = 118, c = 115
Let's assume that the trajectory of the rocket is a perfect parabola.
The time t the rocket will reach its maximum height will be at the symmetry of the parabola.
t = -b/2a
Substitute b and a into the formula
t = -118/-2(4.9)
t = 118/9.8
t = 12.041 seconds
Since NASA launches the rocket at t = 0 seconds, the time it will splash down into the ocean will be 2t.
2t = 2 × 12.041 = 24.08 seconds
Therefore, the rocket splashes down after 24.08 seconds.
B.) At maximum height, time t = 12.041s
Substitute t for 12.041 in the function
h ( t ) = − 4.9 t 2 + 118 t + 115
h(t) = -4.9(12.041)^2 + 118(12.041) + 115
h(t) = -4.9(144.98) + 118(12.041) + 115
h(t) = -710.402 + 1420.82 + 115
h(t) = 825.42 metres
Therefore, the rocket get to the peak at 825.42 metres
One of the most spectacular and least known hummingbirds is the Marvelous Spatuletail, Loddigesia mirabilis, found in only in a single remote valley in northern Peru (see photo below). In this valley the mean density is 3 spatuletails per 100-hectare quadrat. (a) What is the probability a random quadrat contains less than 3 spatuletails
Answer:
P(x < 3) = 0.42319
Step-by-step explanation:
From the given information:
The mean density [tex]\lambda =[/tex] 3
Let x be the random variable that follows a Poisson distribution.
Therefore:
[tex]\mathtt{P(x) = \dfrac{e^{-\lambda} \lambda ^x}{x!}}[/tex] for x =1, 2, 3...
However, the probability that a random quadrat contains less than 3 spatuletails can be computed as:
[tex]\mathtt{P(x <3 ) = \dfrac{e^{-3}3 ^0}{0!}+ \dfrac{e^{-3}3 ^1}{1!}+ \dfrac{e^{-3} 3 ^2}{2!} }[/tex]
[tex]\mathtt{P(x <3 ) =e^{-3} \begin{pmatrix} \dfrac{3 ^0}{0!}+ \dfrac{3 ^1}{1!}+ \dfrac{3 ^2}{2!} \end {pmatrix} }[/tex]
[tex]\mathtt{P(x <3 ) =e^{-3} \begin{pmatrix} \dfrac{1}{1}+ \dfrac{3 }{1}+ \dfrac{9}{2} \end {pmatrix} }[/tex]
[tex]\mathtt{P(x <3 ) =e^{-3} \begin{pmatrix} 1+3+ 4.5 \end {pmatrix} }[/tex]
[tex]\mathtt{P(x <3 ) =e^{-3} \begin{pmatrix}8.5 \end {pmatrix} }[/tex]
P(x < 3) = 0.42319
Determine the measure of each angle. Then describe each angle as acute, right, obtuse, or straight.
Find the x-intercept of the graph of the linear equation y = -1/2 x+3.
Help me please!!
Due soon!!
Answer:
6
Step-by-step explanation:
got it right
help me please. 15 POINTS BRAINLEST ANSWER EVER (y+4)–(y–1)=6y
Answer:
5/6
Step-by-step explanation:
y+4-y+1=6y
5=6y
y=5/6
Solution for (y+4)-(y-1)=6y equation:
Simplifying
(y + 4) + -1(y + -1) = 6y
Reorder the terms:
(4 + y) + -1(y + -1) = 6y
Remove parenthesis around (4 + y)
4 + y + -1(y + -1) = 6y
Reorder the terms:
4 + y + -1(-1 + y) = 6y
4 + y + (-1 * -1 + y * -1) = 6y
4 + y + (1 + -1y) = 6y
Reorder the terms:
4 + 1 + y + -1y = 6y
Combine like terms: 4 + 1 = 5
5 + y + -1y = 6y
Combine like terms: y + -1y = 0
5 + 0 = 6y
5 = 6y
Solving5 = 6y
Solving for variable 'y'.Move all terms containing y to the left, all other terms to the right.
Add '-6y' to each side of the equation.
5 + -6y = 6y + -6y
Combine like terms: 6y + -6y = 0
5 + -6y = 0
Add '-5' to each side of the equation.
5 + -5 + -6y = 0 + -5
Combine like terms: 5 + -5 = 0
0 + -6y = 0 + -5
-6y = 0 + -5
Combine like terms: 0 + -5 = -5
-6y = -5
Divide each side by '-6'.
y = 0.8333333333
Simplifying
y = 0.8333333333
Crude oil Imports to one country from another for 2009-2013 could be approximated by the following model where t is time in years since the start of 2000,
(1) --33428001 - 1,000 thousand barrels per day (9 st s 13)
According to the model, approximately when were oil imports to the country greatest? HINT (See Example 1) (Round your answer to two decimal places.)
How many barrels per day were imported at that time? (Round your answer to two significant digits.)
thousand barrels
Answer:
Time = approximately mid 2012Oil import rate = 3600 barrelsStep-by-step explanation:
Unclear part of the questionI(t) = −35t² + 800t − 1,000 thousand barrels per day (9 ≤ t ≤ 13) According to the model, approximately when were oil imports to the country greatest? t = ? SolutionGiven the quadratic function
The vertex of a quadratic function is found by a formula: x = -b/2aAs per given function:
b = 800, a = -35Then
t = - 800/2*(-35) = 11.43 which is within given range of 9 ≤ t ≤ 13This time is approximately mid 2012.
Considering this in the function, to get oil import rate for the same time:
l(11.43) = -35*(11.43)² + 800*11.43 - 1000 = 3571.4285Rounded to two significant figures, the greatest oil import rate was:
3600 barrelsThe reciprocal of 2 4/7 is? a. 7/18 b. 1/2 c. 18/7 d.7/8
[tex]\text{Hello! :)}[/tex]
[tex]\large\boxed{A. 7 / 18}[/tex]
[tex]\text{Convert 2 4/7 into an improper fraction:}\\\\2*7 + 4 = 18 \\\\\text{(To find the numerator of the fraction)}\\\\\text{Fraction in improper form: 18/7}\\\\\text{Reciprocal of fraction: Swap numerator and denominator:}\\\\18/7 \text{ becomes } 7 / 18[/tex]
find the area of the shape below
A small pebble has a mass of
about
20 L
b.
20 ml
20 g
20 kg
d.
Answer:
20g
since mass should be in kg or gram if small then g
Which one of these shapes is not like the other and why?
A and B is not, because if you were to make the A bigger it'll be the same as B, so I think is C
How hard is 6th grade math?
Answer:
super easy i can help you whenever
Step-by-step explanation:
im in high and i had As in 6th
Answer:
a little hard you just have to understand it
Step-by-step explanation: