Express the following fraction in simplest form using only positive exponents.
The fracion 12k⁸/4(k⁵)² expressed in its simplest form is the expression 3/k².
How to simply the expression in fractionTo simplify fraction, we need to factorise the denominator and numerator, and then look for common factors in the numerator and denominator and cancel.
Given the fraction;
12k⁸/4(k⁵)² = 3 × 4 × k⁸/k² × 4 × k⁸ {expressed to get a common factor}
12k⁸/4(k⁵)² = 3 × 4k⁸/k² × 4k⁸
4k⁸ is a common factor to the numerator and denominator, so we cancel it out
12k⁸/4(k⁵)² = 3/k²
Therefore, the simplest form of the fracion 12k⁸/4(k⁵)² is derived as the expression 3/k.
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Tiny's Tattoo Parlor sold 389389 tattoos this month. 4343 of those tattoos were arm tattoos. Based on this data, what is a reasonable estimate of the probability that the next customer does not get an arm tattoo?
If the parlor sold 389389 tattoos and 4343 were arm tattoos, then the probability of next customer does not get an arm tattoos is 0.99
Total number of tattoos sold in this month = 389389 tattoos
Number of arm tattoos = 4343
Number of other tattoos = 389389 - 4343
= 385046
The probability = Number of favorable outcomes / Total number of outcomes
Substitute the values in the equation
The probability of next customer does not get an arm tattoos = 385046 / 389389
Divide the terms
= 0.99
Therefore, the probability of next customer does not get an arm tattoos is 0.99
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Correct answer needed thankyou!!!
The inequality shown by the graph in the question, found by finding the equation for the line of the inequality and taking note of the dashed line and the shaded region, is; y > 2·x - 4
What is an inequality?An equality is a comparison between two expressions that have different values, by joining them with the use of symbols including '<', '≤', '≥', '>', '≠'
Two points on the graph that can be used to find the equation of the line of the inequality are;
(4, 4), and (2, 0)The slope, m, of the line found from the above two points on the line is therefore;
m = (0 - 4)/(2 - 4) = 2
The equation of the line in point-slope form is therefore;
y - 0 = 2·(x - 2) = 2·x - 4
The equation of the line of the inequality is therefore;
y = 2·x - 4
The dashed line and the shaded region indicates that we get;
y > 2·x - 4
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slope of a line that passes through the points (-4,-7) and (-2,-19) in simplest form
Answer:
m=-6
Step-by-step explanation:
use slope formula to solve
m= rise/run=y2-y1/x2-x1
A table with a round top is cut in half so that it can be used against a wall. After it is cut, the edge along the wall is 6 ft
The area of the semicircle table after it is cut in half [tex]=\frac{9}{2}\pi[/tex] square units.
What is a semicircle?A semicircle is a 2 -D shape which is obtained by cutting a circle along with its diameter. a circle has 2 semicircles when it is cut along with its diameter.
What is a formula for the area of a semicircle?The formula for finding the area of a semicircle is half of the area of a circle with the same radius.
area of semicircle = [tex]\frac{\pi r^{2} }{2}[/tex] square units
Given:
A table with a round top is cut in half so now its shape is a semicircle.
After it is cut, the edge along the wall is 6 ft means that the diameter of the semicircle is = 6 ft
Diameter = 6 ft
Radius = diameter / 2
Radius = 6/ 2
Radius = 3 ft
Therefore now we can calculate the area of the table after it is cut in half
Area of the semicircle table after it is cut in half =
[tex]=\frac{\pi r^{2} }{2} \\=\frac{\pi 3^{2} }{2} \\=\frac{9\pi }{2}\\= \frac{9}{2}\pi[/tex]
The area of the semicircle table after it is cut in half [tex]=\frac{9}{2}\pi[/tex] square units.
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A table with a round top is cut in half so that it can be used against a wall. After it is cut, the edge along the wall is 6 feet. What is the area of the table after it is cut in half? Give your answer in terms of pi.
Hahid bought 80 banana at the rate of 4 banan ,for r 5 and old at the rate of 5 bana for r 8
The profit won by Hahid is 28 rupees
What is a simple definition of profit?Profit is the term used to describe the financial gain experienced when the revenue from a business activity outweighs the costs, costs, and taxes incurred to maintain the activity in question.
What are the 3 types of profit?There are three main measures of profit. These are gross profit, operating profit and net profit.
According to given question:-
The total amount with which Hahid bought the bananas are
(5/4)*80=100
The total amount with which Hahid sold the bananas are
(8/5)*80=128
The profit got by Hahid is 128-100=28
Hence the solution is 28
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what is the answer i need answers now I will fail
The amount of fruit juice(orange, grape, cherry) used in the punch is 14 cups. So, option D is correct.
What is meant by mixed fraction?A mixed fraction is one that is represented by both its remainder and quotient. Two is the quotient and one is the remainder in the mixed fraction 2/3, for instance.
You can write mixed numbers with or without the word "and," for example, 5 and 3/4 . The mixed number must have a valid fraction as its fractional component. A correct fraction, such as 37, has a numerator that is less than the denominator.
Given,
The amount of orange juice= 3 [tex]\frac{1}{3}[/tex] cups
The amount of grape juice=6 [tex]\frac{1}{2}[/tex] cups
The amount of cherry juice= 4 [tex]\frac{1}{8}[/tex] cups
The amount of club soda=1 [tex]\frac{1}{4}[/tex] cups
So, 3 [tex]\frac{1}{3}[/tex]+6 [tex]\frac{1}{2}[/tex] + 4 [tex]\frac{1}{8}[/tex]
=(10/3)+(13/2)+(33/8)
=(10/3)+(13/2)+(33/8)
=(80+156+99)/24
=335/24
=13.95
≈14 cups approximately
Therefore, the amount of fruit juice(orange, grape, cherry) used in the punch is 14 cups.
So, option D is correct.
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This is a multiple choice question
The area under the standard normal curve corresponding to -0.3 < Z < 1.6 is…?
A. 0.3273
B. 0.4713
C. 0.5631
D. 0.9542
Answer:
Option (A) and (B)
Step-by-step explanation:
The area under the standard Normal curve corresponding to –0.3 < Z < 1.6 is answer choices 0.3273, and 0.4713.
Area = 0.3273. Ergo, the answer is A.
Step-by-step explanation:
0.9953/2 - 0.3085/2
NEED ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!
Triangle A C F is shown. Lines are drawn from each point to the opposite side and intersect at point D. Line segments A E, F B, and C G are formed. The length of line segment A D is 12 and the length of line segment D E is 4.
Based on the diagram, can point D be the centroid of triangle ACF? Explain.
Yes, point D is the point of intersection of segments drawn from all three vertices.
Yes, DE is three-quarters of the length of the full segment.
No, DE should be longer than AD.
No, the ratio between AD and DE is 3:1.
Answer: No, the ratio between AD and DE is 3:1.
Step-by-step explanation:
The centroid splits the median in a 2:1 ratio from vertex to side.
Answer:
It is letter D; No, the ratio between AD and DE is 3:1.
Step-by-step explanation:
A rectangle has an area of 943 square feet. Its width is five feet less than twice the length. Find the measures
of the length and width of the rectangle.
Answer: the rectangle is 23 x 41
Step-by-step explanation:
x = length
2x - 5 = width
A = length x width = (x)(2x-5) = 943
2[tex]x^{2}[/tex] - 5x - 943 = 0
use quadratic equation to solve for x:
a = 2, b = -5, c = -943
roots are 23, -20.5
x = 23 (length)
2x - 5 = 2(23) - 5 = 46 - 5 = 41 (width)
Ariane borrow $500 on a 3−year loan. She i charged 5% imple interet per year. How much interet i he charged for 3 year? What i the total amount he ha to pay back?
The interest charged for 3 years would be $75 ($500 x 0.05 x 3). The total amount Ariane has to pay back would be $575 ($500 + $75).
What does a simple interest mean?Simple interest is calculated based on the principal of a loan or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay interest on interest that has already accrued.
How is a simple interest calculated?To calculate simple interest, multiply the principal sum by the time period, interest rate, and time period. Simple interest is calculated as follows: "Simple Interest = Principal x Interest Rate x Time." This equation provides the simplest method for calculating interest.
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The polynomial p(x)=-2x+3x+4 is given. Which conclusion is valid if p(1)=5
The value of the polynomial p(x) = -2x + 3x + 4 when x is 5 will be 9
How to calculate the value of the polynomial?A polynomial is an expression made up of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division.
A polynomial is an expression made up of indeterminates and coefficients that only uses addition, subtraction, multiplication, and positive-integer powers of variables. x2 4x + 7 is an example of a polynomial with a single indeterminate x.
p(x) = -2x + 3x + 4
when x = 5
= -2x + 3x + 4
= -2(5) + 3(5) + 4
= -10 + 15 + 4
= 9
Note that the information you gave wasn't complete.
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Find the sum of all three - digit numbers which give a remainder of 5 when they are divided by 7 immediately
Answer: As Devansh Sehta has calculated, there are 82 terms and 82=7×11+5. When each term of S is divided by 7, the remainders, in order are 6, 3, 0, 4, 1, 5, 2, and these repeat.
Step-by-step explanation:
For any arithmetic sequence, record the remainders when successive terms are divided by n. Then the sum of every set of n consecutive remainders is divisible by 7. In this case, the first 77 terms add to a multiple of 7 as do the 5 remaining terms.
Find an equation for the perpendicular biector of the line egment whoe endpoint are (7,-1) and (-9,-5)
Perpendicular bisector passes through midpoint of the line joining the given two points so the equation for this perpendicular bisector of the line segment whose endpoint are (7,-1) and (-9,-5) is 4x-y=29.
What is a bisector of a line?To divide a segment or an angle into two congruent sections is to bisect it. The midpoint of a line segment will be traversed by its bisector. A line segment's perpendicular bisector is parallel to the line segment and passes through its midpoint.
Is a bisector always a straight line?A straight line called a bisector divides an angle or a line into two equal pieces. The bisector of a segment always travels through the middle of the segment.
For this problem you have to find the mid point of the line joining
the given points and also the slope of the perpendicular line.
Here, A(7,-1) and B(-9,-5) are the given two points.
let
C is the mid point and CD is the perpendicular through C
Midpoint of AB=[x1+x2)/2,(y1+y2)/2]
C=((7-9)/2,(-1-5)/2)
C=(-1,-3)
Slope of AB=(y2−y1)/(x2−x1)
=(-5+1)/(-9-7)
=4/16
=1/4
Slope of CD=4
Equation of line;
(y−y1)=m(x−x1)
(y+1)=4(x−7)
Y+1=4x-28
4x-y=29
this is our required solution.
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What is the slope of a line parallel to the line whose equation is 12x+2y=24Fully simplify your answer.
Answer:
The slope is -6
Step-by-step explanation:
12x+2y=24
We want to find the slope of a line that is parallel to this line.
Parallel lines have the same slope, so we need to find the slope of this line.
We can get this equation in slope intercept form to find the slope
y = mx+b where m is the slope
Subtract 12x from each side
2y = -12x+24
Divide each side by 2
y = -12x/2 +24/2
y = -6x+12
The slope is -6
write y+1=-1/4(x-3) in standard form
Step-by-step explanation:
Tha answer in standard form is x + 4y = -1
When adding , what step must be completed first? finding the least common denominator. Reducing the fractions. Adding the numerators, but keeping the denominators. Adding the denominators, but keeping the numerators.
The least common factor of 3 and 5 was chosen as the first step in order to combine the fractions 2/3 + 4/5, leading to option (A) Finding the least common denominator.
What is the lowest common multiple?The smallest multiple that any two numbers have in common is called the lowest common multiple.
It implies that we can divide both numbers by that and that this is the lowest number by which both numbers may be divided.
The LCM of 2 and 8 is 8, for instance.
So, using the two fractions provided:
2/3 + 4/5
15 is the least frequent factor between 3:
(10 + 12)/15
Thus, we used LCM in the first phase.
Therefore, the least common factor of 3 and 5 was chosen as the first step in order to combine the fractions 2/3 + 4/5, leading to option (A) Finding the least common denominator.
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Complete question:
When adding 2/3 + 4/5, what step must be completed first?
A)Finding the least common denominator.
B)Reducing the fractions.
C)Adding the numerators, but keeping the denominators.
D)Adding the denominators, but keeping the numerators.
Write an equation in slope-intercept form of the line that passes through the points (2, 15) and (5, 21).
The equation of the line that passes through the points (2, 15) and (5, 21) is y = 2x + 11
The coordinates of the first point = (2, 15)
The coordinates of the second point = (5, 21)
The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values in the equation
The slope of the line = (21-15) / (5-2)
= 6 / 3
= 2
The slope intercept form is
y = mx + b
Substitute the values
15 = 2(2) + b
15 = 4 + b
b = 15 - 4
b = 11
Substitute the values in the equation
y = 2x + 11
Therefore, the equation of the line in slope intercept form is y = 2x + 11
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In a race, Jason's position was −11 1/5 feet relative to the leader after 1 3/4 minutes. On average, how much did Jason's position relative to the leader change per minute? Enter your answer as a mixed number, in simplified form, in the box.
The way Jason's position relative to the leader changed per minute is; 6²/₅ ft/minute
How to solve fractions?We are told that Jason's position was 11 ¹/₅ feet relative to the leader after 1 ³/₄minutes.
Now, the fractions are in mixed fraction form and so let us convert them to improper fractions to get;
⁵⁶/₅ and ⁷/₄
Thus, the way Jason's position relative to the leader changed per minute is; ⁵⁶/₅ ÷ ⁷/₄
= ⁵⁶/₅ * ⁴/₇
= 32/5
= 6²/₅ ft/minute
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What is the rate of change of y with respect to x?
The rate of change of y with respect to x will be;
⇒ 10
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The table is shown in figure.
Now,
Since, The table is shown in figure.
Let two points from the table as;
(x, y) = (- 8.5 , - 92) (- 6.5, - 72)
We know that;
⇒ Rate of change = dy/dx = (y₂ - y₁) / (x₂ - x₁)
Substitute all the values we get;
⇒ Rate of change = (- 72 - (-92)) / (- 6.5 - (-8.5))
= 20 / 2
= 10
Thus, The rate of change of y with respect to x will be;
⇒ 10
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the pearson product moment correlation measures the linear relationship between two interval- and/or ratio-scaled variables (scale variables) such as those depicted conceptually by scatter diagrams. true false
the Pearson product moment correlation measures the linear relationship between two interval- and/or ratio-scaled variables (scale variables) such as those depicted conceptually by scatter diagrams: True.
What is Pearson product moment correlation?A measure of the degree and direction of relationship between two variables assessed on at least an interval scale is the Pearson product-moment correlation coefficient, or Pearson's correlation.
If you want to determine whether there is a linear relationship between two quantitative variables, you may use Pearson's correlation. The expectation of a linear relationship between those variables is the sole part of the study hypothesis.
This approach finds the precise amount or degree of correlation between any two variables and tells if there is or is not any correlation between them.
Thus, the given statement is true.
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If m is a real number such that m² + 1 = 3m , the value of [tex]\frac{2m^{5} - 5m^{4} + 2m^{2} - 8m^{2} }{m^{2} + 1 }[/tex]
The required solution of the given expression is 1/3 [m²-2m-6].
Given that,
To simplify the [2m⁵ -5m₄ +2m² -8m²]/[m²+1], when m² + 1 = 3m.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
= [2m⁵ -5m₄ +2m² -8m²]/[m²+1]
When substituting the value m² + 1 = 3m in the above expression we get.
= m/3 [m²-2m-6]
Thus, the required solution of the given expression is 1/3 [m²-2m-6].
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can someone help with this thank you so much .
Answer:
NO=6
Step-by-step explanation:
If MP=16 and NP=13 that means MN=3 and MO=9 so that makes NO=6
9. There are 9 apples in a bag; 5 are red and 4 are yellow. Two apples are selected at random, one after another without
replacement, and the color of each is noted. Find the probability that the second apple is red.
A. 5/9
B. 5/18
C. 1/6
D. 3/8
E. 1/2
F. None of these.
Answer:
I believe the answer is D. 3/8
Thomas is facing towards town A, which is at a bearing of 300° from him. If he turns 125° clockwise, he will be facing towards town B. What is the bearing of town B from Thomas?
The required bearing angle of town B from Thomas is 65°.
Bearing is basically an angle that is measured clockwise from the north. Bearing are generally written in three figure.
Given that Thomas is facing towards town A, which is at a bearing of 300°.
Implies that town A is 300° from north.
If Thomas turns 125° clockwise, then he faces towards town B,
The bearing angle will be 300+125 = 425°
Since, one complete round makes angle 360°, therefore
The required bearing angle = 425 - 360 = 65
The bearing angle of town B from Thomas is 65°.
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I need help on these questions.
DJ was going to meet his family at the beach in NC. He looked on a map and saw that the beach he was going to was 800 km from his house and he knew he would average 110 km/hr on the highway. How long is it going to take him to get to the beach?
On average, it is going to take DJ 7.27 hours to get to the beach.
What is the average?Average refers to the quotient when a numerator is divided by a denominator.
In this situation, the average refers to the time, which is the quotient of the distance and speed.
The total distance going to the beach from his family = 800 km
The average speed = 110 km/hr
The time to cover the distance of 800 km at 110 km/hr = 7.27 hours (800/110).
Thus, DJ will take 7.27 hours to cover 800 km at 110 km/hr.
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The Pythagorean Theorem, given by the formula a² + b² = c², relates the
three sides of a right triangle. Solve the formula for the positive value of b in
terms of a and c.
Answer:
Below
Step-by-step explanation:
a^2 + b^2 = c^2 subtract a^2 from both sides
b^2 = c^2 - a^2
take the positive sqrt of both sides ( since you can't have a negative length)
b = sqrt (c^2 - a^2)
Please help it about calculus
The total distance travelled by the particle is 24 units.
What is displacement?
Displacement is defined as a change in an object's position. An object's displacement is defined as how far it has moved from its starting point. The dependent variable in the displacement time graph is displacement, which is represented on the y-axis, and the independent variable is time, which is represented on the x-axis. Position-time graphs are another name for displacement time graphs.
The displacement curve is given for 0 ≤ t ≤ 18.
We need to find the total distance of the curve, it will be the positive sum of all displacements.
So, total distance = (7-0) + (3-0) + (2+3) + (2+4) + (7-4)
= 7 + 3 + 5 + 6 + 3
= 24
Hence, the total distance is 24 units.
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The area of each square is 16 square units. Find the perimeter of the figure. (see imagine attached) :)
Answer:
48
Step-by-step explanation:
If the area of each square is 16, then each side length has side length of 4 because the area of a square is:
[tex]s^2=A[/tex]
[tex]s^2=16\\s=4[/tex]
Each of the outer edges has 4+4+4 and there are four of them so:
[tex](4+4+4)*4=48[/tex]