Answer:
Step-by-step explanation:
Hello!
2 4 5 ∟ 70
-2 1 3, 5
------------------------
3 5 0
3 5 0
- --------------------------------
0 0 0
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
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.
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]
Consider the following sample space, S, and several events defined on it. S = {Albert, Betty, Abel, Jack, Patty, Meagan}, and the events are: F = {Betty, Patty, Meagan}, H = {Abel, Meagan}, and P = {Betty, Abel}. FH is ___________.
Answer:
FnH = {Meagan}
Step-by-step explanation:
Given the following sets and events:
S = {Albert, Betty, Abel, Jack, Patty, Meagan}
F = {Betty, Patty, Meagan},
H = {Abel, Meagan}
P = {Betty, Abel}.
In order to get FnH
The intersection of F and H is the element that is common to both sets. Hence for the set given, we can see that Meagan is common to both sets, therefore:
FnH = {Meagan}
A camera with a price of d dollars is discounted 25%. write two expressions to represent the price of the camera with the discount.
Answer:
17d/20
Step-by-step explanation:
100-25=85
85/100×d
=17/20×d
=17d/20
What is the range of the function
Answer: [tex]-\infty < y < \infty[/tex] which is choice A
This is the set of all real numbers.
===========================================================
Explanation:
If you were to graph this function, then it spans infinitely upward and infinitely downward as well. That means that we can land on any y value we want, and that's why the range is the set of all real numbers.
Another approach we could take is to swap x and y to get [tex]x = \sqrt[3]{y+8}[/tex] which solves to [tex]y = x^3-8[/tex] . This is the inverse of the original function your teacher gave you. Recall that the domain and range swap roles when going from the original function to the inverse. What this means is that because the domain of
Domain of inverse = set of all reals
Range of original = set of all reals
Oil is pumped continuously from a well at a rate proportional to the amount of oil left in the well. Initially there were 2 million barrels of oil in the well; six years later 1,000,000 barrels remain.
Required:
a. At what rate was the amount of oil in the well decreasing when there were 1,200,000 barrels remaining?
b. When will there be 100,000 barrels remaining?
Answer:
A. It was decreasing by -138,629.44 barrels
B. 26 years of time
Step-by-step explanation:
Due to the length of this question solution, I was unable to type it. The answer is contained in the attachment.
A. At 1200000
Bt = 1200000
-1/6ln2 x 1200000
Solve this using a calculator
= -138,629.4361
So the amount of oil is decreasing by -138,629.44 barrels
Please help, I really need this
9514 1404 393
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.
When the function f(x) = 4(2)x is changed to f(x) = 4(2)x − 13, what is the effect? (5 points)
Select one:
a. There is no change to the graph because the exponential portion of the function remains the same.
b. The x-intercept is 13 spaces higher.
c. The y-intercept is 13 spaces lower.
d. All input values are moved 13 spaces to the left.
Answer:
C
If x = o then f(0) = 4(2) * 0 = 0
If f(x) = 4(2) 0 - 13
then f(x) = -13 at x = 0
Answer:
it will indeed be c
Step-by-step explanation:
deesnuts
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]
Solve for x Round to the nearest tenth one place after the decimal !
Answer:
x = 14.4
Step-by-step explanation:
x is sin(angle 24/30)×24
how do we get the angle at 24/30 ?
by using the extended Pythagoras for baselines opposite other than 90 degrees.
c² = a² + b² - 2ab×cos(angle opposite of c)
in our example the angle 24/30 is opposite of the side 18.
so,
18² = 24² + 30² - 2×24×30×cos(angle 24/30)
324 = 576 + 900 - 1440×cos(angle 24/30)
324 = 1476 - 1440×cos(angle 24/30)
1440×cos(angle 24/30) = 1152
cos(angle 24/30) = 1152/1440 = 576/720 = 288/360 = 144/180 = 72/90 = 36/45 = 12/15 = 4/5
angle 24/30 = 36.9 degrees
x = sin(36.9) × 24 = 14.4
Given f(x) = 6x + 2, find f(x – 3).
A. f(x – 3) = 6x – 1
B. f(x – 3) = 6x – 16
C. f(x - 3) = x - 1
D. f(x – 3) = 6x2 – 16x - 6
Answer: B. f(x - 3) = 6x - 16
Concept:
When encountering a question that gives you a function and the evaluation value, then basically plug the given value into the function.
Solve:
Given function and value
f(x) = 6x + 2
f(x - 3)
Substitute the value into the given expression
f(x - 3) = 6 (x - 3) + 2
f(x - 3) = 6x - 18 + 2
f(x - 3) = 6x - 16
Hope this helps!! :)
Please let me know if you have any questions
31
?
40
Find the measure of the indicated angle to the nearest whole degree.
Answer:
51°
Step-by-step explanation:
Reference angle (θ) = ?
Opposite side length = 31
Hypotenuse length = 40
Apply SOH, which is;
Sin θ = Opp/Hyp
Plug in the values
Sin θ = 31/40
θ = sin^{-1}(31/40)
θ = 51° (neatest whole degree)
Consider the triangle.
Which statement is true about the lengths of the sides?
O Each side has a different length.
O Two sides have the same length, which iS less than
the length of the third side.
O The three sides have the same length.
O The sum of the lengths of two sides is equal to the
length of the third side.
Answer:
the last one
Step-by-step explanation:
this is because it is an equalactral triangle meaning that the line at the side is the only one which its degrees is 90 so if u add 45 and 45 its 90(hope this helps)
Answer:
Two sides have the same length, which iS less than
the length of the third side.
Step-by-step explanation:
Hypotenuce is a sode opposite to right angle, which is always bigger then any side of right triangle. since both angles are the same, Adjacent and Opposite are similar size as well.
Find two numbers that have 2, 5, and 7 as factors.
Step-by-step explanation:
One easy way to find a number that has all of these numbers as factors is to multiply them all together, so 2 * 5 * 7 = 10 * 7 = 70, which is one number.
To find the other number, we can multiply the number we already have by any integer greater than 1, e.g. 2, to get 70* 2= 140 as our other number, making our numbers 70 and 140
If you were going to install a new window in your bathroom, what needs to be measured? What
else might you need to consider?
measure horizontally
measure vertically
measure depth..
Help please, thanks
Answer: B. X It passes the vertical line test :)
Step-by-step explanation:
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.
9514 1404 393
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.
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:
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]
Question 8 of 53
How much would $700 be worth after 8 years, if it were invested at 5%
interest compounded continuously? (Use the formula below and round your
answer to the nearest cent.)
A(t) = P•e^rt
A. $5887.12
B. $1044.28
C. $6432.11
D. $38,218.71
9514 1404 393
Answer:
B. $1044.28
Step-by-step explanation:
Putting the given numbers into the given formula, we have ...
A(8) = $700•e^(0.05•8) ≈ $1044.28
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]
$o,
f-¹(x)=[tex]\frac{x+3}{5}[/tex]
we conclude that
f-¹(x)≠g(x)
Each pair of function are not inverses.
g(x)=x/5+3
let g(x)=y
y=x/5+3
interchanging role of x and y
x=y/5+3
x-3=y/5
doing crisscrossed multiplication
5(x-3)=y
y=5x-15
g-¹(x)=5x-15
So
g-¹(x)≠f-¹(x)
Each pair of function are not inverses.
use complete sentences to describe the transformation of triangle ABC into its image.
Answer:
Move triangle ABC over 2 and up 1
Step-by-step explanation:
A transformation in geometry is to essentially move a shape. To move ABC onto A1B1C1 you would move triangle ABC over 2 and up 1.
Please help! Identify the recursive formula for the sequence 20, 28, 36, 44, . . . .
Answers below in picture:
Option A
Answered by GauthMath if you like please click thanks and comment thanks
Find an odd natural number x such that LCM (x, 40) = 1400
Answer:
175.
Step-by-step explanation:
40 = 2*2*2*5
1400 = 2*2*2*5*5*5*7
So by inspection we have x = 5*5*7 = 175
Supposed we saved 55$ 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!!!
Which word MOST affects the tone of this sentence?
A slender woman walked into the room wearing a pink dress and a gaudy hat.
A- room
B- gaudy
C- woman
D- slender
Answer:
B
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. :)
By examining past tournaments, it's possible to calculate the probability that a school wins their first game in the national college basketball tournament. Each school's rank going into the tournament is a strong indicator of their likelihood of winning their first game.
Find the linear regression equation that models this data.
The linear regression model which models the data is :
y = -6.41053X + 103.83509
Obtaining the regression equation could be performed using either the formula method or using technology (excel, calculator, online regression calculators )
Using technology :
• Enter the data into the columns provided ;
The regression equation obtained for the data is : y = -6.41053X + 103.83509
Where ;
Slope = -6.41053
Intercept = 103.83509
X = Rank
y = probability percentage
Hence, from the linear regression equation obtained, we could see that a negative linear relationship exists between rank and probability as implied from it's negative slope value.
Learn more on linear regression : https://brainly.com/question/12164389
The weight of bags of fertilizer is normally distributed with a mean of 50 pounds and standard deviation of 6 pounds. What is the probability that a bag of fertilizer will weigh:
a. Between 45 and 55 pounds?
b. At least 56 pounds?
c. At most 49 pound?
Answer:
Following are the solution to the given points:
Step-by-step explanation:
Normal Distribution:
[tex]\mu=50\\\\\sigma= 6\\\\Z=\frac{X-\mu}{\sigma} \sim N(O,l)[/tex]
For point a:
[tex]P(X< 56)=\frac{(56-50)}{6}= \frac{6}{6}=1\\\\[/tex]
[tex]=P(Z<1)\ From\ \sigma \ Table=0.8413\\\\P(X>= 56)=(1-P(X< 56))=1-0.8413=0.1587\\\\[/tex]
For point b:
[tex]P(X< 49)=\frac{(49-50)}{6}=-\frac{1}{6} =-0.1667\\\\=P(Z<-0.1667)\ From\ \sigma \ Table\\\\=0.4338[/tex]
For point c:
To Find [tex]P(a\leq Z\leq b)= F(b) - F(a)\\\\[/tex]
[tex]P(X< 45)=\frac{(45-50)}{6}=\frac{-5}{6} =-0.8333\\\\P (Z<-0.8333) \ From \ \sigma \ Table\\\\=0.20233\\\\P(X< 55)=\frac{(55-50)}{6} =\frac{5}{6}=0.8333\\\\P ( Z< 0.8333) \ From \ \sigma\ Table\\\\=0.79767\\\\P(45 < X < 55) =0.79767-0.20233 =0.5953[/tex]
