Hi can someone help me to solve this? I would be so appreciated if you willing to help me
Nora and Farhan were asked to simplify (2x²/y)³
Nora wrote this : (2x²/y)³ = 2x⁶/y³
Farhan wrote this : (2x²/y)³ = 8x⁵/y
Both Nora and Farhan obtained the wrong solutions.
(i) Highlight the possible misconceptions that Nora and Farhan might have.
Nora's misconceptions:
Farhan's misconceptions:
(ii) provide the correct solution :
Answers
Answer:
HOPE ITS HELPFUL TO yours
Related Questions
Watches and bacteria: A group of researchers investigated the contamination of medical personnel watches at a New York hospital, since there is a potential for patient exposure to potentially dangerous bacteria.They sampled watches worn by physicians, physician assistants, and medical students at a teaching hospital in New York. Nearly half (46.6%) of the watches tested harbored microorganisms that can cause illness. By comparison, only one of the 10 watches worn by security guards tested positive for a disease-carrying microorganism. The researchers want to determine if the difference is statistically significant.Which of the following is an appropriate statement of the null hypothesis, H0?A. The proportion of contaminated wrist-watches from medical personnel is the same as the proportion of contaminated wrist-watches from security guards, i.e., H0: p = 46.6%.B. The proportion of contaminated wrist-watches from medical personnel is not the same as the proportion of contaminated wrist-watches from security guards, i.e., H0: p not equal 46.6%.C. The proportion of contaminated wrist-watches from medical personnel is greater than the proportion of contaminated wrist-watches from security guards, i.e., H0: p > 46.6%.
Answers
An appropriate statement of the null hypothesis, H₀ is that: A. The proportion of contaminated wrist-watches from medical personnel is the same as the proportion of contaminated wrist-watches from security guards, i.e., H0: p = 46.6%.
What is a null hypothesis?In Mathematics, a null hypothesis (H₀) can be defined the opposite of an alternate hypothesis (Ha) and it asserts that two (2) possibilities are the same.
For an experiment to test the contamination of medical personnel wrist-watches at a New York hospital, the appropriate null hypothesis and alternative hypothesis would be given by this mathematical expression:
H₀: p = 10.
Ha: p < 10.
In this context, we can logically that the proportion of contaminated wrist-watches would be the same for both sample proportion i.e., H₀: p = 46.6%.
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The diagonal of a square is 6√3. Find the perimeter
Answers
Using the formulas
P=4a
d=2a
Solving forP
P=22d=2·2·6≈16.97056
The radius of a circle is 5 inches
What is the circumference of the circle?
Answers
Answer: 31.41592654 inches
Step-by-step explanation:
C = pi (d)
C = pi (10)
C = 31.41592654 inches
is 6>x a open or closed dot
Answers
Answer:
It will be an open dot.
Step-by-step explanation:
By math textbook states that if a symbol is greater than or less than, it has an open dot.
If it has greater than or less than symbol with a line under it, that means it is a closed dot.
Hope this helps!
Solve the following quadratic function
by utilizing the square root method.
y = 25x2 - 100
x = +[?]
Answers
Answer:
x = ±√(y/25 + 4)
Step-by-step explanation:
Given the expression;
y = 25x² - 100
We are to make x the subject of the formula;
-25x² = -y - 100
25x²= y + 100
x² = y/25 + 100/25
x²= y/25 + 4
x = ±√(y/25 + 4)
This give the value of x
Graph f(x) = log base 3 x-1
Answers
Hello there. To solve this question, we have to remember how to graph a function.
First, remember that the logarithm in any base is an injective function (one-to-one).
We have to find its key-features before graphing it.
These key-features includes: x-intercept, y-intercept (if it exists), its vertical asymptote.
Okay. To find the x-intercept, set the function equal to zero:
\(f(x)=\log_3(x)-1=0\)Adding 1 on both sides, we get
\(\log_3(x)=1\)Apply the property:
\(\log_a(b)=c\Rightarrow b=a^c\)Hence we have
\(x=3^1=3\)So the x-intercept happens at x = 3.
To determine whether or not it has an y-intercept, we check if the limit as x goes to zero from both sides exists and are equal:
\(\begin{gathered} \lim_{x\to0^+}\log_3(x)-1=-\infty \\ \\ \lim_{x\to0^-}\log_3(x)=-\infty \end{gathered}\)In this case, this means we cannot evaluate this function at x = 0, so it doesn't have y-intercept(s).
Next, to determine its vertical asymptote, we check the value of x for which the argument goes to zero, that is
\(x=0\)Therefore it has a vertical asymptote at x = 0.
The graph is then given by:
This is a sketch of the graph of the function.
The final answer to this question is contained in the last option.
Adeline is A years old.taneous Write an expression for a b C i Adeline's age in 10 years' time ii Adeline's age 6 years ago. Use the information from Adeline to write an equation for A. Solve the equation to find Adeline's age now. C
Answers
Answer:
Let's represent Adeline's age now as A.
i. Adeline's age in 10 years' time can be expressed as A + 10.
ii. Adeline's age 6 years ago can be expressed as A - 6.
So, we can write an equation for A as follows:
A + 10 = A - 6
Solving for A, we can simplify the equation as follows:
16 = A - 6
Adding 6 to both sides, we get:
22 = A
Therefore, Adeline's age now is 22 years old.
Solve for x , assume all segments that appear tangent are tangent.
Answers
Answer:
Step-by-step explanation:
x = 5
The value of x in the given angle is 5.
What is circle?A circle is a particular type of ellipse in mathematics or geometry where the eccentricity is zero and the two foci are congruent. A circle is also known as the location of points that are evenly spaced apart from the centre. The radius of a circle is measured from the centre to the edge.
Labelling the figure,
We have,
Measure of complete angle of circle = 360 degree
∠ABC = 360 - (81 + 74)
= 205 degree
Now from figure,
∠APE = (205 - 81 )/2
= 62 degree
Since we know that,
∠APE = 17x - 23
Therefore,
17x - 23 = 62
17x = 85
x = 5 degree,
Hence,
Required value is 5.
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1. Estimate twenty-nine percent of forty-eight. Please again no decimal form!
2. Estimate sixty-two percent of one hundred twenty-four. no decimal form please!
3. WORK Karl made $365 last month doing odd jobs after school. If 75% of the money he made was from doing yardwork, about how much did Karl make doing yardwork?
Answers
\(\boxed{29\;percent\;of\;48=(?)}\)
Mariam is selling cakes at a summer fete.
She spends a total of £36 on ingredients.
She makes a total of 60 cupcakes to sell at £1.50 each.
She sells all of the cupcakes.
Calculate her percentage profit.
Answers
36/90= 40%
The test scores for the Chapter 5 test in Algebra I were:
75.95.90.95,60,95,75,95,90.
Question:
a. Find the mean, median, mode, and range of the data.
b. Which measure best describes the set of data? Why?
c. If test scores of 65 and 75 were added to the set, what would happen to the mean?
es )))
Answers
Answer Question 1: Mean literal number 85.55556 Not sure if there allowing you to round to the nearest tenth of digit
Median 90
Mode 95
Range 35
Question 2: Median is the best way because it gives you the overall average of a set of numbers.
Question 3: The mean would change because if you are adding new numbers you have to recount the mean meaning there is now a new average.
Colette ha an exterminator viit regulary to control an ongoing cockroach 3,800 15% 3 year
Answers
If the initial population is 3800. The population of cockroaches after 3 years will be 1603.
Consider the function:
y = a(1 ± r)ⁿ
where n is the number of times growth/decay, a = initial amount, and r = fraction by which this growth/decay occurs.
If there is a plus sign, there is exponential growth happening by r fraction or r%.
If there is a minus sign, there is exponential decay happening by r fraction or r%.
If the population is currently 3,800 cockroaches.
The expression is given as
y = 3800(0.75)ⁿ
The population of cockroaches after 3 years will be
y = 3800(0.75)³
y = 3800 x 0.4218
y = 1603.125
y ≅ 1603
Hence, the population of cockroaches after 3 years will be 1603.
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The complete question is:
Colette has an exterminator visit regularly to control an ongoing cockroach problem. it's been working, and the population has declined by 15% every year. if the population is currently 3,800 cockroaches, how many will there be in 3 years? if necessary, round your answer to the nearest whole number.
DUE FRIDAY WELL WRITTEN ANSWERS ONLY !!!!!!!HELP
The value of tan(3π/4) is -1. How does the value of tan(3π/4 – π) compare? Explain your reasoning.
Answers
Answer:
The value of tan(3π/4) is indeed -1.
Now, to evaluate tan(3π/4 - π), we can use the following trigonometric identity:
tan(a - b) = (tan(a) - tan(b)) / (1 + tan(a)*tan(b))
Applying this identity to the expression tan(3π/4 - π), we get:
tan(3π/4 - π) = (tan(3π/4) - tan(π)) / (1 + tan(3π/4)*tan(π))
Substituting the values of tan(3π/4) = -1 and tan(π) = 0, we get:
tan(3π/4 - π) = (-1 - 0) / (1 + (-1)*0) = -1
So the value of tan(3π/4 - π) is also -1, which is the same as the value of tan(3π/4).
In other words, the value of tan(3π/4 - π) is equal to the value of tan(3π/4) because π is equal to 180 degrees, which is a full rotation. Subtracting a full rotation from an angle simply results in an equivalent angle in the opposite direction. Thus, the values of tangent for both angles remain the same.
Which of the following tests can be used to assess whether variances are equal between multiple groups? Welch's test Shapiro-Wilk test Goodness of Fit test Levene test 26 10 points Cancer patients were treated with a new cell-based therapeutic to aid in reducing tumor size. The data table below shows the patients' adverse reactions to this treatment: Weak reaction Strong reaction Male patients Medium reaction 203 110 213 138 182 Female patients 154 Is the sex (male or female) of the patient linked to the severity of the adverse reaction that is observed? Show your work and explain your logic below. Bold or circle your final answer. 0000 The correlation coefficient (r) is used for linear, exponential, and logarithmic relationships. True False
Answers
The test that can be used to assess whether variances are equal between multiple groups is the Levene test.
The Levene test is a hypothesis test for the equality of variances in a statistical population. It is named after the American statistician Howard Levene. It is commonly used to check the null hypothesis of homoscedasticity or equal variances across k groups. The test is used to determine if two or more groups have different variances or if the variance is unequal. The null hypothesis of the Levene test is that the variance of the populations from which the groups are drawn is equal. The Levene test is an alternative to the F-test for equal variances. Therefore, it can be concluded that the Levene test can be used to assess whether variances are equal between multiple groups.
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The box office at a Movie theatre sold 206 tickets for the evening show, and collected $2,572. How many $15 adult and how many $8 child tickets were sold? Number of adult tickets sold =Number of child tickets sold =
Answers
STEP - BY - STEP EXPLANATION
What to find?
• Number of adult tickets sold.
,• Number of child tickets sold.
Given:
Total number of tickets sold = 206
Amount of total ticket sold =$2572
Cost of adult ticket = $15
Cost of chold ticket =$8
Let x be the number of adult tickets sold and y be the number of child tickets sold.
Step 1
Model the equation.
\(x+y=206\text{ ------------\lparen1\rparen}\)\(15x+8y=2572----------(2)\)
Step 2
Solve the above system of linear equations by any suitable methods.
Using the substitution method;
From equation (1)
x = 206 - y ---------(3)
Step 3
Substitute equation (3) into equation (2)
\(\begin{gathered} 15(206-y)+8y=2572 \\ \\ 3090-15y+8y=2572 \\ \\ -7y=-518 \\ \\ y=74 \end{gathered}\)Step 4
Substitute the alue of y into equation (3) and simplify.
\(\begin{gathered} x=206-y \\ x=206-74 \\ \\ x=132 \end{gathered}\)ANSWER
• Number of adult tickets sold =132
,• Number of child tickets sold=74
N a class of 50 students, 42% wish to go to Peaceful School of the Philippines (PSP). How many students wish to go to PSP?.
Answers
Answer:
Hope it will help you a lot.
find the area of a triangle 4cm height 6cm base
Answers
Answer:
12cm²
Step-by-step explanation:
Area of triangle =1/2×h×b
1/2×4×6
2×6
12cm²
hope dis helps!!!!!
What is the equation of a line perpendicular to y = -1/4 x + 8 and passes
through the point (0, 1)?
Answers
Answer:
y = 4x + 1
Step-by-step explanation:
y = -1/4 x + 8
Slope: -1/4
Slope of the perpendicular line is the negative inverse: 4
y = 4x + a
Point (0,1)
1 = (4)*(0)+a
1 = a
y = 4x + 1
Guys I need help on this please
Answers
Answer:
The correct answer should be the first option.
Step-by-step explanation:
Answer:
First option. The graphs domain is -∞<x<∞ and its range is -5 ≤ y < ∞
Step-by-step explanation:
I graphed this function
Domain: x ∈ R
Range: y ∈ [-5, + ∞
Minimum (1, -5)
Verticle intercept (0, -4)
Will give brainlist if answer is correct :)
Answers
Answer:
The answers C if you plug in the answer and re-write it 11.3.04 is correct.
Step-by-step explanation:
pi(r)^2
the diameter is 6 so the radius is 3
plug in 3 for r
pi(3)^2 = 9pi = 28.26
since the rug is a semi circle, divide 28.26 in half which is 14.13
ANSWER: B. 14.13 ft^2
you need to paint office 143. if one gallon of paint covers 50 sf, how many gallons of pant will you need?
Answers
To determine the number of gallons of paint needed to cover office 143, we need to know the square footage of the office.
Once we have that information, we can divide the square footage by the coverage rate per gallon to calculate the required amount of paint.
Let's assume the square footage of office 143 is 800 square feet.
Number of gallons needed = Square footage / Coverage rate per gallon
Number of gallons needed = 800 square feet / 50 square feet per gallon
Number of gallons needed = 16 gallons
Therefore, you would need approximately 16 gallons of paint to cover office 143, assuming each gallon covers 50 square feet.
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Someone please help and please hurry due in 13 minutes :(
Answers
A boy has 800 he spends 160 what fraction of his original money does he have left
Answers
Answer:
Step-by-step explanation:
800-160=640
640/800=64/80
64/80=16/20
16/20=4/5
Answer=4/5
The fraction of his original money does he have left = 4/5 .
What is a fraction in math?
A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.A boy has = 800 and spends = 160
800-160=640
640/800=64/80
64/80=16/20
16/20=4/5
Therefore, his original money left =4/5
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Write the product as a sum:
10 cos(30c) cos(22c) = ____
Answers
We know that cos(A + B) = cos A cos B - sin A sin B. We are to write the product as a sum of the expression 10 cos(30c) cos(22c)Step-by-step explanation :
Therefore, we can write cos(52°) as the sum of cos (30° + 22°)
We know that
cos(30°) = √3/2cos(22°) = √(1 + cos44°)/2cos(44°) = 2 cos²22° - 1 = 2(1 - sin²22°) - 1 = 2 - 2 sin²22° - 1 = 1 - 2 sin²22°
Therefore cos(44°) = √(1 - 2 sin²22°)
We can write 10 cos(30c) cos(22c) as 10 cos(30°) cos(22°)
which is equal to 10 cos(30°) cos(22°) - 10 cos(30°) cos(22°) × sin²22° + 10 cos(30°) cos(22°) × sin²22°= cos(52°) + sin²22° (10 cos(30°) cos(22°))
Therefore,10 cos(30c) cos(22c) = cos(52°) + sin²22° (10 cos(30°) cos(22°)).
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Reasoning Solve the system of linear equations using substitution. Use pencil and paper. Which
expression would be easier to substitute into the other equation, in order to solve this problem?
Explain your reasoning.
X = 4y - 9
X + 4y = 7
The solution is
(Simplify your answer. Type an ordered pair.)
Answers
Answer:
Since the first equation x is equal to 4y - 9, it is easier to substitute 4y - 9 in for x in the second equation.
x = -1 y = 2
Step-by-step explanation:
Since the first equation x is equal to 4y - 9, it is easier to substitute 4y - 9 in for x in the second equation. That would give you
4y - 9 + 4y = 7
8y - 9 = 7
8y = 16
y = 2
x = 4y - 9 = 4(2) - 9 = 8 - 9 = -1
It is always a good idea to check and see if your results satisfy the two equations
The solution for the system of linear equations is (-1, 2).
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 9 is an equation.
We have,
x = 4y - 9 _____(1)
x + 4y = 7 ______(2)
Substituting (1) in (2) we get,
4y - 9 + 4y = 7
8y = 7 + 9
8y = 16
y = 2
Now,
x = 4 x 2 - 9
x = 8 - 9
x = -1
Thus,
The solution is (-1, 2).
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find the slope of the line that is (a) parallel and (b) perpendicular to the line through the pair of points (-6,-1) and (1.7)
Answers
Answer:
Step-by-step explanation:
1. Calculate the slope for the line with points (-6,-1) and (1,7). Rise/Run, so take the difference between the two points for both x and y:
Change in x (the run) is 1 - (-6) = 7
Change in y (the rise) is 7 - (-1) = 8
The slope is rise/run so 8/7.
Any line of the form y=mx+b, where m is the slope, will be parallel to this line if it has the same slope: y = (8/7)x + whatever.
Any line in the same format with be perpendicular if the slope is the negative inverse of the reference line. In this case the perpendicular slope would be (-7/8). y = (-7/8)x + whomever.
What is the answer??????
Answers
Answer:
\(\frac{-2}{3}\)
Step-by-step explanation:
First, change the mixed numbers to improper fractions to make the solving process easier.
1 2/3 = 5/3
2 1/3 = 7/3
Now, subtract.
5/3 - 7/3 = -2/3
Answer: -2/3
hope this helps!! p.s. i really need brainliest :)
Compare the solution strategies used by Kaleigh and Destiny. What do you notice about the properties each student used? Compare the solution strategies used by Kaleigh and Destiny. What do you notice about the properties each student used?
Kaleigh
4(3x + 2) = 8x + 4
12x + 8 = 81 +4
4x = -4
x = -1
Destiny
4(3x + 2) = 8x + 4
4(3x + 2) 8x + 4
4
4
3x + 2 = 2x + 1
x = -1
Answers
Answer:
who's asking?
Step-by-step explanation:
A hiker is lost in the forest, but has his cell phone with a weak signal. Cell phones with GPS can give an approximate location through triangulation, which works by giving distances from two known points. Suppose the hiker is within distance of two cell phone towers that are 22.5 miles apart along a straight highway (running east to west, double-dashed line). Based on the signal delay, it can be determined that the signal from the hiker's phone is 14.2 miles from Tower A and 10.9 miles from Tower B. Assume the hiker is traveling a straight path south reach the highway quickly. How far must the hiker travel to reach the highway
Answers
Answer:
The distance the hiker must travel is approximately 5.5 miles
Step-by-step explanation:
The distance between the two cell phone towers = 22.5 miles
The distance between the hiker's phone and Tower A = 14.2 miles
The distance between the hiker's phone and Tower B = 10.9 miles
The direction of the highway along which the towers are located = East to west
The direction in which the hiker is travelling to reach the highway quickly = South
By cosine rule, we have;
a² = b² + c² - 2·b·c·cos(A)
Let 'a', 'b', and 'c', represent the sides of the triangle formed by the imaginary line between the two towers, the hiker's phone and Tower A, and the hiker's hone and tower B respectively, we have;
a = 22.5 miles
b = 14.2 miles
c = 10.9 miles
Therefore, we have;
22.5² = 14.2² + 10.9² - 2 × 14.2 × 10.9 × cos(A)
cos(A) = (22.5² - (14.2² + 10.9²))/( - 2 × 14.2 × 10.9) ≈ -0.6
∠A = arccos(-0.6) ≈ 126.9°
By sine rule, we have;
a/(sin(A)) = b/(sin(B)) = c/(sin(C))
∴ sin(B) = b × sin(A)/a
∴ sin(B) = 14.2×(sin(126.9°))/22.5
∠B = arcsine(14.2×(sin(126.9°))/22.5) ≈ 30.31°
∠C = 180° - (126.9° - 30.31°) = 22.79° See No Evil
The distance the hiker must travel, d = c × sin(B)
∴ d = 10.9 × sin(30.31°) ≈ 5.5
Therefore, the distance the hiker must travel, d ≈ 5.5 miles.
8. 26 is 65% of what number? (1 point)
; 250
ОО
х 65
26 100
х 65
; 26
26 100
26 65
; 40
х 100
х 65
; 17
26 100
Answers
Answer:
40
Step-by-step explanation:
This question can be represented with the equation \(x*0.65 = 26\) where x is the solution. 0.65 is just the decimal form of the percentage 65%. If you solve this equation you find that x = 40. Here are the steps to solving:
\(x*0.65 = 26\)
divide by 0.65 on each side of the equation
\(x= 40\)