[tex] \begin{array}{l} 2^x = 3^y = 12^z \\ 2^x = 3^y = 2^{2z} \cdot 3^z \\ \Rightarrow 3 = 2^{\frac{x}{y}} \\ \Rightarrow 2^x = 2^{2z} \cdot 2^{\frac{xz}{y}} \\ \Rightarrow x = 2z + \frac{xz}{y} \\ \Rightarrow xy = 2zy + xz \\ \Rightarrow 2zy = xy - xz \\ \text{Dividing both sides by }xyz,\text{ we get:} \\ \dfrac{2}{x} = \dfrac{1}{z} - \dfrac{1}{y} \end{array} [/tex]
The table of values represents a linear function g(x), where x is the number of days that have passed and g(x) is the balance in the bank account:
Part A: Find and interpret the slope of the function. (3 points)
Part B: Write the equation of the line in point-slope, slope-intercept, and standard forms. (3 points)
Part C: Write the equation of the line using function notation. (2 points)
Part D: What is the balance in the bank account after 5 days? (2 points)
Answer:
see below
Step-by-step explanation:
Part A
The slope is found by
m = ( y2-y1)/(x2-x1)
= ( 1200-1500)/(4-0)
= -300/4
=-75
Part B
point slope y-y1 = m(x-x1) where m is the slope and (x1,y1) is a point on the line
y-1200 = -75(x-4)
slope intercept y = mx+b where m is the slope and b is the y intercept
y = -75x + 1500
standard form Ax+By =C
75x + y = 1500
Part C
Change y to g(x) in the slope intercept form
g(x) = -75x + 1500
Part D
Let x = 5
g(5) = -75(5) + 1500
=-375+1500
=1125
Armando's carpet has an area of 220 square feet. He hires the Carpet Pro carpet cleaning service, which is able to clean 9 square feet of his carpet every minute. Therefore, in the first minute, CarpetPro is able to clean 9 square feet of Armando's carpet (leaving 211 square feet remaining to be cleaned). In the second minute, the cleaner is again able to clean 9 square feet of carpet (leaving 202 square feet to be cleaned), etc. Which of the following functions expresses the number of square feet that still remain to be cleaned after t minutes from the time that the carpet cleaner began cleaning this carpet.
a. A(t) = 220 - 9
b. A(t) = 220 - 0.1
c. A(t) = 220(0.1)
d. A(t) = 220(0.96)
e. A(t) 220 - 0.96
Answer:
The answer is A
Step-by-step explanation:
The answer needs to be in slope-intercept form or y=mx+b because the amount of carpet being cleaned every minute is a constant decrease of 9 square feet.
So our b value (or how much carpet cleaned at 0 minutes) is 220
And our m value (or slope or how much carpet is being cleaned every minute) is 9
So if we plug the variables with the tangible numbers we get A(t) = -9x+220 or A(t) = 220-9x.
provided by gauth math
Find the missing numerator: 3 1/3 = x/6
[tex]\sf\huge\underline\color{pink}{༄Answer:}[/tex]
[tex]\tt3 \frac{1}{3} = \frac{x}{6} \\ = \tt \frac{10}{3} = \frac{x}{6} \\ = \tt \frac{x}{6} = \frac{10}{3} \\ = \tt6 \frac{x}{6} = 6( \frac{10}{3} ) \\ = \tt\large\boxed{\tt{\color{pink}{x = 20}}}[/tex]
[tex]\color{pink}{==========================}[/tex]
#CarryOnLearning
Convert 110101 in base 2 to base 10
Answer:
base-2 base-10
110011 = 51
110100 = 52
110101 = 53
110110 = 54
21 more rows
What is the equation of exponential regression equation? Round all numbers you your answer to three decimal places
Given:
The given values are:
[tex]a=0.2094539899[/tex]
[tex]b=2.507467975[/tex]
[tex]r^2=0.9435996398[/tex]
[tex]r=0.9713905701[/tex]
To find:
The exponential regression equation for the given values (Rounded to three decimal places).
Solution:
The general form of exponential regression equation is:
[tex]y=a\cdot b^x[/tex] ...(i)
Where, a is the initial value and b is the growth/decay factor.
We have,
[tex]a=0.2094539899[/tex]
[tex]b=2.507467975[/tex]
Round these numbers to three decimal places.
[tex]a\approx 0.209[/tex]
[tex]b\approx 2.507[/tex]
Substitute [tex]a=0.209, b=2.507[/tex] in (i) to find the exponential regression equation.
[tex]\hat{y}=0.209\cdot 2.507^x[/tex]
Therefore, the correct option is C.
What is 1.25 x 10^8 in standard form?
Answer:
125000000
Step-by-step explanation:
1.25 x 10^8
Move the decimal 8 places to the right
1.25
We can move it two places
125
We need to add 6 more zeros
125000000
Answer: 125,000,000
Step-by-step explanation:
The differential equation of a certain system is 20y′′+cy′+80y=0
, where c is called damping constant for what value of c critical damping hapens
Options:
110
64
50
60
Answer:
c=80
Step-by-step explanation:
Based on my reading the critical damping occurs when the discriminant of the quadratic characteristic equation is 0.
So let's see that characteristic equation:
20r^2+cr+80=0
The discriminant can be found by calculating b^2-4aC of ar^2+br+C=0.
a=20
b=c
C=80
c^2-4(20)(80)
We want this to be 0.
c^2-4(20)(80)=0
Simplify:
c^2-6400=0
Add 6400 on both sides:
c^2=6400
Take square root of both sides:
c=80 or c=-80
Based on further reading damping equations in form
ay′′+by′+Cy=0
should have positive coefficients with b also having the possibility of being zero.
9. The theater club of a local high school is planning a production. The amount of time t needed to assemble the set is inversely
proportional to the number people n working. Twelve people can assemble the set in 5 hours.
Write an equation to represent the situation.
Answer:
The situation that represents this situation is:
[tex]t = \frac{60}{n}[/tex]
Step-by-step explanation:
The amount of time t needed to assemble the set is inversely proportional to the number people n working.
This means that:
[tex]t = \frac{k}{n}[/tex]
In which k is the constant of proportionality.
Twelve people can assemble the set in 5 hours.
This means that for [tex]n = 12, t = 5[/tex]. We use this to find k.
[tex]t = \frac{k}{n}[/tex]
[tex]5 = \frac{k}{12}[/tex]
[tex]k = 12*5 = 60[/tex]
Write an equation to represent the situation.
[tex]t = \frac{60}{n}[/tex]
15. Five boys went to see the CIRCUS. Four of them had Rs.5 each and the fifth boy had Re.1 more than the entrance ticket price. IF with the whole amount (which the 5 boys had), the boys were able to just buy the entrance ticket for all the 5, cost of the entrance ticket per person was
Answer:
20+(x+1) = 5x
x=21/4
x= 5.25
The entrance ticket per person can be calculated using algebraic equation. We have create the algebraic expression as per the question.
The entrance ticket per person is Rs. 5.25.
Given:
Total boys are 5
4 boys has 5 rupee each so total rupee are [tex]=5\times 4=20[/tex].
Let the entrance ticket per boy is [tex]x[/tex].
One boy had 1 rupee more than entrance ticket [tex](x+1)[/tex].
Write the algebraic expression to calculate the entrance ticket per person.
[tex]5x=20+(x+1)\\5x=20+x+1\\5x-x=20+1\\4x=21\\x=5.25[/tex]
Thus, the entrance ticket per person is Rs. 5.25.
Learn more about algebraic expression here:
https://brainly.com/question/953809
What is the measure of the angle in red?
70°
Answer:
See pic below.
Answer: C. 380°
Step-by-step explanation:
The sum of two numbers is 41. The larger number is 17 more than the smaller number. What are the numbers?
Larger number:
Smaller number:
Please help me with the answers
Answer:
slope= 3/1
y-intercept (0,2)
y= 3/1 b + 2
Which of the following quadratic equations is written in general form?
The 3rd one
Step-by-step explanation:
Reason being that it has no factors, meaning it cannot be simplified any further, but quadratic method can be used to attain factors.
hope it makes sense :)
1. Ten times the sum of -270 and a number gives -20.
9514 1404 393
Answer:
equation: 10(-270 +n) = -20number: 268Step-by-step explanation:
If n represents the number, we have ...
10(-270 +n) = -20 . . . an equation for n
__
The solution can be found as ...
-270 +n = -2 . . . . . divide by 10
n = 268 . . . . . . . add 270
The number is 268.
simplify 7-(3n+6)+10n
Answer:
1 + 7n
Step-by-step explanation:
7-(3n+6)+10n
7 - 3n - 6 + 10 n
1 - 7n
Answered by Gauthmath
The height of a projectile launched upward at a speed of 48 feet/second from a height of 160 feet is given by the function h(t)=-16sup(t,2)+48t+160. How long will it take the projectile to hit the ground?
Answer:
Hello,
5 s
Step-by-step explanation:
[tex]h(t)=-16t^2+48t+160\\=-16(t^2-3t-10)\\=-16(t^2-5t+2t-10)\\=-16(t(t-5)+2(t-5))\\=-16(t-5)(t+2)\\\\h(t)=0 \Longleftrightarrow\ t=-2\ or\ t=5\\\\Only\ t=5\ is \ a\ answer.(time\ must\ be\ positive)[/tex]
The coordinates of the preimage are:
A(−8,−2)
B(−4,−3)
C(−2,−8)
D(−10,−6)
Now let’s find the coordinates after the reflection over the x-axis.
A′(−8,
)
B′(−4,
)
C′(−2,
)
D′(−10,
)
And now find the coordinates after the reflection over the y-axis.
A′′(
,2)
B′′(
,3)
C′′(
,8)
D′′(
,6)
This is also the same as a rotation of 180∘.
9514 1404 393
Answer:
A'(-8, 2) ⇒ A"(8, 2)B'(-4, 3) ⇒ B"(4, 3)C'(-2, 8) ⇒ C"(2, 8)D'(-10, 6) ⇒ D"(10, 6)Step-by-step explanation:
Reflection over the x-axis changes the sign of the y-coordinate. Reflection over the y-axis changes the sign of the x-coordinate. We can summarize the transformations as ...
preimage point ⇒ reflection over x ⇒ reflection over y
A(−8,−2) ⇒ A'(-8, 2) ⇒ A"(8, 2)
B(−4,−3) ⇒ B'(-4, 3) ⇒ B"(4, 3)
C(−2,−8) ⇒ C'(-2, 8) ⇒ C"(2, 8)
D(−10,−6) ⇒ D'(-10, 6) ⇒ D"(10, 6)
Suppose the variable x is represented by a standard normal distribution. What is the probability of x > 0.3 ? Please specify your answer in decimal terms and round your answer to the nearest hundredth (e.g., enter 12 percent as 0.12).
Answer: 0.38
Step-by-step explanation:
Since the variable x is represented by a standard normal distribution, the probability of x > 0.3 will be calculated thus:
P(x > 0.3)
Then, we will use a standard normal table
P(z > 0.3)
= 1 - p(z < 0.3)
= 1 - 0.62
= 0.38
Therefore, p(x > 0.3) = 0.38
The probability of x > 0.3 is 0.38.
Pls give this anwere with explanation spammer will be reported
Answer:
Whole number —> X
Twice the square of the number —> 2X²
X + 2X² = 10
2X²+X –10 =0
(2x + 5) ( x–2) =0
2x +5=0 —> 2x= – 5 —> x= – 5/2 = —> x= - 2.5 (rejected)
x–2=0 —> x= 2
So Ans ; X= 2 ( the number )
I hope I helped you^_^
The triangles are similar. Find x.
Please help me!
GIVEN -> Triangles r similar
so sides r in ratio
[tex] \frac{2.4}{3} = \frac{2.8}{x} \\ 0.8 = \frac{2.8}{x} \\ x = \frac{2.8}{0.8} \\ x = \frac{28}{8} \\ x = 3.5 \: \: ans[/tex]
Answer:
3.5
Step-by-step explanation:
We can write a ratio to solve
2.4 2.8
----- = --------
3 x
Using cross products
2.4x = 3(2.8)
2.4x =8.4
Divide each side by 2.4
2.4x /2.4 = 8.4/2.4
x = 3.5
Choose the best answer from the choices below:
If a radius of a circle bisects a chord which is not a diameter, then ____.
Answer: the radius is perpendicular to the chord.
If a radius of a circle bisects a chord which is not diameter, then the radius is perpendicular to the chord.
Answered by Gauthmath must click thanks and mark brainliest
The radius is perpendicular to the chord.
Does the radius of the circle bisect the string?If the radius of the circle is perpendicular to the chord of the circle, the radius bisects the chord. The two strings are congruent only if they are equidistant from the center of the circle.
No, not all strings in a circle are diameters because the diameter passes through the center of the circle. Therefore, all the diameters of a circle are also strings, not all the strings of a circle.
Learn more about chord at
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Cars arrive at an automatic car wash system every 10 minutes on average. The cars inter-arrival times are exponentially distributed. Washing time for each is 6 minutes per car and is purely deterministic (i.e., the waiting line system is M/D/c). Assuming that the car wash has a single bay to serve the cars, what is the average number of cars waiting in line (L.)?
Answer:
the average number of cars waiting in line L[tex]q[/tex] is 0.45
Step-by-step explanation:
Given the data in the question;
Cars arrive at an automatic car wash system every 10 minutes on average.
Car arrival rate λ = 1 per 10 min = [ 1/10 × 60 ]per hrs = 6 cars per hour
Washing time for each is 6 minutes per car
Car service rate μ = 6min per car = [ 1/6 × 60 ] per hrs = 10 cars per hour
so
P = λ/μ = 6 / 10 = 0.6
Using the length of queue in M/D/1 system since there is only one service bay;
L[tex]q[/tex] = [tex]\frac{1}{2}[/tex][ P² / ( 1 - P ) ]
so we substitute
L[tex]q[/tex] = [tex]\frac{1}{2}[/tex][ (0.6)² / ( 1 - 0.6 ) ]
L[tex]q[/tex] = [tex]\frac{1}{2}[/tex][ 0.36 / 0.4 ]
L[tex]q[/tex] = [tex]\frac{1}{2}[/tex][ 0.9 ]
L[tex]q[/tex] = 0.45
Therefore, the average number of cars waiting in line L[tex]q[/tex] is 0.45
Please help me solve the question...
Answer:
All of area is πr²
Step-by-step explanation:
and we should write the area kind of radian. So if all area is π*(12)²= 144π - this for 360°- and 240° is 96π
but we must add area of the triangle which has two same side and has 6 high so it's area is 6*12√3/2 = 36✓3
our answer is 96π+ 36✓3
2x³=10 what is x
what is x
Answer:
x=1.7099
Step-by-step explanation:
2x³=10
x³=10/2
x³=5
x=∛5
x=1.7099
I need help wit this ASAP 6 minutes
A boat can travel 21 miles on 7 gallons of gasoline. How far can it travel on 17 gallons?
Answer:
51 miles
Step-by-step explanation:
Boat with 7 gallons of gas = 21 miles
Boat with 1 gallon of gas = 21/7 = 3 miles
Boat with 17 gallons of gas = 17 x 3 = 51 miles
Answer:
51 miles
Step-by-step explanation:
1 gallon = 3 miles
17 gallons = ? miles
17 * 3 = 51 miles
Question 1 of 10
The value of 9 is not-3 because
Answer:
It's a negative.
Step-by-step explanation:
The value of a positive number is still a positive number.
7 times a certain number less four times that same number minus 2 is -58 what is the number
Step-by-step explanation:
7 times a certain number :
Let the unknown number be x
[tex]7 \times x[/tex]
is less four times that same number -2 is 58 :
7x - 4x -2 = 58
Collect like terms
7x-4x = 58+2
3x = 60
3x/3 = 60/3
x = 20
Let the number be x
ATQ
[tex]\\ \sf\longmapsto 7x-4x-2=58[/tex]
[tex]\\ \sf\longmapsto 3x-2=58[/tex]
[tex]\\ \sf\longmapsto 3x=58+2[/tex]
[tex]\\ \sf\longmapsto 3x=60[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{60}{3}[/tex]
[tex]\\ \sf\longmapsto x=20[/tex]
Don’t understand this problem
Answer: I'm not Einstein sorry
Step-by-step explanation:
Have to be smart as Einstein.................Which I'm not
A bag contains 8 red balls and 3 white balls. Two balls are drawn without replacement. (Enter your probabilities as fractions.) (a) What is the probability that the second ball is white, given that the first ball is red
Answer:
12/55
Step-by-step explanation:
Probability is the ratio of the number of possible outcomes to the number of total outcomes.
Given that the bag contains 8 red balls and 3 white balls, the probability of picking a red ball
p(r) = 8/(8+3) = 8/11
Probability of picking a white ball
= 3/11
when a red ball is picked first, the total number of balls reduces to 10 hence the probability that the second ball is white, given that the first ball is red
=8/11 * 3/10
= 24/110
= 12/55
