Answer:
((90*3)+(40*6))/9
=(90+90+90+40+40+40+40+40+40)/9
=66.66
Step-by-step explanation:
A, higher than her sisters score
Find the work done by the gas for the given volume and pressure. Assume that the pressure is inversely proportional to the volume. (See Example 6.) A quantity of gas with an initial volume of 2 cubic feet and a pressure of 1000 pounds per square foot expands to a volume of 3 cubic feet. (Round your answer to two decimal places.)
810.93
Step-by-step explanation:Let the pressure be given by P and the volume be V.
Since pressure is inversely proportional to volume, we can write;
P ∝ [tex]\frac{1}{V}[/tex]
=> P = [tex]\frac{c}{V}[/tex] -------------(i)
Where;
c = constant of proportionality.
When the volume of the gas is 2 cubic feet, pressure is 1000 pounds per square foot.
V = 2 ft³
P = 1000lb/ft²
Substitute these values into equation (i) as follows;
1000 = [tex]\frac{c}{2}[/tex]
=> c = 2 x 1000
=> c = 2000 lbft
Substituting this value of c back into equation (i) gives
P = [tex]\frac{2000}{V}[/tex]
This is the general equation for the relation between the pressure and the volume of the given gas.
To calculate the work done W by the gas, we use the formula
[tex]W = \int\limits^{V_1}_{V_0} {P} \, dV[/tex]
Where;
V₁ = final volume of the gas = 3ft³
V₀ = initial volume of the gas = 2ft³
Substitute P = [tex]\frac{2000}{V}[/tex], V₁ = 3ft³ and V₀ = 2ft³
[tex]W = \int\limits^{3}_{2} {\frac{2000}{V} } \, dV[/tex]
Integrate
W = 2000ln[V]³₂
W = 2000(In[3] - ln[2])
W = 2000(0.405465108)
W = 810.93016
W = 810.93 [to 2 decimal places]
Therefore, the work done by the gas for the given pressure and volume is 810.93
Consider the following quadratic equation. y = x2 – 8x + 4 Which of the following statements about the equation are true? The graph of the equation has a minimum. When y = 0, the solutions of the equation are a = 4 + 2V3 o When y = 0, the solutions of the equation are r x = 8 + 2V2. o The extreme value of the graph is at (4,-12). The extreme value of the graph is at (8,-4). U The graph of the equation has a maximum. Submit
Answer:
The graph of the equation has a minimum.
When y = 0, the solutions are [tex]4 \pm 2\sqrt{3}[/tex]
The extreme value of the graph is (4,-12).
Step-by-step explanation:
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]
[tex]\Delta = b^{2} - 4ac[/tex]
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
y = x2 – 8x + 4
Quadratic equation with [tex]a = 1, b = -8, c = 4[/tex]
a is positive, so it's graph has a minimum.
Solutions when y = 0
[tex]\Delta = b^2-4ac = 8^2 - 4(1)(4) = 64 - 16 = 48[/tex]
[tex]x_{1} = \frac{-(-8) + \sqrt{48}}{2} = \frac{8 + 4\sqrt{3}}{2} = 4 + 2\sqrt{3}[/tex]
[tex]x_{2} = \frac{-(8) - \sqrt{48}}{2} = \frac{8 - 4\sqrt{3}}{2} = 4 - 2\sqrt{3}[/tex]
When y = 0, the solutions are [tex]4 \pm 2\sqrt{3}[/tex]
Extreme value:
The vertex. So
[tex]x_{v} = -\frac{-8}{2} = 4[/tex]
[tex]y_{v} = -\frac{48}{4} = -12[/tex]
The extreme value of the graph is (4,-12).
HELP?!?
Write the prime factorization for these numbers
1. 235
2. 460
3. 582
4. 297
5. 777
6. 624
Step-by-step explanation:
hear is answer in attachment
Answer:
1. 5 x 47 show tree of 5 x 47 and then stop both are pf
2. 2^2 × 5 × 23 show tree of 10 x 46 and then 2 x 5 (under10) and 2x23 (under 46) and then stop 2,2,5,23 are all pf
3. 2 x 3 x 97 show tree 3 x 194 and 2 x 97 and circle pf 2,3,97
4. 3^3 x 11 show tree of 3 x 99 then 3 x 33 then 3 x 11 to show 3,3,3,11 as pf
5. 3 x 7 x 37 show tree as 777/7 = 111/37 = 3 to show 3,7,37 as pf
6. 2^4 x 3 x 13 show tree as 2 x 312 2 x 156 2 x 78 2 x 39 3 x 13 to show 2,2,2,2,3,13 all as pf
Step-by-step explanation:
33. Given the following algebraic expression 5x² + 10 Which statement is true?
a. The coefficient is 5
b. The constant is 2
C. The power is 10
d. The constant is 5
Answer:
Given the following algebraic expression 5x² + 10 Which statement is true?
a. The coefficient is 5. ( true)
b. The constant is 2
C. The power is 10
d. The constant is 5
Which statement is true about the function f(x) = negative StartRoot x EndRoot?
Answer:
It has the same domain and range as the function f(x) = StartRoot x EndRoot. It has the same range but not the same domain as the function f(x) = StartRoot x EndRoot. It has the same domain and range as the function f(x) = negative StartRoot negative x EndRoot.
Step-by-step explanation:
Approximately 70% of U.S. adults had at least one pet as a child. We randomly survey 60 U. S. adults. We are interested in the number that had at least one pet as a child. The probability that at least 3 adults had at least one pet as a child means:
A. P(X=0)+P(X=1)+P(X=2)+P(X=3)
B. P(X=0)+P(X=1)+P(X=2)
C. P(X=4)+P(X=5)+P(X=6)+ ...
D. P(X=3)+P(X=4)+P(X=5)+ ...
Answer:
D. P(X=3)+P(X=4)+P(X=5)+ ...
Step-by-step explanation:
Given
[tex]n =60[/tex]
[tex]pr = 70\%[/tex] -- proportion of adults with pet
Required
Represent at least 3 adult with pet as a probability
At least 3 means 3 or more than.
So, the probability is represented as:
[tex]P(x \ge 3) = P(3) + P(4) + P(5) + ........[/tex]
Hence;
(d) is correct
Can someone answer the question?
Answer:
[tex]\frac{\sqrt{3} }{3} }(cos(\frac{19\pi}{12})+isin(\frac{19\pi}{12}))[/tex]
Step-by-step explanation:
Division of complex numbers in polar form is [tex]z_1/z_2=\frac{r_1}{r_2}cis(\theta_1-\theta_2)[/tex] where [tex]z_1[/tex] and [tex]z_2[/tex] are the complex numbers being divided, [tex]r_1[/tex] and [tex]r_2[/tex] are the moduli, [tex]\theta_1[/tex] and [tex]\theta_2[/tex] are the arguments, and [tex]cis[/tex] is shorthand for [tex]cos\theta+isin\theta[/tex]. Therefore:
[tex]\frac{9(cos(\frac{11\pi}{6})+isin(\frac{11\pi}{6})) }{3\sqrt{3}((cos\frac{\pi}{4})+isin(\frac{\pi}{4})) }[/tex]
[tex]\frac{9}{3\sqrt{3} }cis(\frac{11\pi}{6}-\frac{\pi}{4})[/tex]
[tex]\frac{\sqrt{3} }{3} }cis(\frac{19\pi}{12})[/tex]
[tex]\frac{\sqrt{3} }{3} }(cos(\frac{19\pi}{12})+isin(\frac{19\pi}{12}))[/tex]
Find the height of the cylinder. Round your answer to the nearest whole number.
Volume
= 113 m 3
Answer:
C
Step-by-step explanation:
3² * pi * 4 = 113
113 / pi / 3²
gives you 4
this time the radius was squared correctly XD
Answer:
C. 4m
Step-by-step explanation:
Work backwards from the formula of volume cylinder:
Formula = πr²h
113 = 3.14 * 9 * h
113/9 = 3.14 * h
12. 6 = 3.14 / h
4 = h
h = 4
Check:
Volume = 3.14*9*4
Volume = 3.14 * 36
volume = 113.04 ≈ 113
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Pythagorean theorem
Answer:
hello
Step-by-step explanation:
a²+b²=c²
16²+b²=65²
256+b²=4225
b²=4225-256
b²=3969
[tex]b = \sqrt{3969}[/tex]
b=63
b=63 mi
have a nice day
Answer:
b = 63
Step-by-step explanation:
In a right angled triangle, hypotenuse squared is equal to the sum of the square of the other sides.
c² = a² + b² (where c is the hypotenuse, and a and b are the other two sides)
c = 65 , a = 16 b = ?
65² = 16² + b²
4225 = 256 + b²
4225 - 256 = b²
b² = 3969
b = [tex]\sqrt{3969}[/tex]
b = 63
check
c² = 16 ² + 63²
= 256 + 3969
= 4225
c = √4225
c = 65
A company's sales force makes 400 sales calls, with + 0.25 probability that a sale will be made on a call. What is the probability that greater than 55 (exclusive) but less than 75 (exclusive) sales will be made? Enter your answer as a decimal value, rounded to 4 decimal places.
Answer:
0.0016 probability that greater than 55 (exclusive) but less than 75 (exclusive) sales will be made.
Step-by-step explanation:
We use the normal approximation to the binomial distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
A company's sales force makes 400 sales calls, with 0.25 probability that a sale will be made on a call.
This means that [tex]n = 400, p = 0.25[/tex]
Mean and standard deviation:
[tex]\mu = E(X) = np = 400*0.25 = 100[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{400*0.25*0.75} = \sqrt{75}[/tex]
What is the probability that greater than 55 (exclusive) but less than 75 (exclusive) sales will be made?
Using continuity correction, this is [tex]P(55+0.5 \leq X \leq 75-0.5) = P(55.5 \leq X \leq 74.5)[/tex], which is the p-value of Z when X = 74.5 subtracted by the p-value of Z when X = 55.5.
X = 74.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{74.5 - 100}{\sqrt{25}}[/tex]
[tex]Z = -2.94[/tex]
[tex]Z = -2.94[/tex] has a p-value of 0.0016
X = 55.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{55.5 - 100}{\sqrt{25}}[/tex]
[tex]Z = -5.14[/tex]
[tex]Z = -5.14[/tex] has a p-value of 0
0.0016 - 0 = 0.0016
0.0016 probability that greater than 55 (exclusive) but less than 75 (exclusive) sales will be made.
HELPPP PLSSSSSSSSSSS
Answer:
45 + m<DBC = 180
Step-by-step explanation:
m<ABD + m<DBC = 180
45 + m<DBC = 180
write a rational number between root2 and root3
Answer:
prational number between root2
PLEASE HELP ILL MARK BRAINLIEST
1.
If the measures of three angles of a quadrilateral
are 30, 70, and 110, find the measure of the fourth
angle.
Answer:
150
Step-by-step explanation:
The sum of the angles of a quadrilateral are 360. Let x be the unknown angle
30+70+110+x = 360
Combine like terms
210 +x = 360
Subtract 210 from each side
210+x-210 = 360-210
x = 150
Answer:
The measures of the fourth angle is 150 .
Step-by-step explanation:
Given :-The measures of three angles of quadrilateral are 30 , 70 and 110.
To find :-Find the measures of fourth angle.
Solution :-Let, the measures of fourth angle be x.
We know that sum angles of quadrilateral are 360 .
30 + 70 + 110 + x = 360
combine like terms
210 + x = 360
subtract 210 from 360.
x = 360 - 210
x = 150
Therefore, the fourth angle of quadrilateral is 150.
Identify the figure. Then name the bases, faces, edges, and vertices. PLEASE ANSWER FAST ILL MARK BRAINLIEST.
Answer:
Square pyramid1 square base (on the bottom)5 faces8 edges5 verticesOn the first day of training, Aretha holds a plank position for 30 seconds. She increases her time by 20% each day. What is the first day on which Aretha holds a plank for over a minute? Show your work
Answer:
5 th day
Step-by-step explanation:
Given :
1st day :
Time = 30 seconds
Time increases by 20% each day :
2nd day = 20% * 30 = (1.20 * 30) = 36 seconds
3rd day = 1.20 * 36 = 43.2 seconds
4th day = 1.20 * 43.2 = 51.84 seconds
5th day = 1.20 * 51.84 = 62.208
First day Aretha hold a plank for over 1 minute is the 5th day
PLS HELP ASAP! FIND THE VOLUME OF X.
Answer:
Step-by-step explanation:
5x + 150 = 180
5x = 30
x = 6
Hope this help!!!
Have a nice day!!!
What is the result of subtracting the second equation from the first
Answer:
[tex]5x -2y = -2[/tex]
Step-by-step explanation:
Given
[tex]-2x + y = 0[/tex]
[tex]-7x + 3y = 2[/tex]
Required
Subtract (2) from (1)
This gives:
[tex]-2x - -7x +y - 3y = 0 -2[/tex]
[tex]5x -2y = -2[/tex]
Rounding in the calculation of monthly interest rates is discouraged. Such rounding can lead to answers different from those presented here. For long-term loans, the differences may be pronounced.
Assume that you take out a $3000 loan for 30 months at 8.5% APR. What is the monthly payment? (Round your answer to the nearest cent.)
$
Answer:
111.35
Step-by-step explanation:
effective rate: .085/12= .007083333333333333
payment=x
[tex]3000=x(\frac{1-(1+.007083333333333333)^{-30}}{.007083333333333333})\\x=111.35[/tex]
Step-by-step explanation:
111.35
Step-by-step explanation:
effective rate: .085/12= .007083333333333333
payment=x
\begin{gathered}3000=x(\frac{1-(1+.007083333333333333)^{-30}}{.007083333333333333})\\x=111.35\end{gathered}
3000=x(
.007083333333333333
1−(1+.007083333333333333)
−30
)
x=111.35
write an equation of the line below
Use trigonometric identities to verify each expression is equal. sin(x)/1-cos(x)-cot(x)=csc(x)
Answer:
See Below.
Step-by-step explanation:
We want to verify the identity:
[tex]\displaystyle \frac{\sin x}{1 - \cos x} - \cot x = \csc x[/tex]
We can multiply the fraction by 1 + cos(x):
[tex]\displaystyle \frac{\sin x(1+\cos x)}{(1 - \cos x)(1+\cos x)} - \cot x = \csc x[/tex]
Difference of Two Squares:
[tex]\displaystyle \frac{\sin x(1+\cos x)}{1-\cos^2 x} - \cot x = \csc x[/tex]
From the Pythagorean Theorem, we know that sin²(x) + cos²(x) = 1. Rearranging, we acquire that sin²(x) = 1 - cos²(x). Substitute:
[tex]\displaystyle \frac{\sin x(1+\cos x)}{\sin^2 x} - \cot x = \csc x[/tex]
Cancel:
[tex]\displaystyle \frac{ 1 + \cos x}{\sin x}-\cot x = \csc x[/tex]
Let cot(x) = cos(x) / sin(x):
[tex]\displaystyle \frac{ 1 + \cos x}{\sin x}-\frac{\cos x}{\sin x} = \csc x[/tex]
Combine Fractions:
[tex]\displaystyle \frac{ 1 + \cos x - \cos x}{\sin x}= \csc x[/tex]
Thus:
[tex]\displaystyle \frac{1}{\sin x}=\csc x = \csc x[/tex]
Hence proven.
I’ve been staring at this problem for 10 minutes and still have no idea
9514 1404 393
Answer:
B. (-∞, 1) ∪ (1, 2]
Step-by-step explanation:
When you are looking for answers to domain questions, you are looking for values of the variable(s) that make the function undefined. Here, there is a square root involved, and the rational function has a denominator that might be zero.
The function is only defined for square roots of non-negative numbers. That is ...
2-x ≥ 0 ⇒ x ≤ 2
The rational function is only defined for non-zero denominators, so ...
x-1 ≠ 0
x ≠ 1
__
So, you're looking for a domain description that includes all numbers less than or equal to 2, and excludes x=1. The attached number line shows a graph of this.
The domain divides into two parts: all numbers less than 1, and those numbers between 1 and 2 (including 2). This will be the union ...
(-∞, 1) ∪ (1, 2]
While eating your yummy pizza, you observe that the number of customers arriving to the pizza station follows a Poisson distribution with a rate of 18 customers per hour. What is the probability that more than 4 customers arrive in a 10 minute interval
Answer:
0.1848 = 18.48% probability that more than 4 customers arrive in a 10 minute interval.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
Rate of 18 customers per hour.
This is [tex]\mu = 18n[/tex], in which n is the number of hours.
10 minute interval:
An hour has 60 minutes, so this means that [tex]n = \frac{10}{60} = \frac{1}{6}[/tex], and thus [tex]\mu = 18\frac{1}{6} = 3[/tex]
What is the probability that more than 4 customers arrive in a 10 minute interval?
This is:
[tex]P(X > 4) = 1 - P(X \leq 4)[/tex]
In which:
[tex]P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]
Then
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0498[/tex]
[tex]P(X = 1) = \frac{e^{-3}*3^{1}}{(1)!} = 0.1494[/tex]
[tex]P(X = 2) = \frac{e^{-3}*3^{2}}{(2)!} = 0.2240[/tex]
[tex]P(X = 3) = \frac{e^{-3}*3^{3}}{(3)!} = 0.2240[/tex]
[tex]P(X = 4) = \frac{e^{-3}*3^{4}}{(4)!} = 0.1680[/tex]
[tex]P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex] = 0.0498 + 0.1494 + 0.2240 + 0.2240 + 0.1680 = 0.8152[/tex]
And
[tex]P(X > 4) = 1 - P(X \leq 4) = 1 - 0.8152 = 0.1848[/tex]
0.1848 = 18.48% probability that more than 4 customers arrive in a 10 minute interval.
The probability that a person has blue eyes is 16%. Three unrelated people are selected at random. a. Find the probability that all three have blue eyes b. Find the probability that none of the three have blue eyes c. Find the probability that one of the three has blue eyes
Answer:
Step-by-step explanation:
All three have blue eyes.
P(1 has blue eyes) = 16/100 = 4/25
P(3 have blue eyes) = 4/25 * 4/25 * 4/25
P(3 have blue eyes ) = 64/15625
If you need the decimal answer, it is .004096
No one has blue eyes out of three
The probability for this is very large.
P(no blues) = 1 - 64/15625
P(no blues) = 15561/15625
If you need the decimal answer, it is 0.996
One has blue eyes (the other two do not).
P(1 has blue eyes) = 16/100 * 84/100*84/100
P(1 has blue eyes) = 112896/1000000
P(1 has blue eyes) = 0.112896
WILL GIVE BRAINLIEST (Right angle) Trigonometry
please help!
Answer:
<A = 41.4°
Step-by-step explanation:
Recall, SOH CAH TOA
Reference angle = <A
Hypotenuse length = 8
Adjacent length = 6
Since Hypotenuse and Adjacent are involved, we would apply CAH, which is:
Cos A = Adj/Hyp
Plug in the values
Cos A = 6/8
Cos A = 0.75
[tex] A = Cos^{-1}(0.75) [/tex]
A = 41.4096221° ≈ 41.4° (nearest tenth)
PLEASE PLEASE HELP ASAP I NEED THIS DONE BY TODAY WILL GIVE BRAINLIEST!!!!
Match the basic trigonometric ratio for the similar triangles.
Answer:
cos E = 6/10
cos G = 8/10
sin E = 8/10
sin G = 6/10
tan E = 8/6
tan G = 6/8
Express 0.1 as a percent.
Find the volume of the prism.
With composte solids, all you have to do is find the volume of each and then add them together
Answer:
1760 cm³
Step-by-step explanation:
Volume For top "trapezoidal" prism : (14 * 4)/2 * 20 = 28 * 20 = 560
Volume for bottom rectangular prism = 6 x 10 x 20 = 60 x 20 = 1200
1200 + 560 = 1760 cm³
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
m(x) = x2 + 4x
n(x) = x
(mn)(x) =
x2 + 4x(x)
(x2 +4x)(x)
Answer:
Answer:
1. B. (x^2 + 4x)(x)
2. A. (x^3+4x^2)
3. 9
4. 0
5. 1
Step-by-step explanation:
Melissa will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $65 and costs an additional $0.50 per mile driven. The second plan has no initial fee but costs per mile driven. How many miles would Melissa need to drive for the two plans to cost the same?
Answer:
Melissa needs to drive 325 miles for the two plans to cost the same
Step-by-step explanation:
Plan A
Initial Fee = 65
Additional cost per mile = 0.50 per mile
Plan B
Initial Fee = 0
Additional cost per mile = 0.70 per mile
Required
Mile both plans will cost the same
Let
[tex]y \to cost[/tex]
[tex]x \to miles[/tex]
So, we have:
[tex]y = Initial\ Fee + Additional * x[/tex]
For plan A
[tex]y = 65+ 0.50* x[/tex]
[tex]y = 65+ 0.50x[/tex]
For plan B
[tex]y = 0 + 0.70*x[/tex]
[tex]y = 0.70x[/tex]
So, we have:
[tex]y = 65+ 0.50x[/tex] --- plan A
[tex]y = 0.70x[/tex] --- plan B
Both plans will cost the same when
[tex]y = y[/tex]
[tex]0.70x = 65 +0.50x[/tex]
[tex]0.70x -0.50x= 65[/tex]
[tex]0.20x= 65[/tex]
Divide by 0.20
[tex]x= 325[/tex]