Simplify [tex]\frac{6a^2 b^-^2}{8a^-^3 b^3}[/tex] Assume a≠0 and b≠0
Answer:
sorry i thought i knew it
Step-by-step explanation:
Answer:
3rd option
Step-by-step explanation:
using the rules of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex] : nm > n
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]\frac{1}{a^{(n-m)} }[/tex] : n > m
[tex]\frac{6a^2b^{-2} }{8a^{-3b^3} }[/tex] ← separate the variables
= [tex]\frac{6}{8}[/tex] × [tex]\frac{a^2}{a^{-3} }[/tex] × [tex]\frac{b^{-2} }{b^3}[/tex]
= [tex]\frac{3}{4}[/tex] × [tex]a^{2-(-3)}[/tex] × [tex]\frac{1}{b^{3-(-2)} }[/tex]
= [tex]\frac{3}{4}[/tex] × [tex]a^{2+3}[/tex] × [tex]\frac{1}{b^{3+2} }[/tex]
= [tex]\frac{3}{4}[/tex] × [tex]a^{5}[/tex] × [tex]\frac{1}{b^{5} }[/tex]
= [tex]\frac{3a^{5} }{4b^{5} }[/tex]
someone please help me in this question i need step by step sol with explaination
Converting the portions to decimal, the grade that has the greatest portion of students is: 3rd grade.
How to Compare Percentage, Decimals, and Fractions?The bigger the digit that is close to the decimal point, the bigger the number given.
Also, percentage can be converted to decimal by dividing the given percent by 100. Percent means over 100.
Fractions can also be converted to decimals by simply dividing the numerator by the denominator.
To compare the portion of students interested in playing an instrument in each grade, let all the portions be in decimals.
Converting 25/36 to decimal, we have: 0.694 (3rd grade)
Converting 61.24% to decimal, we have: 61.24/100 = 0.6124 (4th grade)
From the rest of the portions given, 0.694 is greater than the others.
Therefore, the grade that has the greatest portion of students is: 3rd grade.
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A ship left a port and sailed east at the rate of 30 miles per hour. One hour later, a second ship left the same port at the rate of 40 miles per hour, also traveling east. In how many hours did the second ship overtake the first ship?
Answer:
3 hours
Step-by-step explanation:
When the ships meet each other, that means the the distance travelled for both ships are the same, that is where the 2nd ship will overtake the ship.
Distance = Speed * Time
So, given information from the question, and letting x be the time in hours (from when the 1st ship departs), we can deduce:
Distance travelled of 1st ship = Distance travelled of 2nd ship
30x = 40(x-1)
30x = 40x - 40
-10x = - 40
x = [tex]\frac{-40}{-10}[/tex]
= 4
Since we are calculating based on the 2nd ship,
Time taken for 2nd ship to overtake first ship = x - 1 = 4 - 1 = 3 hours.
2. The product of two consecutive even numbers is 168. What are the numbers?
Answer:
12 and 14
Step-by-step explanation:
12 * 14 = 168
Answer:
12 & 14
Step-by-step explanation:
the work: x = first even number, (x+2) = second even number
The equation
[tex]x(x+2)=168[/tex]
[tex]x^{2} +2x=168[/tex]
[tex]x^{2} +2x-168=0[/tex]
Factoring
[tex](x-12)(x+14)=0[/tex]
first factor
[tex]x-12=0\\x=12[/tex]
Second factor
[tex]x+14=0\\x=-14[/tex]
The solution is the positive number
x = 12 is the first even number
x + 2 = 12 + 2 = 14 is the second even number
Hope this helps
A town has a population of 1.23 x 10 and grows at a rate of 6.7% every year. Which
equation represents the town's population after 4 years?
At the growth rate of [tex]6.7\%[/tex], the population of the town after 4 years can be represented by the equation, [tex]A=1.23\times 10\times(1.067)^4[/tex].
What is the formula for the population?The growth rate of a population is a measure of how fast a population increases.If the initial population is [tex]P[/tex] and the growth rate is [tex]r\%[/tex] every year, then the population after [tex]t[/tex] years will be given by the following formula: [tex]A=P(1+\frac{r}{100})^t[/tex].Here, the initial population is [tex]P=1.23\times 10[/tex] and the growth rate is [tex]r=6.7\%[/tex].
So the population after [tex]t=4[/tex] years will be:
[tex]A=P(1+\frac{r}{100})^t\\\Longrightarrow A=1.23\times 10\times(1+\frac{6.7}{100})^4\\\Longrightarrow A=1.23\times 10\times(1.067)^4[/tex]
Therefore, at the growth rate of [tex]6.7\%[/tex], the population of the town after 4 years can be represented by the equation, [tex]A=1.23\times 10\times(1.067)^4[/tex].
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(SAT prep) If the lengths of two sides of a triangle are 3 and 5 then the lenght of the third side cannot be:
Answer:
A)
Step-by-step explanation:
3+3=6 6>5
3+5=8 3<8
A)
Write 636,000 in scientific notation.
HELP ME PLEASE
Ms. Callahan had 250 sheets of paper. She used 6 sheets of paper. She then gave each student 3 sheets of paper. Which expression represents the number of sheets of paper Ms. Callahan had left after she gave paper to n students?
Answer:
250 - 6 - 3n
Step-by-step explanation:
Let n equal the number of students.
Please see the attached photo. I do not know how to calculate any of this using my TI 84+ CE calculator and the answers I am getting when trying to calculate by hand are not correct.
The decision is to fail to reject the null given that p value is not ≤ 0.05.
How to solve for the z statistical testThe hypothesis
H0 = p = 0.63
H1 = p < 0.63
α = 0.05
sample proportion = 71/125 = 0.568
x = 71
n = 125
standard error of the proportion
√0.63(1-0.63)/125
= 0.0431
The null hypothesis follows a standard normal distribution. This is a left tailed test.
We are to reject the null if the p value is less than 0.05
p < 0.05
This probability test is a z probability test.
Z test = 0.568 - 0.63 / 0.0431
test statistic = -1.436
-Z0.05 =
Critical value = -1.645
p(z < -1.436)
p value = 0.0755
The decision would be to fail to reject the null hypothesis. The reason would be due to the fact that p value is greater than significance.
P-value is not ≤ α 0.05
0.0755 > 0.05
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√2n +6=6
n =
Answer?
Answer:
your question is not correct i can not find the answer
13
Company A has 800 employees, and it decides to grant each of the employees 50 share options as
part of its new rewards plan. The options are exercisable over 5 years and subject to a 3-year
service condition. The fair value of each option at the grant date is $16. The company estimates
that 80% of its employees will meet the service condition required for receiving the options.
Calculate the total share-based payment expense for Company A assuming that 80% of the
employees actually meet the service condition.
$512,000
$853,333
$341,333
$170,667
Option A. The total share expense that the company would share would be given as 512,000
What is meant by share expense?These are the necessary expenses that are needed for the smooth functioning of a particular business that are not within the confinement of the O and M agreement. It has to do with shared facilities.
How to solve for the share expenseThe total number of the employees that are knwon to satistfy condition are given as
800 * 0.8
= 640
The options that are estmated that would be exercised
This is given as the employees * share option
= 640×50
=32000.
The total shae for the company would be gotten as
= 32000× $16
This gives us $512,000.
Hence it can be concluded that the total share of the company if they have 80 percent meeting the condition is $512000.
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How to solve these questions?
(with work)
The angles and length of the triangle area as follows:
∠CBD = 61°∠A = 35°AD = 32.77 unitsBD = 22.94 unitsBC = 11.12 unitsCD = 9.73 unitsHow to find the sides and angle of a triangle?The sum of angles in a triangle is 180 degree.
Therefore,
∠DBC = 180 - 29 - 90 = 61°
Hence,
∠A = 180 - 29 - 61 - 55 = 35°
∠CBD = 61°
Using trigonometric ratios,
sin 55 = opposite / hypotenuse
sin 55 = AD / 40
AD = 40 sin 55
AD = 32.7660817716
AD = 32.77 units
cos 55 = adjacent / hypotenuse
cos 55 = BD / 40
BD = 40 cos 55
BD = 22.943057454
BD = 22.94 units
sin 29 = 22.94 / BC
BC = 22.94 sin 29
BC = 11.1215326885
BC = 11.12 units
cos 29 = CD / 11.12
CD = 11.12 cos 29
CD = 9.72577114339
CD = 9.73 units
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Factor x² - 4x + 5.
Prime
O(x + 5)(x - 1)
O(x - 5)(x - 1)
(x+5)(x + 1)
Answer:
(x-5)(x+1)
Step-by-step explanation:
x² - 4x + 5 = (x-5)(x+1)
Establish the identity.
(2 cos 0-6 sin 0)² + (6 cos 0+2 sin 0)2 = 40
Rewriting the left-hand side as follows,
[tex](2\cos\theta-6\sin \theta)^2 +(6\cos \theta+2\sin \theta)^2\\\\=4\cos^2 \theta-24\cos \theta \sin \theta+36 \sin^2 \theta+36 \cos^2 \theta+24 \cos \theta \sin \theta+4 \sin^2 \theta\\\\=40\cos^2 \theta+40 \sin^2 \theta\\\\=40(\cos^2 \theta+\sin^2 \theta)\\\\=40[/tex]
help answer this please
Answer:
Step-by-step explanation:
2x + 5y = 8
-5 -5
2x = 8 - 5y
divide both sides by 2
[tex]\frac{2x}{2} = \frac{8-5y}{2}[/tex]
divide by 2 undoes the multiplication by 2
x = [tex]\frac{8- 5y}{2}[/tex]
divide 8 - 5y by 2
x = - [tex]\frac{5}{2}[/tex] y + 4
Which linear inequality is represented by the graph?
y ≤ One-thirdx − 1
y ≥ One-thirdx − 1
y < 3x − 1
y > 3x − 1
Tthe inequality that describes this graph is y ≤ 1/3x - 4/3
How to determine the linear inequality represented by the graph?The graph that completes the question is added as an attachment
From the attached graph, we have the following points
(0, -1.3) and (3, -0.3)
The slope is calculated as:
m = (y2 - y1)/(x2 - x1)
Substitute the known values in the above equation
m = (-0.3 + 1.3)/(3 - 0)
Evaluate
m = 1/3
The equation is then calculated as:
y = m(x - x1) + y1
This gives
y = 1/3(x - 0) - 1.3
Evaluate
y = 1/3x - 4/3
From the graph, we have the following highlights:
The line of the graph is a closed lineThe upper part is shadedThe first highlight above implies, the inequality can be any of ≥ and ≤
While the second highlight above implies, the inequality is ≤
Hence, the inequality that describes this graph is y ≤ 1/3x - 4/3
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Consider the parametric equations below.
x = t^2 − 3, y = t + 2, −3 ≤ t ≤ 3
Eliminate the parameter to find a Cartesian equation of the curve.
for
−1 ≤ y ≤ 5
Solve the second equation for [tex]t[/tex], then substitute it into the first equation.
[tex]y = t + 2 \implies t = y-2[/tex]
[tex]x = t^2 - 3 \implies \boxed{x = (y-2)^2 - 3}[/tex]
PLWASW HELP ALOT OF POINTS Charlie used construction paper, scissors and a ruler to construct an
isosceles triangle with a pair of sides each 3 inches long and an acute
angle on top. He drew an altitude from the acute angle to the base and
wrote down his observations. He then created another isosceles triangle
with a pair of sides of 7 inches long with an obtuse angle on top, drew a
altitude to the base, and recorded his observations.
Which of these is the best conjecture for Charlie to develop?
The best conjecture for Charlie to develop is that an altitude drawn to the base of the isosceles triangle creates the smaller congruent triangles by the HL postulate.
What is conjecture?It should be noted that conjecture simply means a conclusion that's proffered on a tentative basis without any proof.
From the information, Charlie used construction paper, scissors and a ruler to construct an isosceles triangle with a pair of sides each 3 inches long and an acute angle on top.
Here, the best conjecture for Charlie to develop is that an altitude drawn to the base of the isosceles triangle creates the smaller congruent triangles by the HL postulate.
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For each equation, determine whether it represents a direct variation, an inverse variation, or neither.
Find the constant of variation when one exists and write it in simplest form.
The equation 15x + 5y = 0 is a direct variation and the constant of variation is -3 while the equation -5x + 8y = 3 is neither a direct variation nor an inverse variation
How to categorize the type of each equation?As a general rule, we have the following forms of equation:
Direct variation: y =kx
Inverse variation: y = k/x
Where k represents the constant of variation
The equations 15x + 5y = 0 can be rewritten as:
5y = -15x
Divide by 5
y = -3x
The above equation take the form y = kx
This means that k = -3
Hence, the equation 15x + 5y = 0 is a direct variation and the constant of variation is -3
However, the equation -5x + 8y = 3 do not take any of the given forms
Hence, the equation -5x + 8y = 3 is neither a direct variation nor an inverse variation
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Find the equation to the line below.
y =
Answer:
[tex]y=\frac{-3}{4}x-3[/tex]
Step-by-step explanation:
This is a linear graph so the equation will be in the format of y=mx+b.
b, the y-intercept, will be -3, as that is where the line crosses the y-axis.
m, the slope, is [tex]\frac{-3}{4}[/tex], calculated from the change in y over the change in x from points (-4,0) to (0,-3).
Now substitute the values in our equation:
[tex]y=\frac{-3}{4}x-3[/tex]
Answer:
y= -3/4+[-3]
Step-by-step explanation:
PLEASE HELP
Determine which quadratic equation reveals its maximum or minimum value without changing the form of the equation.
y=x² + 4x-3
y = -3(x+4)² + 1
y=(x-9)(x + 7)
y=2x²-5x+4-10
y=x²+(3+1)x-3
y=x²+3x+1x-3
y=x(x+3)-1(x+3)
y=(x-1)(x+3)
Do companies that provide mobile wifi hotspots see your history?
Yes, companies that provide mobile wifi hotspots can see your history.
What is a Wi-Fi hotspots?A Wi-Fi hotspots can be defined as the hotspots that makes it possible for other mobile user connected to a wifi hotspots to browse or to connect to the internet.
For a mobile user to connect to the internet through the mobile wifi hotspot, the mobile hotspot wifi owner must have giving access to mobile user to browse .
Hence, companies that provide mobile wifi hotspots can see your history of the site you visit.
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En la final de un concurso escolar de
matemática participan 6 alumnos de los
cuales 3 son alumnos del colegio A. Si se
premia a los dos primeros con regalos
diferentes, entonces la probabilidad de que
los alumnos del colegio A obtengan los dos
premios (no hay empates), es:
Usando la distribución hipergeométrica, la probabilidad de que los alumnos del colegio A obtengan los dos premios (no hay empates), es: 0.2 = 20%.
¿Qué es la fórmula de distribución hipergeométrica?La fórmula es:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Los parámetros son:
x es el número de éxitos.N es el tamaño de la población.n es el tamaño de la muestra.k es el número total de resultados deseados.Los valores de los parámetros son:
N = 6, k = 3, n = 2.
La probabilidad de que los alumnos del colegio A obtengan los dos premios (no hay empates), es P(X = 2), por eso:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,6,2,3) = \frac{C_{3,2}C_{3,0}}{C_{6,2}} = 0.2[/tex]
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1. Suppose Robin borrowed $3,600 on October 21 and repaid the loan on February 21 of the
following year. What simple interest rate was charged if Robin repaid $3,694.63?
well, keeping in mind that a year has 365 years, so let's see
[tex]\stackrel{Oct}{10}~~ + ~~\stackrel{Nov}{30}~~ + ~~\stackrel{Dec}{31}~~ + ~~\stackrel{Jan}{31}~~ + ~~\stackrel{Feb}{21}\implies 123~days[/tex]
so the 3600 were borrowed for only 123 days of a year, that'd be 123/365 of a year, thus
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$3694.63\\ P=\textit{original amount deposited}\dotfill & \$3600\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &\frac{123}{365} \end{cases}[/tex]
[tex]3694.63=3600[1+(\frac{r}{100})(\frac{123}{365})]\implies \cfrac{3694.63}{3600}=1+\cfrac{123r}{36500} \\\\\\ \cfrac{3694.63}{3600}-1=\cfrac{123r}{36500}\implies \left( \cfrac{36500}{123} \right)\left( \cfrac{3694.63}{3600}-1 \right)=r\implies \stackrel{\%}{7.8}\approx r[/tex]
7.8% is the simple interest rate was charged if Robin repaid $3,694.63.
What is simple InterestSimple interest is based on the principal amount of a loan or the first deposit in a savings account.
A=P(1+rt)
A is final amount, P is principle amount, r is rate of interest and t is time.
We know that in a year we have 365 days.
But the time here is from oct 21 to feb 21, which has 123 days.
so the 3600 were borrowed for only 123 days of a year, that'd be 123/365 of a year, thus
Apply these values in formula
A=P(1+rt)
3694.63=3600(1+r/100(123/365))
3694.63=3600(1+123r/36500)
3694.63/3600=1+123r/36500
3694.63/3600-1=123r/36500
(3694.63-3600)/3600=123r/36500
94.63/3600=123r/36500
Apply cross multiplication
3453995=442800r
7.80=r
Hence 7.8% is the simple interest rate was charged if Robin repaid $3,694.63.
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Find the mean and standard deviation for the set of data. {25,16,28,6,30,7,26,20,22}
Answer: 8.7 the mean is 20
Step-by-step explanation:
Maths Questions box 51.The function f: R→ R is twice differentiable and for any x ER we have g(x) = f(4-x²), if f'(1) = -5 and f" (1) = -1 than what is g" (√3)?
By the chain rule,
[tex]g(x) = f(4 - x^2) \\\\ \implies g'(x) = -2x f'(4 - x^2) \\\\ \implies g''(x) = -2 f'(4 - x^2) + 4x^2 f''(4 - x^2)[/tex]
Observe that
[tex]4 - x^2 = 1 \implies x^2 = 3 \implies x = \pm\sqrt3[/tex]
Then
[tex]g''(\sqrt3) = -2 f'(1) + 4\left(\sqrt3\right)^2 f''(1) = -2(-5) + 4(3)(-1) = \boxed{-2}[/tex]
the width of a large butterfly is about 0.08. What is the width when it is written in scientific notation
Answer: 8 x 10^2
Step-by-step explanation:
scientific notation has to be greater than 1, less than 10
therefore:
0.08 = 8 x 10^2
Which of the following describes the transformations of g (x) = negative (2) Superscript x + 4 Baseline minus 2 from the parent function f (x) = 2 Superscript x?
Using translation concepts, the transformations are described as follows:
Reflection over the x-axis.Shifted up 4 units.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
In this problem, the parent function is:
[tex]f(x) = 2^x[/tex]
The transformed function is:
[tex]g(x) = -2^x + 4[/tex]
We have that the transformations in this problem can be described as follows:
f(x) was multiplied by -1, hence it was reflected over the x-axis.4 was added to the function, hence it was shifted up 4 units.More can be learned about translation concepts at https://brainly.com/question/28098112
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A TEACHER IS CONSTRUCTING A MATHEMATICS TEST
CONSISTING OF 10 QUESTIONS. SHE HAS A POOL OF 28 QUESTIONS, WHICH ARE
CLASSIFIED BY LEVEL OF DIFFICULTY AS FOLLOWS: 6 DIFFICULT QUESTIONS, 10
AVERAGE QUESTIONS, AND 12 EASY QUESTIONS. HOW MANY DIFFERENT 10
QUESTION TESTS CAN SHE CONSTRUCT FROM THE POOL OF 28 QUESTIONS IF
HER TEST IS TO HAVE 3 DIFFICULT, 4 AVERAGE, AND 3 EASY QUESTIONS?
The number of ways of constructing questions from the pool of 28 questions if her test is to have 3 difficult, 4 average and 3 easy questions is 924, 000 ways
How to determine the combinationNote that the formula for combination is given as;
Combination = [tex]\frac{n!}{r!(n-r)!}[/tex]
From the information we have that;
There are 28 questions in the pool
The test should have a total of 10 questions;
6 difficult , 10 average and 12 easy questions
We are asked to determine the combination of;
3 difficult questions
4 average questions
3 easy questions
6C3 = [tex]\frac{6!}{3!(6-3)!}[/tex]
6C3 = [tex]\frac{720}{36}[/tex]
6C3 = 20
10C4 = [tex]\frac{10!}{4!(10-4)!}[/tex]
10C4 = [tex]\frac{3628800}{17280}[/tex]
10C4 = 210
12C4 = [tex]\frac{12!}{4!(12-4)!}[/tex]
12C4 = 220
The number of ways of constructing the questions is
= 20 × 210 × 220
= 924, 000 ways
Thus, the number of ways of constructing questions from the pool of 28 questions if her test is to have 3 difficult, 4 average and 3 easy questions is 924, 000 ways
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What is the equation of the line in standard form of the graph below?
Answer:
Step-by-step explanation:
