28 years
Step-by-step explanation:
Co-relating their ages:Let's say, the cat is x years old.The dog is twice as old as the cat
That makes the dog 2x years old.The monkey is twice as old as the dog.
That is, 2 × (2x) = 4x years old- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Calculating the total:Their total age is 4 years 2 months.
1 year has 12 months
=> 4 years have (4 × 12)
= 48 months
Since, the total age is 4 years 2 months, we can express it in "months" by adding "48" and "2".
= 50 months
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solving for x:Sum of their ages = 50 months
=> x + 2x + 4x = 50
=> 7x = 50
=>x = 50/ 7 months
If we write this in mixed fractions the whole number will represent the number of years.
=
[tex] \mathsf{7 \frac{1}{7} \: \: months}[/tex]
[tex] = \mathsf{7 \: years \: \frac{1}{7} \: \: months}[/tex]
The value of 1/ 7 is really small,I.e., 0.1428...
So, we can ignore the fraction while rounding off the term that makes it
[tex] \mathsf{x = 7yrs.(approx.)}[/tex]
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Recall:x is the age of the cat.
The monkey's age is "4x"
= 4 × 7
= 28 years.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Answer:So, the monkey's age is approximately 28 years
Compute the integral Z Z Z U y dV , where U is the part of the ball of radius 2, centered at (0, 0, 0), that lies in the 1st octant. Recall that the first octant is the part of the 3d space where all three coordinates x, y, z are nonnegative. (Hint: You may use cylindrical or spherical coordinates for this computation, but note that the computation with cylindrical coordinates will involve a trigonometric substitution - so spherical cooridnates should be preferable.)
As the hint suggests, convert to spherical coordinates using
x = p cos(u) sin(v)
y = p sin(u) sin(v)
z = p cos(v)
dV = dx dy dz = p² sin(v) dp du dv
Then U is the set
[tex]U = \left\{ (p,u,v) \mid 0\le p\le2 \text{ and } 0\le u\le \dfrac{\pi}2 \text{ and } 0\le v\le\dfrac{\pi}2\right\}[/tex]
and the integral of y over U is
[tex]\displaystyle \iiint_U y \, dV = \iiint_U p\sin(u)\sin(v) \cdot p^2 \sin(v) \, dV[/tex]
[tex]\displaystyle \iiint_U y \, dV = \int_0^{\frac\pi2} \int_0^{\frac\pi2} \int_0^2 p^3 \sin(u) \sin^2(v) \, dp \, du \, dv [/tex]
[tex] \displaystyle \iiint_U y \, dV = \frac{2^4-0^4}4 \int_0^{\frac\pi2} \int_0^{\frac\pi2} \sin(u) \sin^2(v) \, du \, dv [/tex]
[tex]\displaystyle \iiint_U y \, dV = 4 \cdot \left(-\cos\left(\frac\pi2\right) + \cos(0)\right) \int_0^{\frac\pi2} \sin^2(v) \, dv [/tex]
[tex]\displaystyle \iiint_U y \, dV = 4 \cdot \frac12 \int_0^{\frac\pi2} (1-\cos(2v)) \, dv [/tex]
[tex]\displaystyle \iiint_U y \, dV = 2 \left(\left(\frac\pi2 - \frac12 \sin\left(2\cdot\frac\pi2\right)\right) - \left(0 - \frac12 \sin\left(2\cdot0\right)\right) \right)[/tex]
[tex]\displaystyle \iiint_U y \, dV = \pi - \sin(\pi) = \boxed{\pi}[/tex]
30. What is the solution to the system of equations?
3x + 3y - Z=1
Z=8
-X-3y + 2z = 13
A: (3, 0, 8)
B: (3, 0, -8)
C: (-3, 0,8)
D: (3, 2, 8)
Answer:
x = 3
y = 0
z = 8
Step-by-step explanation:
a) 3x + 3y - z = 1
b) z = 8
c) -x -3y + 2z = 13
a) 3x + 3y - 8 = 1 (substitution)
a) 3x + 3y = 9
c) - x - 3y + 2(8) = 13 (substitution)
c) -x - 3y + 16 = 13
c) -x - 3y = -3
(3x + 3y = 9) + (-x -3y = -3)
= 2x = 6
x = 3
a) 3(3) + 3y - 8 = 1
9 + 3y - 8 = 1
y = (1 -9 + 8)/3
y = 0
The graph of the function f(x) = (x + 2)(x + 6) is shown
below.
Which statement about the function is true?
O The function is positive for all real values of x where
x>-4.
6
14-
O The function is negative for all real values of x where
-6 < x < -2.
The function is positive for all real values of x where
x <-6 orx > -3.
O The function is negative for all real values of x where
x < -2.
24
-2
2
4
6
х
4
Answer:
The function is negative for all real values of x where
-6 < x < -2.
Step-by-step explanation:
f(x) = (x +2)(x + 6)
x + 2 = 0 or x + 6 = 0
x = -2 or x = -6
After graphing the function is negative between -6 < x < -2
The true statement about the graph is (a) The function is negative for all real values of x where -6 < x < -2.
The equation of the function is given as:
[tex]f(x) = (x + 6)(x + 2)[/tex]
From the graph, we have the following highlights
The values of the function decreases from negative infinity till x = -4The values of the function increases from x = -4The values of the function is negative for x = -6 to x = -2The above means that:
The function is negative for all real values of x where -6 < x < -2.
Hence, the true statement about the graph is (a)
Read more about quadratic graphs at:
https://brainly.com/question/7988424
the probability that a tin of paint is dented is 0.07 out of 3000 tins of paint,how many would you expect to be dented?
Answer:
3000×0.07=210 tins
Step-by-step explanation:
210 tins
Step-by-step explanation:
3000÷100×0.07
=2.1
MARK ME BRAINLIEST PLS!!I need to know how to subtract fractions 4 2/3 - 3/4
Answer: The answer would be 3.91666666667
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{4 \dfrac{2}{3} - \dfrac{3}{4}}[/tex]
[tex]\mathsf{= \dfrac{4\times3+2}{3} - \dfrac{3}{4}}[/tex]
[tex]\mathsf{= \dfrac{12 + 2}{3} - \dfrac{3}{4}}[/tex]
[tex]\mathsf{= \dfrac{14}{3} - \dfrac{3}{4}}[/tex]
[tex]\mathsf{= \dfrac{56}{11} - \dfrac{9}{12}}[/tex]
[tex]\mathsf{= \dfrac{14\times4}{12 - 0}}[/tex]
[tex]\mathsf{= \dfrac{56 - 9}{12}}[/tex]
[tex]\mathsf{= \dfrac{47}{12}}[/tex]
[tex]\mathsf{= 3 \dfrac{11}{12}}[/tex]
[tex]\huge\textsf{Therefore, your answer should be: }\huge\boxed{\\\mathsf{\dfrac{47}{12} \ or\ 3 \dfrac{11}{12}}}\huge\checkmark[/tex]
[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]
The width of a rectangle is 6 kilometers
a
less than twice its length. If its area is
56 square kilometers, find the
dimensions of the rectangle.
Answer:
9,333333333333333 and 6 Km
Step-by-step explanation:
The width of a rectangle is 6 kilometers
less than twice its length. If its area is
56 square kilometers, find the
dimensions of the rectangle.
the area of the rectangle is found by multiplying the width by the height, you have the area and the width, divide the area by the width and find the length
56 : 6 = 9,333333333333333 Km
-----------------------------
check
9,333333333333333 * 6 = 56
the answer is good
Please help me answer this question!!!
Answer:
B
Step-by-step explanation:
<STR = <SRT Given the markings of the triangle
<STR + <STU = 180 Supplementary angles
(2x - 9) + 7x = 180 Remove the brackets
2x - 9 + 7x = 180 Combine
9x - 9 = 180 Add 9 to both sides
9x = 180 + 9 Combine
9x = 189 Divide by 9
9x/9 = 189/9
x = 21
What is the volume, in cubic inches, of a rectangular prism with a height of 7 inches, a width of 10 inches, and a length of 9 inches?
Answer:
Step-by-step explanation:
87
Answer:
630 in.³
Step-by-step explanation:
To find the volume of a rectangular prism, you can multiply the height, times the width, times the length. So, let's go ahead and do that with the values of the given prism.
7 × 10 × 9 = 70 × 9 = 630
So, our volume is 630...but not so fast. We also have to put in our units. Our units are inches × inches × inches, or inches³. So our final value is 630 in.³
Hopefully that's helpful! :)
Umm how to do rates
The definition of a rate in math is, the speed of something being gained in a problem, let's say we have a hot pipe that can full up a pool in 6 hours, our rate would be 1/6 of the pool per hour.
pls help with khan academy
Answer:
c
Step-by-step explanation:
because the rest are just way off
Answer:
The answer is C, bro
Step-by-step explanation:
hope this helped.
Can some please help me I will mark u brilliant
Question 2: -4/3
Question 3: -7/20
Find one value of x for F(x)=-4
F(x) = -4 means y = -4. That means whatever the x is, the answer is going to be -4.
10% of $70 = what is the answer i do not now it.
Answer:
10% 0f 70 is 7
Step-by-step explanation:
70÷10=7
10%=7
PLEASE ANSWER ASAP (no links please)
Solve for the indicated variable
g/h = e - 10 for g
Answer:
g = he - 10h
Step-by-step explanation:
which of the following does not require the use of chain rule to find dy/dx.
C. For each term in this expression, you can just apply the power rule.
[tex]y = 3x^2 - \sqrt x + \dfrac2x = 3x^2 - x^{\frac12} + 2x^{-1}[/tex]
[tex]\implies \dfrac{dy}{dx} = 2\cdot3x^{2-1} - \dfrac12 x^{\frac12-1} + (-1)\cdot2x^{-1-1}[/tex]
[tex]\implies \dfrac{dy}{dx} = 6x - \dfrac12 x^{-\frac12} - 2x^{-2}[/tex]
[tex]\implies \dfrac{dy}{dx} = 6x - \dfrac1{2\sqrt x} - \dfrac2{x^2}[/tex]
Every other choice involves composite functions that do require the chain rule to differentiate.
Option C : [tex]y = 3x^2 - \sqrt{x} + \dfrac{2}{x}\\[/tex] can be differentiated without using chain rule.
The differentiation of [tex]y = 3x^2 - \sqrt{x} + \dfrac{2}{x}\\[/tex] without using chain rule can be done as follows:
[tex]\begin{aligned}\dfrac{dy}{dx} &= \dfrac{d}{dx}(3x^2 - \sqrt{x} + \dfrac{2}{x})\\\\&= \dfrac{d}{dx}(3x^2 - x^{\frac{1}{2}} + 2x^{-1})\\&= 6x - (1/2)x^{-\frac{3}{2}} -2x^{-2}\\\end{aligned}[/tex]
The rest of the functions are composite, which means, that after differentiating them with some other base, you need to change the base and differentiate again, thus applying chain rule.
Thus, the function [tex]y = 3x^2 - \sqrt{x} + \dfrac{2}{x}\\[/tex] can be differentiated without using chain rule.
Thus, option C: [tex]y = 3x^2 - \sqrt{x} + \dfrac{2}{x}\\[/tex] is correct option.
Learn more here:
https://brainly.com/question/5543508
in which system are the lines parallel ?
Five students share the writing of a term
paper evenly. If each person writes more
than six pages, how long is the paper?
Answer:
Over 30
Step-by-step explanation:
There is no definite answer if you don't know how many pages each person. All you have to do is multiply 5 by 6
rewrite 12/12 as a whole number
9514 1404 393
Answer:
1
Step-by-step explanation:
Any (non-zero) number divided by itself is 1.
_____
This is a fact that has many uses in problem solving and units conversion.
Robert has 4 times as many pennies as he does nickels. If Robert has $1.44 worth of pennies and nickels, how many nickels does he have?
Find the length of the hypotenuse, side c, of a right triangle with legs of length a = 4 and b = 5. Use a calculator to estimate the
square root to one decimal place.
answer:
6.4
Step-by-step explanation:
4^2+5^2=c^2
16+25
square root of 41
c^2=6.4
Either enter exact answer in terms of pie or 3.14
Answer:
18 π ≈ 56.52
Step-by-step explanation:
The formula for the volume of a cylinder is V = π · r² · h.
This cylinder has a height (h) of 2 and a radius (r) of 3.
Therefore the volume is:
V = π · r² · h = π · 3² · 2 = 18 π ≈ 56.52.
What is 11 divided by 1/4
Maya earned $225.oo at her job when she worked for 10 hours. What did she earn in one hour?
We are flying at 30 000 feet.
Our speed is 500 miles per hour.
Our total flight time will be 10 hours and 20 minutes.
Mark knows the distance from London to Cancun is 4944 miles. He asks his daughter to check the information given by the pilot. She knows this formula for speed.
s = dt
s = speed (miles per hour) d = distance (miles)
t = time (hours)
Evaluate the information given by the pilot.
Show calculations to support your answer.
Answer:
Step-by-step explanation:
500 mph with a flight time of 10 hours and 20 minutes [(20 min)*(1 h/60 min) = 0.333 hr]
Distance = Speed * Time
Time = 10.333 hours
Distance = (500 miles/hr)*(10.333 hrs) = 5166.5 miles
The pilot's numbers indicate a distance of 5167 miles, compared to Mark's number of 4944 miles. That is a 4.3% reduction from the pilot's numbers. Not too bad, so we might question 1) Mark's knowledge, or 2) the impact that the approach and landing speeds have of the total miles flow.
My preference would be to trust the pilot's data. I don't know where Mark got his math education.
Multiplying polynomials
Steps are in the attachment.
________
Hope it helps :)) ⚜
HELP! Can anyone help me i need help it this question
Average rate = distance / time
Rewrite distance as an improper fraction":3 1/3 = 10/3
Now you have 10/3 / 1/3
When dividing by a fraction flip the second fraction over and multiply:
10/3 x 3/1 = (10 x 3) / (3/1) = 30/3 = 10
Average rate was 10 miles per hour
here is the other question
Answer:
1. -3 × A1 + A2 --> B2
2. [tex]-\frac{1}{7}[/tex] × B2 --> C2
Step-by-step explanation:
1. -3 × A1 + A2 --> B2
(4x × -3) + 12x = -12x + 5x = -7x
(2y × -3) + 6y = -6y + 6y = 0y
(-10 × -3) + -9 = 30 - 9 = 21
2. [tex]-\frac{1}{7}[/tex] × B2 --> C2
-7x × [tex]-\frac{1}{7}[/tex] = 1x
21 × [tex]-\frac{1}{7}[/tex] = -3
Same process as last time
how to do surface area
Answer:
Step-by-step explanation:
Multiply the length and width, or c and b to find their area. Multiply this measurement by two to account for both sides. Add the three separate measurements together. Because surface area is the total area of all of the faces of an object, the final step is to add all of the individually calculated areas together.
Answer:
Surface area is the sum of the areas of all faces (or surfaces) on a 3D shape. We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surface area.
Step-by-step explanation:
I need help for these 5 questions
Answer:
1. 6²=36
2. 289[tex]\frac{1}{2}[/tex] = 17
3. [tex]14^{-2}[/tex] = [tex]\frac{1}{196}[/tex]
4. 10³=1000
5. [tex]5^{4}[/tex]=625
Step-by-step explanation:
Answer:
1. 6² = 36
2. 289^1/2 = 17
3. 14^-2 = 1/196
4. 10³ = 1000
5. 5⁴ = 625
Step-by-step explanation:
I just used the rule that logₓy = n means that xⁿ = y and a logarithm without a base, has a base of 10 (called a "common logarithm").
A company that bakes chocolate chip cookies averages 5.2 chocolate chips per cookie. Assume that the number of chocolate chips per cookie follows the Poisson distribution. What is the probability that a randomly selected cookie will contain two or more chocolate chips
Answer 12
Step-by-step explanation:
A shipment of 12 microwave ovens contains three defective units. A vending company has ordered four units, and because each has identical packaging, the selection will be random. What is the probability that (a) all four units are good, (b) exactly two units are good, and (c) at least two units are good?
I hope that helped?