Answers
By power algebra method,
a) [tex]\frac{16}{81}[/tex]
b) [tex]\frac{2xy}{3}[/tex]
c) [tex]\frac{16x^4}{y^8}[/tex]
d) [tex]\frac{3y^2}{x^3}[/tex]
What is dividing power property?According to the Quotient of Powers Property, you can maintain the base and subtract the exponents when dividing two exponents by the same base. Since you cannot divide by zero, this characteristic will always hold true as long as the base is not zero. For more information on this property, use the interactive below.
The Exponents Power Rule: am*n = (am)n. Multiply the exponent by the power to increase a number with an exponent to that power.
You divide them by the highest exponent in the numerator (the numerator) and the lowest exponent in the denominator (the bottom exponent).
a) [tex](\frac{2}{3})^4[/tex] = [tex]\frac{2*2*2*2}{3*3*3*3}[/tex] = [tex]\frac{16}{81}[/tex]
b) [tex]\frac{2x^2y}{3x}[/tex] = [tex]\frac{2*x*x*y}{3*x}[/tex] = [tex]\frac{2xy}{3}[/tex]
c) [tex](\frac{2x}{y^2})^4[/tex] = [tex]\frac{2x*2x*2x*2x}{y^2*y^2*y^2*y^2}[/tex] = [tex]\frac{16x^4}{y^8}[/tex]
d) [tex]\frac{3xy^4}{x^3}[/tex][tex].\frac{y}{xy^3}[/tex] = [tex]\frac{3x*y*y*y*y}{x*x*x} . \frac{y}{x*y*y*y}[/tex] = [tex]\frac{3y^2}{x^3}[/tex]
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Related Questions
The quality-control inspector of a production plant will reject a batch of syringes if two or more defective syringes are found in a random sample of eight syringes taken from the batch. Suppose the batch contains 5% defective syringes. A button hyperlink to the SALT program that reads: Use SALT.
(a) Make a histogram showing the probabilities of r = 0, 1, 2, 3, , 7 and 8 defective syringes in a random sample of eight syringes.
(b) Find μ. (Enter your answer to two decimal places.) μ = syringes What is the expected number of defective syringes the inspector will find? (Enter your answer to two decimal places.) syringes
(c) What is the probability that the batch will be accepted? (Round your answer to three decimal places.) (
d) Find Ï. (Round your answer to three decimal places.) Ï = syringes
Answers
a) Histogram (figure attached)
b) The expected number of defective is equal to 0.4 syringes.
c) Probability that the batch will be accepted is equal to 0.94275.
d) The standard deviation is 0.6164.
It is a binomial distribution "DISCRETE probability distribution that encapsulates the likelihood that a value will take one of two independent values when a particular set of conditions is met. The assumptions for the binomial distribution are that each trial has a single possible outcome, each trial has an equal chance of success, and each trial is independent of the others or mutually exclusive ".
Let X be the number of syringes being defective as a binomial random variable.
We are given that in the batch, there can be assumed to be 5% defective syringes.
∴ n = 8
Probability of syringes being defective, p = 0.05
Probability of syringes being not defective , q = 1-p = 1-0.05 = 0.95
a) Histogram (figure attached)
b) We know that the formula for Expectation in binomial distribution is;
μ =n×p = 8×0.05
=0.4 syringes
Therefore, the inspector will find the expected number of defective is equal to 0.4 syringes.
c) We have to find binomial probability for that we will use the binomial probability distribution is given by:
P(X=x) = ⁿCₓpˣ (1-p)^n-x, x = 0,1,2,3 ..8
Therefore,
P(x<2) = P(X=0) + P(X=1)
= ⁸C₀(0.05)⁰(1-0.05)⁸ + ⁸C₁(0.05)¹(1-0.05)⁷
= 0.66342 + 8×0.05×0.6983
= 0.66342 + 0.27933
= 0.94275
Therefore, probability that the batch will be accepted is equal to 0.94275.
d) We first find the variance:
σ² = Var(X) = n×p×(1-p)
= 8 × 0.05 ×(1-0.05)
= 0.38
Thus, the standard deviation is
σ = [tex]\sqrt{0.38}[/tex] = 0.6164
Thus,
a) Histogram (figure attached)
b) The expected number of defective is equal to 0.4 syringes.
c) Probability that the batch will be accepted is equal to 0.94275.
d) The standard deviation is 0.6164.
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given the graph of f(x)on the right,determine the type of the function help for number 2
Answers
The first function is an odd and the second one is neither even nor odd. The correct options are (1) and (2).
What is a function?A function y = f(x) is a one to one relationship between two sets X and Y where the set X is called the domain and Y the range of function f(x) ans x ∈ X and y ∈ Y.
The given problem can be solved as follows,
(2) The graph of the given function shows the following,
The value of the function is positive for positive x and negative for negative x.
It can be mathematically written as,
f(-x) = -f(x).
Which shows the given graph is of an odd function.
(3) The given function is f(x) = 4x³ + 2x² - x⁵.
In order to check the type of the function, find its value at the same value of x with different signs as,
f(1) = 4 × 1³ + 2 × 1² - 1⁵ = 5
And, f(-1) = 4 × -1³ + 2 × -1² - -1⁵ = -1
Since, f(1) ≠ f(-1), the function is not even.
And f(-1) ≠ -f(1), the function is not odd.
Thus, the given function is neither even nor odd.
Hence, the first and the second functions of the given problem are odd and neither even nor odd respectively.
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A graph is shown
For which line does y decrease as x increases
A.line 1
B.line 2
C.line 3
D.line 4
Answers
Answer:
Line 2
Step-by-step explanation:
This would represent a negative slope. A negative slope goes down if you start on the left side and go down.
1. The population of a town was 7420 in 2010. The population grows at a rate of 2.3% annually. (a) Use the exponential growth model to write an equation that estimates the population t years after 2010. (b) Estimate the population of the town in 2022. Show your work.
Answers
Hello,
I hope you and your family are doing well!
(a) The exponential growth model is given by the equation P(t) = P0 * r^t, where P(t) is the population t years after 2010, P0 is the population in 2010 (7420), and r is the annual growth rate (2.3%).
Substituting the given values into the equation gives us:
P(t) = 7420 * 1.023^t
This is the equation that estimates the population t years after 2010.
(b) To estimate the population of the town in 2022, we can substitute t = 12 into the equation:
P(12) = 7420 * 1.023^12
Calculating this gives us:
P(12) = 7420 * 1.023^12 = 7420 * 1.291891 = 9593.45
So the estimated population of the town in 2022 is approximately 9593
Happy to help!
5. My sister and I wanted to go to the circus. A ticket was 10% less on a Tuesday than it was on a Saturday. We paid $27 each to attend Tuesday's show. What would our total cost have been had we attended the circus on Saturday?
Answers
Hello,
I hope you and your family are doing well!
If a ticket to the circus was 10% less on a Tuesday than it was on a Saturday, then it was 90% of the Saturday ticket price. If you paid $27 each to attend Tuesday's show, then the Saturday ticket price was $27 / 0.9 = $30.
Since you bought two tickets, the total cost of attending the circus on Saturday would have been 2 * $30 =60
Therefore, your total cost would have been $60 had you attended the circus on Saturday.
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Happy Holidays and New Year!
Graph the inequality on the axes below.
-x + 2y > 4
Answers
Answer:
Check out the image shown above/below
Identify the vertex, axis of symmetry, and the direction of opening of the graph of g(x) = |x| − 8. A. (0, −8); y = −8; opens up B. (0, −8); x = 0; opens up C. (8, 0); x = 0; opens down D. (−8, 0); x = −8; opens down
Answers
The vertex of the absolute function g(x) will be (0, -8). And the function opens up. Then the correct option is A.
What is an absolute function?The absolute function is also known as the mode function. The value of the absolute function is always positive.
If the vertex of the absolute function is at (h, k). Then the absolute function is given as
f(x) = | x - h| + k
The absolute function is given below.
g(x) = | x | - 8
Compare the function g(x) with the function f(x), then the vertex of the absolute function is as,
(h, k) = (0, -8)
The absolute function opens up because there is a positive sign before mode.
The vertex of the absolute function g(x) will be (0, -8). And the function opens up. Then the correct option is A.
The graph is given below.
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You are playing a game that involves tossing a single die. If you roll a one, you win $50. If you roll a 2, you win $25. If you roll anything else, you lose $15. What are you expected winnings?
Answers
Step-by-step explanation:
chances of rolling 1= 1/6
chances of rolling 2=1/6
chances of rolling anything else=2/3
Ann made $35.000 in taxable income last year. Suppose the income tax rate is 10% for the first $8000 plus 16% for the amount over $8000. How much must Ann pay in income tax for last year?
Answers
Answer:
Ann must pay $800 in income tax for the first $8,000 of her taxable income because 8000 * .1 = 800
Ann must pay $4,600 in income tax for the amount of her taxable income over $8,000 because (35000 - 8000) * .16 = 4600
Therefore, Ann must pay a total of $800 + $4,600 = $<<800+4600=5400>>5,400 in income tax for last year.
Answer:
$5,120 in taxes, total
Step-by-step explanation:
Ann made $35,000 in taxable income last year. Suppose the income tax rate is 10% for the first $8,000 plus 16% for the amount over $8,000. How much must Ann pay in income tax for last year?
8,000 * 10% = 800 in taxes for first $8,000
remaining: 35,000 - 8,000 = $27,000 to be taxed at 16%
27,000 * 16% = $4,320
$800 + $4,320 = $5,120 in taxes, total
Find the solution set of the inequality < 25.
Why is (x:x<5} not the solution set of x² < 25?
I will mark as brainest please help
Answers
We can substitute the number in the inequality to find if the inequality holds true. If the inequality holds true, it is a valid solution. This is very similar to substituting a number in an equation, in order to check if it holds.
The same holds true for others.
Solve for all values of x by factoring x2-53=-4
Answers
The values of x in the given equation, x² - 5x = -4, are x = 4 and x = 1
Solving Quadratic equations: Determining the values of xFrom the question, we are to solve the given equation by factoring
The given equation is
x² - 5x = -4
To solve the equation by factoring, transfer the constant to the other side of the equation
x² - 5x + 4 = 0
Factorize the left hand side expression
x² -x -4x + 4 = 0
x(x - 1) -4(x -1) = 0
(x - 4)(x - 1) = 0
x - 4 = 0 OR x - 1 = 0
x = 4 OR x = 1
Hence, the values of x are 4 and 1
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Solve the following equation below. Show each step and check your work. 87 + 87 y = 1218 + 174
Answers
The value of y is 15.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
87 + 87 y = 1218 + 174
Now, Solving
87+ 87y= 1392
87y= 1392- 87
87y= 1305
y= 1305/ 87
y= 15
Hence, the value of y is 15.
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Tristan has $1.40 worth of nickels and dimes. He has twice as many nickels as dimes. Write a system of equations that could be used to determine the number of nickels and the number of dimes that Tristan has. Define the variables that you use to write the system.
Answers
The system of equations that Tristan needs to solve is:
x*0.05 + y*0.10 = 1.40
x = 2*y
How to write the system of equations?
Let's define the variables:
x = number of nickels.
y = number of dimes.
Knowing that the net is $1.40 and that he has twice as many nickels as dimes, we can write:
x*0.05 + y*0.10 = 1.40
x = 2*y
That is our system of equations that Tristan can use to find the numbers of nickels and dimes.
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Quel est le plus grand nombre que l' on puisse obtenir avec les chiffres 2,3 et 5?
Answers
Find the perimeter of the following polygon. Be sure to include the correct unit in your answer.
7m
16 m
9cm
15 m
Answers
The perimeter of the polygon is 57 meters.
What is polygon?A polygon is an enclosed two-dimensional shape with three or more straight sides that are connected together. It can be regular or irregular and can be made up of triangles, squares, rectangles, and other shapes. Polygons are classified by the number of sides they have, such as triangles (3 sides), quadrilaterals (4 sides), pentagons (5 sides), and hexagons (6 sides). Polygons can also be classified by their internal angles, such as acute (less than 90 degrees), right (90 degrees), obtuse (greater than 90 degrees), and reflex (greater than 180 degrees). Polygons are used in many mathematical problems and can be used to represent a variety of real-world objects, such as buildings, mountains, and stars.
The perimeter of the polygon is 57 meters.
The perimeter is calculated by adding up the lengths of each side. 7m + 16m + 9cm + 15m = 57m.
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(2) Solve the system of linear equations by elimination. CH
8x - 5y = 11
4x
3y = 5
Answers
By solving the system of linear equations by elimination we get the value of x= 2 and y = 1.
What is the system of linear equations?
A grouping of one or more linear equation containing the same variables is known as a system of linear equations.
Here, we have
Given: 8x - 5y = 11....(1), 4x - 3y = 5...(2)
We solve equation(2) and find the value of x
4x = 5+ 3y
x = 5/4 + 3y/4
Now, we put the value of x in equation (1) and we get
8(5/4 + 3y/4) - 5y = 11
5×2 + 2×3y - 5y = 11
10 + y = 11
y = 1
Now, we put the value of y in equation(2) and we get
4x = 5+ 3(1)
4x = 8
x = 2
Hence, by solving the system of linear equations by elimination we get the value of x= 2 and y = 1.
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Im desperate for help in these grade 7 questions please help
Answers
What percentage of $680 is 490? ANSWER: 138.78%
The price is reduced from $680 to $490. What is the percentage decrease? ANSWER: 72.06%
Step-by-step explanation:
ANSWER: 138.78%
How did I get 138.78%?690 & 490 can be written as a fraction
which would be 680/490, how do I find the percentage?
you have to find an equivalent fraction with denominator of 100 for the problem we"ll get [tex]\frac{680}{490} x\frac{100}{100}[/tex] ( 680/490 x 100/100 ) Next divide the top and the bottom, 680 into 100 ( 680 x 100 ) and the bottom which would be 490 into 100 ( 490 x100 ), [tex]\frac{680x100}{490}[/tex] x [tex]\frac{1}{100}[/tex] if you cannot see: ( 680 x 100/490 x 1/100 Equation you have is: [tex]\frac{680 x 100}{490} x \frac{1}{100} = \frac{138.78}{100}[/tex]The final answer will be 138.78%, so the percentage is 138.78%. If your trying to figure it out on the calculator just type 680 divided by 490x100 which will also give the answer.72.06%How did I get 72.06%?490 and 680 can be written as a fraction
which would be 490/680, how do I find the percentage?
you have to find an equivalent fraction with denominator of 100 for the problem we"ll get [tex]\frac{490}{680} x\frac{100}{100}[/tex] ( 490/680 x 100/100 ) Next divide the top and the bottom, 490 into 100 ( 490 x 100 ) and the bottom which would be 680 into 100 ( 680x100 )now start solving it, [tex]\frac{490x100}{680}[/tex] x [tex]\frac{1}{100}[/tex] if you cannot see: ( 490 x 100/680 Equation you have is: [tex]\frac{490 x 100}{680} x \frac{1}{100} = \frac{72.06}{100}[/tex]The final answer will be 72.06%, so the percentage decreased by 72.06%. If your trying to figure it out on the calculator just type 490 divided by 680x100 which will also give the answer.
An initial sample of 458 grams of a radioactive substance decays according to the function A(t)=458e^-0.038t. What is the half-life of the substance?
Answers
If initial sample of 458 grams of a radioactive substance decays according to the function [tex]A(t)=458e^{-0.038t}[/tex] then the half-life of the substance is 0.
What is half life?Half-life is the time required for a quantity (of substance) to reduce to half of its initial value.
Given,
An initial sample of 458 grams of a radioactive substance decays according to the function
[tex]A(t)=458e^{-0.038t}[/tex]
We need to find the half life
[tex]458=458e^{-0.038t}[/tex]
Divide both sides by 458
[tex]1=e^{-0.038t}[/tex]
Take log on both sides
[tex]log1=-0.038t[/tex]
0=-0.038t
t=0
Hence, the half-life of the substance is 0.
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Hurry please I will give brainly need this in about 15 mins help me help meee
Answers
Answer:
x = -2
Step-by-step explanation:
The first thing we can notice about this figure is that the two small outer triangles are congruent because of the given side congruence markings as well as the fact that the large triangle ABC is isosceles, thus angle A is congruent to angle C.
Using the above information, we can construct the equation:
3x + 2 = 2x
and solve it for x.
x = -2
The equation we constructed simply equates the corresponding sides of the two small outer triangles, as they are congruent by the CPCTC theorem.
Geometry Support 4. Given: 6x-4 = 3x + 8. Prove: x = 4
Answers
Answer:
6(4)-4=3(4)+8
24-4=12+8
20=20
Step-by-step explanation:
To prove x=4, substitute four into the equation
6(4)-4=3(4)+8
24-4=12+8
20=20
Therefore x=4 is proved
Answer:
(Answer in Image)
Step-by-step explanation:
6x-4=3x+8
6x-4-3x=3x+8-3x subtract -3x on both sides
3x-4=8
3x-4+4=8+4 add four on both sides
3x=12 simplify
3/3x=12/3 divide both sides by 3
x=4
If $300 is invested at an interest rate of 2.5% per year, find the amount of the investment at the end of 10 years for the
following compounding methods. (Round your answers to the nearest cent.)
(a) Annually
$
(b) Semiannually
$
(c) Quarterly
$
(d) Continuously
Answers
Preston bought a
drum set priced at $187.90. The sales tax
was found by multiplying the price of the
drum set by 0.08. What was the total cost
of the drum set with sales tax? Round to
the nearest cent.
(Show All Work)
Answers
Graph the line with y-intercept -5 and slope -1/3
can you mark the points on the graph pleases
Answers
Answer:
(0,-5) , (3, -6) , (6, -7) ,(9, -8)
Step-by-step explanation:
I apologize for being unable to graph, but here are some of the points.
(0,-5) <-- The "y intercept"
slope is y2-y1/x2-x1, so "-1" is added to the "y" of the coordinate, and 3 is added to the "x"
(3,-6)
(6,-7)
(9,-8)
Hope this helps :)
Look at HIJ. Which of the triangles below can be proven similar to HIJ based only on the given information? Select all that apply.
Answers
The tringles ΔKLM, ΔXYZ, and ΔUVW are similar to the ΔHIJ.
What is the similarity of the triangles?
When it comes to Euclidean geometry, two things are said to be comparable if they have the same shape or the same shape as each other's mirror image. One can be created from the other more precisely by evenly scaling, possibly with the inclusion of further translation, rotation, and reflection.
We have,
In ΔHIJ
∠HIJ = 64°
∠JHI = 96°
and the side are
HI = 2 unit
IJ = 5.5 unit
HJ = 5 unit
So, the third angle will according to the sum of the angles of a triangle:
∠IJH = 20°
the triangles similar to ΔHIJ are:
A) It is similar to ΔHIJ cause,
∠HIJ ≅ ∠KLM
∠IJH ≅ ∠LMK
so, the third also will be equal:
∠JHI ≅ ∠LKM
D) It is similar to ΔHIJ cause,
∠IJH ≅ ∠XZY
HI/YX = 2/4 = 1/2
HJ/YZ = 5/10 = 1/2
C) It is similar to ΔHIJ cause,
HI/UV = 2/4 = 1/2
HJ/UW = 5/10 = 1/2
IJ/VW = 5.5/11 = 1/2
Hence, the tringles ΔKLM, ΔXYZ, and ΔUVW are similar to the ΔHIJ.
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I need help please!!
Answers
Answer:
it is 3/5
Step-by-step explanation:
cos is the adjuacent devided by hypotenuse so it is 27/45 and that is 3/5
STATISTICS HOMEWORK HELP !! Please attach a photo of the homework problems solved in the comments. Or if you can't post a photo then please just do your best to explain the answers in text.
Answers
The required solution for the hypothesis testing is shown,
The T - statistic is the ratio of the predictive value of a parameter from its hypothesized value to its standard disputable values.
n = 16, ss = 960, and [tex]\bar x = 55,[/tex]
[tex]S.D, s = \sqrt{ \ [ss/n - 1]\\s = \sqrt{960/15} \\s = 8[/tex]
The test statistic is,
[tex]t = \bar x - mu / [s /\sqrt{n} ]\\t = 55 - 50 / [8/\sqrt{16} ]\\t = 2.5[/tex]
df = n - 1 = 15 , let α = 0.05
tcrp = 2.131 [from t - table]
Since t > 2.131
The result is significant
(b)
Cohen's d = mean difference /SD
= 55 - 50 / 8 = 0625.
Thus, the required solution for the hypothesis testing is shown,
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Look at this graph:
What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answers
Answer:
4/3
Step-by-step explanation:
you use the slope formula y^1 - y^2 over x^1 over x^2, substitute the said values and are left with the slope of 4/3 in its improper form.
Hope this helps!!! :3
The functions f(x) = x2 – 2 and g(x) = –x2 + 5 are shown on the graph.
Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the solution set be identified?
y > x2 – 2
y ≥ –x2 + 5
Answers
Change the equations to inequalities to modify the graph and the solutions are (-1.871, 1.5) and (1.871, 1.5)
How to modify the graphsThe graph is the given parameter
From the graph, we have the following equations
f(x) = x² - 2
g(x) = -x² + 5
To modify the graph, we simply change the equations to inequalities
How to identify the solution setAfter the modifications in (a), we have:
f(x) > x² - 2
g(x) ≥ -x² + 5
From the graph of the inequalities, the curves of the inequalities intersect at (-1.871, 1.5) and (1.871, 1.5)
Hence, the solutions are (-1.871, 1.5) and (1.871, 1.5)
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It takes Martin 1 hour to drive 65 miles, 2 hours to drive 130 miles and 3 hours to drive 195 miles. Is this a proportional relationship? Define variables and write an equation to represent the relationship.
Answers
Yes, it is a proportional relationship. The relationship is distance (d) is directly proportional to time(t). The equation of the relationship is d= 65t
What is direct variation?Direct Variation is said to be the relationship between two variables in which one is a constant multiple of the other. For example, when one variable changes the other, then they are said to be in proportion. If d( distance) is directly proportional to t( time) the equation is of the form d= kt (where k is a constant).
When d =65miles and t= 1hour, k =d/t
k= 65/1= 65
for other values of d and t, k = 65
Therefore the relationship between the distance and time is a proportional relationship. And the equation of the relationship is d= 65t
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4.4 times 2.727 the answer with explanation
Answers
Answer:
11.9988
Step-by-step explanation:
Use a calculator.