Answer:
hello mateee ;)
Step-by-step explanation:
lets go step by step...
216 cub root = 6
x^3 cube root = 3/3 = power 1 = x
y^6 cube root = 6/3 = power 2 = y^2
z^12 cube root = 12/3 = power 4 = z^4
final ans becomes 6x y^2 z^4 hence option a is correct
glad for brainliest <3
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 1 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:
Seth would need 10 hours to paint the room.
Step-by-step explanation:
Let's define:
S = rate at which Seth works
T = rate at which Ted works
When they work together, the rate is S + T
And we know that when they work together they can pint one room in 5 hours, then we can write:
(S + T)*5 h = 1 room.
We also know that Ted alone would need one hour more than Seth alone.
Then if Seth can paint the room in a time t, we have:
S*t = 1room
and
T¨*(t + 1h) = 1room
Then we have 3 equations:
(S + T)*5 h = 1
S*t = 1
T¨*(t + 1h) = 1
(I removed the "room" part so it is easier to read)
We want to find the value of S.
First, let's isolate one variable (not S) in one of the equations.
We can isolate t in the second one, to get:
t = 1/S
Now we can replace it on the third equation:
T¨*(t + 1h) = 1
T¨*( 1/S + 1h) = 1
Now we need to isolate T in this equation, we will get:
T = 1/( 1/S + 1h)
Now we can replace this in the first equation:
(S + T)*5h = 1
(S + 1/( 1/S + 1h) )*5h = 1
Now we can solve this for S
(S + 1/( 1/S + 1h) )= 1/5h
S + 1/(1/S + 1h) = 1/5h
Now we can multiply both sides by (1/S + 1h)
(1/S + 1h)*S + 1 = (1/5h)*(1/S + 1h)
1 + S*1h + 1 = 1/(S*5h) + 1/5
S*1h + 2 = (1/5h*S) + (1/5)
Now we can multiply both sides by S, to get:
(1h)*S^2 + 2*S = (1/5h) + (1/5)*S
Now we have a quadratic equation:
(1h)*S^2 + 2*S - (1/5)*S - (1/5h) = 0
(1h)*S^2 + (9/5)*S - (1/5h) = 0
The solutions are given by the Bhaskara's formula:
[tex]S = \frac{-(9/5) \pm \sqrt{(9/5)^2 - 4*(1h)*(-1/5h)} }{2*1h} = \frac{-9/5 \pm 2}{2h}[/tex]
Then the solution (we only take te positive one) is:
S = (-9/5 + 2)/2h
S = (-9/5 + 10/5)/2h = (1/5)/2h = 1/10h
Then Seth needs a time t to paint one room:
(1/10h)*t = 1
t = 1/(1/10h) = 10h
So Seth would need 10 hours to paint the room.
Please help! Identify the recursive formula for the sequence 20, 28, 36, 44, . . . .
Answers below in picture:
Option A
Answered by GauthMath if you like please click thanks and comment thanks
Given the equation y/x = -6/7 the constant of variation is:
Answer:
[tex]{ \tt{ \frac{y}{x} = - \frac{6}{7} }} \\ { \tt{y = - \frac{6}{7}x }} \\ { \boxed{ \bf{constant = - \frac{6}{7} }}}[/tex]
A candidate running for public office receives 2,000 of the 8, 000 total votes cast from an election. Name the numerator and denominator
of the fraction that represents the candidate's fraction of the total votes.
A set of data is normally distributed with a mean of 75 and a standard deviation of 3. What percent of the data is in the interval 72–78?
Can someone help me please!!! Not sure what to do with the problem or where to start. Thank you for your help!
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Answer:
0.65 ≤ x ≤ 2.35
Step-by-step explanation:
The ± symbol is pronounced "plus or minus." Then 1.5 ± 0.85 means ...
1.5 + 0.85 = 2.35 or 1.5 - 0.85 = 0.65
These are said to be the end points of a closed* interval, so the interval is ...
0.65 ≤ x ≤ 2.35
This is graphed as solid dots at 0.65 and 2.35 and the number line shaded between those dots.
_____
* "closed" means the endpoints are included in the interval. An interval is "open" if the endpoint is not included. The inequality for that is written using the < symbol instead of the ≤ symbol.
I need to know what goes in the periods rate total amount and total interest boxes in why
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Answer:
periods: 4rate: 1%total amount: 598.35total interest: 23.35Step-by-step explanation:
"Periods" will be filled with the number of years (1) times the number of periods per year (quarterly = 4). periods = 4
"Rate" is likely filled with the rate of interest divided by the number of periods per year. rate = 4%/4 = 1%
Then the total amount is found by ...
total amount = principal × (1 + rate)^(periods)
= 575 × (1.01^4) = 598.35
The total interest is the difference between this amount and the principal.
total interest = total amount - principal
= 598.35 -575 = 23.35
_____
We believe we have made reasonable assumptions regarding the intent of the columns in the table. Your best bet is to compare this problem to the worked examples in your curriculum materials.
The area of a rectangle is 3,878 square centimeters. If the rectangle has a width of 14 centimeters, what is its length?
Answer:
277 cm
Step-by-step explanation:
[tex]A=l*w\\3,878=l*14\\l=\frac{3,878}{14} \\l=277[/tex]
Find the critical numbers (x-values) of the function y equals 2 x to the power of 5 plus 5 x to the power of 4 minus 19. Enter your answers as a comma-separated list. Round answers to 2 decimal places, if necessary.
Answer:
[tex]x=0,x=-2[/tex]
Step-by-step explanation:
From the question we are told that:
[tex]y=2x^5+5x^4-19[/tex]
Generally the equation if differentiated is mathematically given by
[tex]y'=10x^4+20x^3-0[/tex]
Where
y'=0
[tex]10x^4+20x^3=0[/tex]
Factorizing,We have
[tex]x=0,x=-2[/tex]
Therefore
The critical points are
[tex]x=0,x=-2[/tex]
A class of kindergarteners is making get well cards for children in the houses how many different cards can be made from 2 shapes 4 card colors 3 colors of glitter and 8 colors of markers
Answer:
192
Step-by-step explanation:
Multiply all numbers together.
2 * 4 * 3 * 8 = 192
Answer:
it's 192 because you have to multiply all of the numbers to get 192
What is the measure of B?
generate a table of values for the equation y = -4.5x - 0.5. Use values for x from -2 to 2, increment by 1 in each row
Answer:
x = -2: y = 8.5
x = -1: y = 4
x = 0: y = -0.5
x = 1: y = -5
x = 2: y = -9.5
Step-by-step explanation:
We find the numeric values for the function from x = -2 to x = 2.
x = -2:
[tex]y = -4.5(-2) - 0.5 = 9 - 0.5 = 8.5[/tex]
x = -1:
[tex]y = -4.5(-1) - 0.5 = 4.5 - 0.5 = 4[/tex]
x = 0:
[tex]y = -4.5(0) - 0.5 = 0 - 0.5 = -0.5[/tex]
x = 1:
[tex]y = -4.5(1) - 0.5 = -4.5 - 0.5 = -5[/tex]
x = 2:
[tex]y = -4.5(2) - 0.5 = -9 - 0.5 = -9.5[/tex]
30 POINTS PLEASE HELP
Answer:
Answer:
Solution given:
f(x)=5x-3
let
y=f(x)
y=5x-3
interchanging role of x and y
x=5y-3
x+3=5y
y=[tex]\frac{x+3}{5}[/tex]
$o,
f-¹(x)=[tex]\frac{x+3}{5}[/tex]
we conclude that
f-¹(x)≠g(x)
Each pair of function are not inverses.
g(x)=x/5+3
let g(x)=y
y=x/5+3
interchanging role of x and y
x=y/5+3
x-3=y/5
doing crisscrossed multiplication
5(x-3)=y
y=5x-15
g-¹(x)=5x-15
So
g-¹(x)≠f-¹(x)
Each pair of function are not inverses.
Two people start from the same point. One walks east at 4 mi/h and the other walks northeast at 8 mi/h. How fast is the distance between the people changing after 15 minutes?
Answer:
5.89 mi/h
Step-by-step explanation:
This problem can be solved by using different methods. I will use vectors since it's the simplest way in which we can solve it. This can be solved by using related rates of change though.
First, we start by drawing a diagram with the velocity vectors.
A= velocity of the first person
B= velocity of the second person
C= velocity in which they are moving away from each other.
Since there is no acceleration in the problem, we can suppose we are talking about constant speeds, so the velocity at which they are moving away from each other will always remain constant. (It doesn't matter what time it is, the velocity will always be the same)
Having said this we can solve this problem by using the components, by using law of cosines or graphically. I will use law of cosines. The idea is to find the length of side c.
Law of cosines:
[tex]C^{2}=A^{2}+B^{2}-2ABcos \gamma[/tex]
so we can solve the formula for C so we get:
[tex]C=\sqrt{A^{2}+B^{2}-2ABcos \gamma}[/tex]
and now we can substitute the values we know:
[tex]C=\sqrt{(4)^{2}+(8)^{2}-2(4)(8)cos 45^{o}}[/tex]
[tex]C=\sqrt{16+64-32\sqrt{2}}[/tex]
[tex]C=\sqrt{80-32\sqrt{2}} mph[/tex]
if we want an exact answer, then that will be the exact answer, which approximates to:
C=5.89 mph
A test has 6 multiple choice questions , each with four possible answers . How man different answer keys are possible?
Answer:
24
Step-by-step explanation:
6 x 4 = 24
Answer:
Step-by-step explanation:
4⁶=4096
calculate the area of the following figure.
Answer:
77 cm²
Step-by-step explanation:
The figure can be decomposed into two rectangles.
✔️Area of rectangle 1:
Area of rectangle 1 = length * width
length = 3.5 cm
width = 8 cm
Area of rectangle 1 = 3.5*8 = 28 cm²
✔️Area of rectangle 2:
Area of rectangle 2 = length * width
length = 14 cm
width = 3.5 cm
Area of rectangle 2 = 14*3.5= 49 cm²
✔️Area of the figure = 28 + 49 = 77 cm²
Ibrahim wants to give each of his six friends 1 2/3 candy bars. How many candy bars does he need to buy?
Answer:
10 candy bars
Step-by-step explanation:
Since each of his friends needs a candy bar, you need to multiply 6 and 1 ⅔ together.
First, convert 1 ⅔ into an improper fraction: this gives us ⁵⁄₃.
Next, multiply ⁶⁄₁ and ⁵⁄₃ together. To do this, you can visualize 6 as ⁶⁄₁ (which is the same thing). Now you have ⁶⁄₁ x ⁵⁄₃.
Simplify:
The 6 in the numerator and the 3 in the denominator cancel out. This gives us ²⁄₁ x ⁵⁄₁ , which is 2 x 5.
2 x 5 = 10
Solve: 1/3a^2-1/a=1/6a^2
Step-by-step explanation:
there are two answers for a
Answer:
The ANSWER IS 1/6
Step-by-step explanation:
Find an odd natural number x such that LCM (x, 40) = 1400
Answer:
175.
Step-by-step explanation:
40 = 2*2*2*5
1400 = 2*2*2*5*5*5*7
So by inspection we have x = 5*5*7 = 175
Supposed we saved 55$ and we saved 6$ each week what’s the total amount of t we will have after w weeks
Answer:
t=55+6w
Hope This Helps!!!
Solve the function.
Plz Help!!
[tex]1\pm\sqrt{2}i[/tex]
Step-by-step explanation:
We already know that one of the roots is x = -4 so we can factor this out to get
[tex]x^3+2x^2-5x+12=(x+4)(x^2-2x+3)[/tex]
Using the quadratic equation on the 2nd factor, we find the roots are
[tex]x= \dfrac{2\pm\sqrt{(2)^2 - 4(1)(3)}}{2}=1\pm\sqrt{2}i[/tex]
In slope-intercept form, what is the equation of a line perpendicular to y = 10x - 8 that passes through the point (0,0)?
O 1
y = -0,1x + 10
O2
y = -0.1x + 1
3
y = -0.1x
04
y = 0.1x
Answer:
y = -0,1x + 1
Step-by-step explanation:
If y is 2,851, 1% of Y is
Excellent question, but let's rephrase it.
Suppose you have a square of surface area of 2851.
What would be a hundredth of such square?
What would be surface area of that hundredth.
Why hundredth? Because percent denotes hundredths cent is a latin word for hundred. You would usually encounter similar word that describes 100 years: century.
Well it is actually very easy. Just divide 2851 into 100 pieces and look at what is the area of one piece.
[tex]2851/100=285.1=y[/tex]
So a single piece has an area of 258.1.
Hope this helps. :)
A committee of 3 is to be selected randomly from a group of 3 men and 2 women.
Let X represent the number of women on the committee. Find the probability
distribution of X.
Total number of ways to select 3 people from the 5 total: 5!/(3! (5 - 3)!) = 10
• Number of ways of picking 0 women:
[tex]\dbinom20\times\dbinom33 = 1\times1 = 1[/tex]
• Number of ways of picking 1 woman:
[tex]\dbinom21\times\dbinom32 = 2\times3 = 6[/tex]
• Number of ways of picking 2 women:
[tex]\dbinom22\times\dbinom31 = 1\times3 = 3[/tex]
• Number of ways of picking 3 women: 0, since there are only 2 to choose from
Then X has the probability mass function
[tex]P(X=x) = \begin{cases}\frac1{10}&\text{if x=0}\\\frac6{10}=\frac35&\text{if }x=1\\\frac3{10}&\text{if }x=2\\0&\text{otherwise}\end{cases}[/tex]
Please help, I really need this
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Answer:
(a) -- the correct choice is highlighted
Step-by-step explanation:
The units of specific heat tell you what quantities make up the ratio.
[tex]\dfrac{390\text{ J}}{1\text{ kg$\cdot^\circ$C}}=\dfrac{-12.0\text{ J}}{0.012\text{ kg}\cdot\Delta T}\\\\\Delta T=\dfrac{-12.0}{0.012\cdot390}\ ^\circ\text{C}\approx-2.56\text{ $^\circ$C}[/tex]
The temperature will decrease by 2.56 C.
The function graphed above is:
Concave up on the interval:
Concave down on the interval:
There is an inflection point at:
Answer:
concave up:(-3, ∞)
concave down: (-∞, -3)
inflection point: (-3, 0)
Step-by-step explanation:
Concave up is when the slope increases, and concave down is when the slope decreases. Here, we can see that, as we move left to right, when x is less than -3, the slope starts out really high (y is increasing rapidly) but is decreasing. Then, as x reaches -3, the slope starts to rise, and the change in y gets higher and higher.
Given this information, we can say that the function is concave down from (-∞, -3) as it is going down from all values until x=-3 and is concave up from (-3, ∞) as it is going up from all values past x= -3 , with an inflection point of (-3, 0) as that is when the change in slope goes from down to up.
1. Assume that as of today, the annualized interest rate on a three-year security is 8 percent, while the annualized interest rate on a two-year security is 6 percent. Use only this information to estimate the one-year forward rate two years from now.
Answer:
r1 = 12.11 %
Step-by-step explanation:
One-year forward rate two years from now = (1+0.08)^3 / ( 1+0.06)^2 - 1
r1 = 1. 2597/1.1236 - 1
r1 = 12.11 %
PLEASE HELPPP ASAPPPPP
Answer:
combination 91 ways
Step-by-step explanation:
This is a combination since order doesn't matter
Permutation are when order matter
14 choose 2 order doesnt matter
14*13
--------
2*1
91 different ways
At a concession stand; three hot dogs and two hamburgers cost $9.75; two hot dogs and three hamburgers cost $10.25. Find the cost of one hot dog and the cost of one hamburger.
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Answer:
hot dog: $1.75hamburger: $2.25Step-by-step explanation:
Let x and y represent the cost of a hot dog and a hamburger, respectively. The the two purchases can be described by ...
3x +2y -9.75 = 0
2x +3y -10.25 = 0
We can list the coefficients of these general-form equations in 2 rows, listing the first one again at the end:
3, 2, -9.75, 3
2, 3, -10.25, 2
Now, we can form differences of cross-products in adjacent pairs of columns:
d1 = (3)(3) -(2)(2) = 9 -4 = 5
d2 = (2)(-10.25) -(3)(-9.75) = -20.50 +29.25 = 8.75
d3 = (-9.75)(2) -(-10.25)(3) = -19.50 +30.75 = 11.25
Then the solutions are found from ...
1/d1 = x/d2 = y/d3
x = d2/d1 = 8.75/5 = 1.75
y = d3/d1 = 11.25/5 = 2.25
The cost of one hot dog is $1.75; the cost of one hamburger is $2.25.
_____
Additional comment
This is my simplification of the "cross-multiplication method" of solving a pair of linear equations. That method can be found described on web sites and in videos. This version, and the versions described elsewhere, are variations on Cramer's Rule and on the Vedic Maths method of solving equations. Each of those do similar differences of cross products, perhaps in less-easily-remembered fashion.
For a given pair of columns with coefficients ...
a b
c d
The cross-product we form is ad -cb.
Which of these shapes have the same area?? help ;-;
Answer:
A and B because if you count they both have 16 and C has 25