Answer:
3b^2 + 2b -8
Step-by-step explanation:
* means multiply
^ means exponent
3b * b = 3b^2
3b * 2 = 6b
-4 * b = -4b
-4 * 2 = -8
3b^2 + 6b -4b -8
3b^2 + 2b -8
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.
8. If 30 cents out of every 1 dollar goes to taxes and the rest is net income, what's the
ratio of taxes to net income?
d
A. 30 : 7
B. 3:10
C. 30 : 1
D. 3:7
Answer:
D. 3:7Step-by-step explanation:
1 dollar = 30 cents tax + 70 cents net income
The ratio of taxes to net income:
30 : 70 = 3 : 7Correct choice is D
If 30cents are out then net income=100-30=70
ratio:-
[tex]\\ \rm\Rrightarrow \dfrac{30}{70}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{3}{7}[/tex]
[tex]\\ \rm\Rrightarrow 3:7[/tex]
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
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∘.
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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)
I need help wit this ASAP 6 minutes
Suppose that a category of world-class runners are known to run a marathon in an average of 147 minutes with a standard deviation of 12 minutes. Consider 49 of the races. Find the probability that the runner will average between 146 and 150 minutes in these 49 marathons. (Round your answer to two decimal places.)
Answer:
0.6524 = 65.24% probability that the runner will average between 146 and 150 minutes in these 49 marathons.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Average of 147 minutes with a standard deviation of 12 minutes.
This means that [tex]\mu = 147, \sigma = 12[/tex]
Consider 49 of the races.
This means that [tex]n = 49, s = \frac{12}{\sqrt{49}} = \frac{12}{7} = 1.7143[/tex]
Find the probability that the runner will average between 146 and 150 minutes in these 49 marathons.
This is the p-value of Z when X = 150 subtracted by the p-value of Z when X = 146. So
X = 150
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{150 - 147}{1.7143}[/tex]
[tex]Z = 1.75[/tex]
[tex]Z = 1.75[/tex] has a p-value of 0.9599
X = 146
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{146 - 147}{1.7143}[/tex]
[tex]Z = -0.583[/tex]
[tex]Z = -0.583[/tex] has a p-value of 0.3075.
0.9599 - 0.3075 = 0.6524.
0.6524 = 65.24% probability that the runner will average between 146 and 150 minutes in these 49 marathons.
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
Please help me with the answers
Answer:
slope= 3/1
y-intercept (0,2)
y= 3/1 b + 2
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]
A parent is buying two types of chocolate truffles for their family. The oldest child can eat twice as much as their younger siblings and prefers white chocolate (W), the younger three like dark chocolate (D) and the spouse likes white chocolate (W). Five white chocolate truffles (W) cost the same as three dark chocolate truffles (D). If the parent bought 6 white chocolate truffles(W) and 10 dark chocolate truffles (D), and spent $34.00, how much was each dark chocolate truffle
Answer:
Each chocolate truffle is $2.125
Step-by-step explanation:
Honestly, I'm not 100% sure if this is correct, and I am truly sorry if this is wrong, but its worth a try :)
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
The figure below is a rectangular prism.
Which edge is parallel to segment BD?
A. HK
B. BM
C. DK
D. AH
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
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 :)
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
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:
After completing the fraction division 5 / 5/3, Miko used the multiplication shown to check her work.
3 x 5/3 = 3/1 x 5/3 = 15/3 or 5
Answer:
its the same above
Step-by-step explanation:
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^_^
You pay $1.25 per pound for x pounds of apples?
Answer:
$1.25x
Step-by-step explanation:
Given :
Cost per pound = $1.25
Number of pounds of apple = x
The total cost of apple = (cost per pound * number of apple in pounds)
Hence,
Total cost of x pounds of apple is :
($1.25 * x)
= $1.25x
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.
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
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.
1. Ten times the sum of -270 and a number gives -20.
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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.
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]
what is heavier ten tons of wool or ten tons of steel
Convert 110101 in base 2 to base 10
Answer:
base-2 base-10
110011 = 51
110100 = 52
110101 = 53
110110 = 54
21 more rows
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
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
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 domain of a composite function (fog)(x) is the set of those inputs x in the domain of g for which g(x) is in the domain of f.
True
False
