The equivalent expression of [tex]\frac{(5ab)^3}{30ab^{-7}}[/tex] is [tex]\frac{25a^{2}b^{10}}{6}[/tex]
How to determine the equivalent expression?The expression is given as:
[tex]\frac{(5ab)^3}{30ab^{-7}}[/tex]
Expand the numerator
[tex]\frac{(5ab)^3}{30ab^{-7}} =\frac{125a^3b^3}{30ab^{-7}}[/tex]
Divide 125 and 30 by 5
[tex]\frac{(5ab)^3}{30ab^{-7}} =\frac{25a^3b^3}{6ab^{-7}}[/tex]
Apply the law of indices
[tex]\frac{(5ab)^3}{30ab^{-7}} =\frac{25a^{3-1}b^{3+7}}{6}[/tex]
Evaluate the exponent
[tex]\frac{(5ab)^3}{30ab^{-7}} =\frac{25a^{2}b^{10}}{6}[/tex]
Hence, the equivalent expression of [tex]\frac{(5ab)^3}{30ab^{-7}}[/tex] is [tex]\frac{25a^{2}b^{10}}{6}[/tex]
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help me please!!! i cant figure it out and its driving me insane
Answer:
y<_0
Step-by-step explanation:
The last answer.
Hope this helps! Have a great day :)
what is the slope of y=-9x-8?
The slope of the linear equation, y = -9x - 8 is determined as: -9.
How to Identify the Slope in an Equation?If the equation of a line is given in a slope-intercept form, y = mx + b, the slope value is represented as m.
Thus, given the equation y = -9x - 8, the slope in the linear equation is -9.
Therefore, slope of y = -9x - 8 is: -9.
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write the exprfession 12-2 in simplest form,
A group of friends are playing a trivia game. players spin a spinner 2 times to find the 2 categories of trivia questions they will be asked. the spinner has 5 sections. the "music" and "sports" sections are each 1-half the size of the 3 larger sections.
to the nearest percentage, what is the probability that a player will be asked a math question ,begin emphasis,and then,end emphasis, a music question? enter the answer in the box.
The probability that a player will be asked a math question and then a music question is 0.03125
How to determine the probability?The size of the sections are given as:
Music = 0.5
Sport = 0.5
Others = 1
So, the total size is:
Total = 0.5 + 0.5 + 1 + 1 + 1
Evaluate
Total = 4
The probability of asking a math question is:
P(Math) = 1/4 = 0.25
The probability of asking a music question is:
P(Music) = 0.5/4 = 0.125
The required probability is:
P(Math and Music) = P(Math) * P(Music)
This gives
P(Math and Music) = 0.25 * 0.125
Evaluate
P(Math and Music) = 0.03125
Hence, the probability that a player will be asked a math question and then a music question is 0.03125
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Twice during the assembly, a student is chosen at random to assist with the presentation. after the first student has finished assisting, the student returns to the group and can be chosen a second time. what is the probability that the first student chosen is a senior and the second student chosen is a sophomore?.
Using it's concept, it is found that the probability that the first student chosen is a senior and the second student chosen is a sophomore is given by:
[tex]p = \frac{11}{320}[/tex]
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Researching this problem on the internet, we have that there are:
31 juniors, 10 sophomores, 17 juniors, 22 seniors.
Then:
Out of 31 + 10 + 17 + 22 = 80 students, 22 are seniors, hence the probability that the first student is a senior is given by [tex]p_1 = \frac{22}{80} = \frac{11}{40}[/tex].All students can be chosen again, hence the probability that the second student is a sophomore is given by [tex]p_2 = \frac{10}{80} = \frac{1}{8}[/tex].The events are independent, hence the probability of both is given by:
[tex]p = p_1p_2 = \frac{11}{40} \times \frac{1}{8} = \frac{11}{320}[/tex]
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Please help its very desperate and if i could get someone to help me on this whole assignment it would be awesome
Write -0.65 as a fraction or mixed number in simplest form. (you may use an improper or a mixed number as your final answer.)
also if someone could help me on this whole assignment my discord is goths#0001
Answer:
-13/20
Step-by-step explanation:
-0.65=-65/100
=13/20
Christian is driving on a long road trip. He currently has 12 gallons of gas in his car.
Each hour that he drives, his car uses up 1.25 gallons of gas. How much gas would be
in the tank after driving for 6 hours? How much gas would bbe left after t hours?
solve pls brainliest
Answer:
1/6Step-by-step explanation:
-2/3 * (-1/4) =
2/3 * 1/4 =
2/12 =
1/6
which graph shows the solution to the system of linear inequalities below?
y<-1/3x+1
y ≤ 2x-1
The graph that shows the solution set for the system of inequalities is graph C.
Which is the graph of the system of linear inequalities?
Here we have the system of linear inequalities:
[tex]y < (-1/3)*x + 1\\\\y \geq 2x- 1[/tex]
For the first one, we can see a line with a negative slope, and y is strictly smaller than that. So we will have a dashed line that goes down, and we need to shade the region below that line.
For the second inequality, we can see that y can be equal to or larger than the line, so this time we will use a solid line (because the points on the line are solutions). and we will shade above that line.
Also notice that this time the slope is positive, so this line goes upwards.
With that general description, we conclude that the correct option will be graph C.
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what is the answer. please help
Answer:
Exact Form:−2/3
Decimal Form:−0.666…
Step-by-step explanation:
y=x^2-20x+32
What are the zeros of the function using the quadratic formula
By the quadratic formula, we find that the two zeroes of the quadratic function y = x² - 20 · x + 32 are x₁ = 10 + 2√17 and x₂ = 10 - 2√17, respectively.
How to find the zeroes of a second order polynomial
A value of x is a zero of a polynomial if and only if [tex]\sum\limits_{i=0}^{n} c_{i}\cdot x^{i} = 0[/tex], the quadratic formula for second order polynomials of the form a · x² + b · x + c = 0 is presented below:
[tex]x =\frac{-b \pm \sqrt{b^{2}-4\cdot a \cdot c}}{2\cdot a}[/tex]
If we know that a = 1, b = -20 and c = 32, then the roots of the second order polynomial are:
[tex]x = \frac{20 \pm \sqrt{(-20)^{2}-4\cdot (1)\cdot (32)}}{2\cdot (1)}[/tex]
[tex]x = 10 \pm 2\sqrt{17}[/tex]
By the quadratic formula, we find that the two zeroes of the quadratic function y = x² - 20 · x + 32 are x₁ = 10 + 2√17 and x₂ = 10 - 2√17, respectively.
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Select the correct answer from each drop-down menu. The product of the polynomials (2ab + b) and (a2 – b2) is . If this product is multiplied by (2a + b), the result is a polynomial with terms. The choices for the terms are (7,8,9,10)
First product
(2ab+b)(a²-b²)a²(2ab+b)-b²(2ab+b)2a³b+a²b-2ab³-b³Second and final product
(2a³b)+a²b-2ab³-b³)(2a+b)2a(2a³b+a²b-2ab³-b³)+b(2a³b)+a²b-2ab³-b³)4a⁴b+2a³b-4a²b³-2ab³+2a³b²+a²b²-2ab⁴-b⁴Answer:
Given polynomials
[tex]2ab+b[/tex][tex]a^2-b^2[/tex]The product of the given polynomials:
[tex]\begin{aligned}(2ab+b)(a^2-b^2) & = 2ab(a^2-b^2)+b(a^2-b^2)\\& = 2a^3b-2ab^3+a^2b-b^3\end{aligned}[/tex]
The product of the given polynomials multiplied by [tex](2a+b)[/tex]:
[tex]\begin{aligned}(2a+b)(2a^3b-2ab^3+a^2b-b^3) & = 2a(2a^3b-2ab^3+a^2b-b^3)+b(2a^3b-2ab^3+a^2b-b^3)\\& = 4a^4b-4a^2b^3+2a^3b-2ab^3+2a^3b^2-2ab^4+a^2b^2-b^4\\& = 4a^4b+2a^3b^2-4a^2b^3-2ab^4+2a^3b+a^2b^2-2ab^3-b^4\end{aligned}[/tex]
Therefore, the resulting polynomial has 8 terms.
A museum groundskeeper is creating a semicircular statuary garden with a diameter of 27 feet. There will be a fence around the garden. The fencing costs $7.75 per linear foot. About how much will the fencing cost altogether? Round to the nearest hundredth. Use 3.14 for π.
The fencing will cost about $
.
To calculate the cost of the fence, we have to find the length of the semi-circle. The cost of fencing the garden would be $328.52 approximately
Circumference of a CircleTo find the length of the fence, we have to calculate the circumference of the semi-circle and divide it by 2
[tex]C = 2\pi r\\l = \frac{c}{2} \\l = \pi r[/tex]
Data;
diameter = 27ft r = diameter/2 = 13.5ft π = 3.14Let's substitute the values and calculate the length of the fence.
[tex]l = \pi r\\l = 3.14 * 13.5\\l = 42.39ft[/tex]
The length of the fence is equal to 42.39ft
The cost of fencing would be
[tex]42.39 * 7.75 = $328.5225[/tex]
The cost of fencing the garden would be $328.52 approximately
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Write an equation in slope-intercept form of the line that contains the point (-2, 2) and has the slope = -5.
Answer:
[tex]y=-5x-8[/tex]
Step-by-step explanation:
Given the following question:
To calculate the slope intercept of a line/point we need to use the formula for slope intercept, substitute, and solve for b.
Formula for slope intercept:
[tex]y=mx+b[/tex]
[tex]m=-5[/tex]
[tex]y=2[/tex]
[tex]x=-2[/tex]
[tex]2=-5(-2)+b[/tex]
Solve for b:
[tex]2=-5(-2)+b[/tex]
[tex]-5(-2)=10[/tex]
[tex]2=10+b[/tex]
[tex]10-10=0[/tex]
[tex]2-10=-8[/tex]
[tex]-8=b[/tex]
[tex]b=-8[/tex]
Substitute for the following:
[tex]y=mx+b[/tex]
[tex]b=-8[/tex]
[tex]m=-5[/tex]
[tex]y=-5x-8[/tex]
Your answer is "y = -5x - 8."
Hope this helps.
A fish tank is full of fish. There are 3 goldfish, 2 guppies, 6 clownfish, and 2 striped fish. If one of the goldfish dies and you remove it from the tank, what is the new probability of selecting a clownfish?
5/13
1/2
5/12
6/13
Answer:
1/2
Step-by-step explanation:
13 total fish
remove one fish
12 total fish
6 total clown fish
6/12 simplified is 1/2
heyyy.... can someone pls help asap.
Rearrange the formula to write r in terms of P and pi.
[tex]p = 2r + \pi \: r[/tex]
Answer:
[tex]r = \dfrac{p}{2 + \pi}[/tex]
Step-by-step explanation:
[tex]~~~~~p = 2r +\pi r\\\\\implies p = r(2 + \pi)\\\\\implies r = \dfrac{p}{2 + \pi}[/tex]
What does a negative AH₁ for a molecule mean?
Answer: C
Step-by-step explanation: I know it trust me
In a a computer game positive numbers represent earning points and negatiive numbers represents.wich number represents losing more than 500 points
Inequalities help us to compare two unequal expressions. The inequality that represents losing more than 500 points is x<-500.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.
It is mostly denoted by the symbol <, >, ≤, and ≥.
Given In a computer game positive numbers represent earning points and negative numbers represent losing points. Therefore, the loss of more than 500 points is given by the inequality,
x< -500
Hence, the inequality that represents losing more than 500 points is x<-500.
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There are 11 cookies in a jar, as listed below. The cookies are all the same size and shape.
•
6 chocolate chips
• 5 oatmeal
One cookie is randomly selected from the jar and not replaced. Then a second cookie is
randomly selected and not replaced. What is the probability they are both chocolate chips?
Answer:
6/11*5/10 = 3/11
Step-by-step explanation:
first we can get 6/11 which is the probability.
then we minus both sides by 1 to get 5/10
then we times them
The average starting salary for an editor at a textbook company is $39,800. The actual salaries can vary by less than $1,300. Which inequality can
be used to determine whether a salary, x, falls within this range? What is the range of starting salaries at the company?
O A 11,300-x) <39,800
The range of salaries is from $38,500 to $39,800.
OB.
|x-39,8001 <1,300
The range of salaries is from $38,500 to $41,100.
OC.
|x+39,800| <1,300
The range of salaries is from $38,500 to $41,100.
O D. x+1,3001 ≥ 39,800
The range of salaries is from $39,800 to $41,100.
The range of salary is (a) the range of salaries is from $38,500 to $39,800.
How to determine the salary range?The given parameters are:
Average salary = 39,800
Vary = Less than $1300
Let the salary be x.
So, we have:
x = 39,800
When the salary varies, the equation becomes
x = 39800 - 1300
Evaluate
x = 38500
This means that the salary is from 38500 to 39800
Hence, the range of salary is (a) the range of salaries is from $38,500 to $39,800.
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A lines slope is 0, and it’s y intercept is 3. What is it’s equation in slope intercept form?
Answer:
y=3
Step-by-step explanation:
y=mx+b where m = slope and b=y-intercept
slope: 0, y-intercept: 3
y=(0)x + 3
y=3
37.6 x ???=3760
this question is basically:
thirty seven point six times ?what? equals three thousand seven hundred and sixty
15 POINTS AVALIBLE + BRAINLIEST !!!!
thanks :)
Answer:
The "what" is 100
Step-by-step explanation:
Rewrite this as 37.6y = 3760 and set out to determine y:
y = 3760/37.6 = 100
The "what" is 100
Which image shows a reflection of Polygon P using line e? Select the correct choice.
Answer:
B.
Step-by-step explanation:
Because the point on the top on the original would still be on top so it is 100% B
Hope This Helped
A boat travelled 60km downstream in 4 hours and the return trip in 5 hours. What is the
speed of the boat in still water in km/h? Write your answer to the nearest tenth.
Answer:
13.3 km/h
Step-by-step explanation:
getting the neutral is adding both the hours and distance, after adding them you can then dicixe the distance by the time getting your average speed (the upstream is what balances the downstream)
I need help ASAP pleaseee!!
Answer:
Vertex(1,7)
Vertex form: [tex]f(x)=-2\left(x-1\right)^2+7[/tex]
Step-by-step explanation:
Vertex form equations for x is [tex]v=-\frac{b}{2a}[/tex]
which the vertex here is
[tex]-\frac{4}{2\left(-2\right)}[/tex]
->
x = 1, plugin to find y, y = 7
Find the sum.
(12x5 - 3x¹ + 2x - 5) + (8x¹ − 3x³ + 4x + 1)
Answer:
[tex]\left(12x^5-3x^1+2x-5\right)+\left(8x^1-3x^3+4x+1\right)[/tex]
=> Expand
[tex]12x^5-3x^1+2x-5+8x^1-3x^3+4x+1[/tex]
=> simplify and group like terms
[tex]12x^5-3x^3+5x^1+6x-4[/tex]
=> simplify further
[tex]12x^5-3x^3+11x-4[/tex]
What number needs to be added to 5 and 3 so that the ratio of the first number to the second becomes 3 : 2?
Answer:
1
Step-by-step explanation:
let x be the number to be added to 5 and 3
expressing the ratios in fractional form
[tex]\frac{5+x}{3+x}[/tex] = [tex]\frac{3}{2}[/tex] ( cross- multiply )
3(3 + x) = 2(5 + x) ← distribute parenthesis on both sides
9 + 3x = 10 + 2x ( subtract 2x from both sides )
9 + x = 10 ( subtract 9 from both sides )
x = 1
then the number to be added to both is 1
Which graph represents the function?
f(x)=√x + 1
Using translation concepts, it is found that graph 3 represents the function [tex]f(x) = \sqrt{x} + 1[/tex].
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the function is:
[tex]f(x) = \sqrt{x} + 1[/tex]
Which is a shift up of one unit of [tex]\sqrt{x}[/tex]. The square root function has y-intercept at (0,0), hence the translated function will have y-intercept at (0,1). Additionally, [tex]\sqrt{4} = 2[/tex], since f(4) = 3, which means that graph 3 is represents the function.
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add or subtract the given percent from
71% subtracted from 100% is 29%
Complete questionAdd or subtract the given percent from 100%.
71%
How to solve the expression?The percentage (p) is given as:
p = 71%
When subtracted from 100%, we have:
100% - p
Substitute p = 71%
100% - 71%
71 subtracted from 100 is 29.
So, we have:
100% - 71% = 29%
Hence, 71% subtracted from 100% is 29%
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A tank contains 180 gallons of water and 15 oz of salt. water containing a salt concentration of 17(1+15sint) oz/gal flows into the tank at a rate of 8 gal/min, and the mixture in the tank flows out at the same rate.
the long-time behavior of the solution is an oscillation about a certain constant level. what is this level? what is the amplitude of the oscillation?
Let A(t) denote the amount of salt (in ounces, oz) in the tank at time t (in minutes, min).
Salt flows in at a rate of
[tex]\dfrac{dA}{dt}_{\rm in} = \left(17 (1 + 15 \sin(t)) \dfrac{\rm oz}{\rm gal}\right) \left(8\dfrac{\rm gal}{\rm min}\right) = 136 (1 + 15 \sin(t)) \dfrac{\rm oz}{\min}[/tex]
and flows out at a rate of
[tex]\dfrac{dA}{dt}_{\rm out} = \left(\dfrac{A(t) \, \mathrm{oz}}{180 \,\mathrm{gal} + \left(8\frac{\rm gal}{\rm min} - 8\frac{\rm gal}{\rm min}\right) (t \, \mathrm{min})}\right) \left(8 \dfrac{\rm gal}{\rm min}\right) = \dfrac{A(t)}{180} \dfrac{\rm oz}{\rm min}[/tex]
so that the net rate of change in the amount of salt in the tank is given by the linear differential equation
[tex]\dfrac{dA}{dt} = \dfrac{dA}{dt}_{\rm in} - \dfrac{dA}{dt}_{\rm out} \iff \dfrac{dA}{dt} + \dfrac{A(t)}{180} = 136 (1 + 15 \sin(t))[/tex]
Multiply both sides by the integrating factor, [tex]e^{t/180}[/tex], and rewrite the left side as the derivative of a product.
[tex]e^{t/180} \dfrac{dA}{dt} + e^{t/180} \dfrac{A(t)}{180} = 136 e^{t/180} (1 + 15 \sin(t))[/tex]
[tex]\dfrac d{dt}\left[e^{t/180} A(t)\right] = 136 e^{t/180} (1 + 15 \sin(t))[/tex]
Integrate both sides with respect to t (integrate the right side by parts):
[tex]\displaystyle \int \frac d{dt}\left[e^{t/180} A(t)\right] \, dt = 136 \int e^{t/180} (1 + 15 \sin(t)) \, dt[/tex]
[tex]\displaystyle e^{t/180} A(t) = \left(24,480 - \frac{66,096,000}{32,401} \cos(t) + \frac{367,200}{32,401} \sin(t)\right) e^{t/180} + C[/tex]
Solve for A(t) :
[tex]\displaystyle A(t) = 24,480 - \frac{66,096,000}{32,401} \cos(t) + \frac{367,200}{32,401} \sin(t) + C e^{-t/180}[/tex]
The tank starts with A(0) = 15 oz of salt; use this to solve for the constant C.
[tex]\displaystyle 15 = 24,480 - \frac{66,096,000}{32,401} + C \implies C = -\dfrac{726,594,465}{32,401}[/tex]
So,
[tex]\displaystyle A(t) = 24,480 - \frac{66,096,000}{32,401} \cos(t) + \frac{367,200}{32,401} \sin(t) - \frac{726,594,465}{32,401} e^{-t/180}[/tex]
Recall the angle-sum identity for cosine:
[tex]R \cos(x-\theta) = R \cos(\theta) \cos(x) + R \sin(\theta) \sin(x)[/tex]
so that we can condense the trigonometric terms in A(t). Solve for R and θ :
[tex]R \cos(\theta) = -\dfrac{66,096,000}{32,401}[/tex]
[tex]R \sin(\theta) = \dfrac{367,200}{32,401}[/tex]
Recall the Pythagorean identity and definition of tangent,
[tex]\cos^2(x) + \sin^2(x) = 1[/tex]
[tex]\tan(x) = \dfrac{\sin(x)}{\cos(x)}[/tex]
Then
[tex]R^2 \cos^2(\theta) + R^2 \sin^2(\theta) = R^2 = \dfrac{134,835,840,000}{32,401} \implies R = \dfrac{367,200}{\sqrt{32,401}}[/tex]
and
[tex]\dfrac{R \sin(\theta)}{R \cos(\theta)} = \tan(\theta) = -\dfrac{367,200}{66,096,000} = -\dfrac1{180} \\\\ \implies \theta = -\tan^{-1}\left(\dfrac1{180}\right) = -\cot^{-1}(180)[/tex]
so we can rewrite A(t) as
[tex]\displaystyle A(t) = 24,480 + \frac{367,200}{\sqrt{32,401}} \cos\left(t + \cot^{-1}(180)\right) - \frac{726,594,465}{32,401} e^{-t/180}[/tex]
As t goes to infinity, the exponential term will converge to zero. Meanwhile the cosine term will oscillate between -1 and 1, so that A(t) will oscillate about the constant level of 24,480 oz between the extreme values of
[tex]24,480 - \dfrac{267,200}{\sqrt{32,401}} \approx 22,995.6 \,\mathrm{oz}[/tex]
and
[tex]24,480 + \dfrac{267,200}{\sqrt{32,401}} \approx 25,964.4 \,\mathrm{oz}[/tex]
which is to say, with amplitude
[tex]2 \times \dfrac{267,200}{\sqrt{32,401}} \approx \mathbf{2,968.84 \,oz}[/tex]