Final answer:
To simplify equations with fractional exponents, divide the digit term of the numerator by the digit term of the denominator and subtract the exponents of the exponential terms. Then multiply the numerators and denominators together and simplify by common factors if needed.
Explanation:
When simplifying equations with fractional exponents, we can follow these steps:
Divide the digit term of the numerator by the digit term of the denominator.Subtract the exponents of the exponential terms.Multiply the numerators and denominators together and simplify by common factors if needed.For example, let's simplify the equation √(x³ / y²). We divide x³ by y², which gives us x/y. Then we subtract the exponents, resulting in √(x/y). Finally, we can simplify the fractional exponent by taking the square root of x/y, which gives us √(x/y).
How many lines of symmetry are
found in a regular polygon with 40
A regular polygon has the same number of lines of symmetry as it has sides. Therefore, a regular polygon with 40 sides will have 40 lines of symmetry.
Explanation:In Mathematics, symmetry is a significant aspect when dealing with geometric figures, such as polygons. In a regular polygon, the number of lines of symmetry is equal to the number of sides. Therefore, a regular polygon with 40 sides will have 40 lines of symmetry.
This is because, in a regular polygon, all sides and angles are equal, meaning it can be reflected or folded over each of its sides and still remain the same shape. So, you can draw a line from each vertex to the opposite side (or vertex in some cases) and get a perfect fold or reflection.
Remember, this is only true for regular polygons, as irregular polygons won't have the same number of lines of symmetry because their sides and angles may not be equal.
Learn more about Symmetry in Regular Polygons here:https://brainly.com/question/33820017
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All real numbers that are less than -3 or greater than it equal to 5
Solve this Multi-Step Equation
7p - (3p + 4) = -2(2p - 1) + 10
4x-8y=24 find the x-intercept and y- intercept on the graph
In a class of 20 students ,40% are boys.25% of theboys and 50% of the girls were glasses.how many students were glassses. show work
Graph y-5 = -2/3 (x+9)
Three consecutive integers have a sum of 114. what are the three integers
Our three consecutive integers are 37, 38, and 39.
Work is provided in the image attached.
Mrs. Reid is going on a trip. She has 9 books that she hasn't read yet, but she wants to bring only 3 on the trip. In how many ways can she choose 3 books to bring on the trip?
♦27
♦84
♦504
♦60,480
Answer:
Option B is right.
Step-by-step explanation:
Given that there are totally 9 books unread by Mrs. Reid. OUt of these she wants to take only 3 books on the trip.
For books order does not count.
Hence combinations would be appropriate to calculate.
3 books out of 9 can be selected in
9C 3 ways
No of ways of selecting 3 books for the trip out of 9 = [tex]\frac{9(8)(7)}{1(2)(3)} =84[/tex]
There are just 84 ways of choosing 3 books to bring on the trip out of 9 unread books.
Option B is right.
The correct answer is 84.
To solve this problem, we can use the concept of combinations from combinatorics. A combination is a way of selecting items from a collection, such that the order of selection does not matter. In this case, Mrs. Reid wants to select 3 books out of 9 without regard to the order in which they are chosen.
The number of ways to choose 3 books from 9 is given by the combination formula:
[tex]\[ C(n, k) = \frac{n!}{k!(n-k)!} \][/tex]
where[tex]\( n \)[/tex] is the total number of items to choose from, [tex]\( k \)[/tex]is the number of items to choose, and [tex]\( ! \)[/tex] denotes factorial, which is the product of all positive integers up to that number.
For Mrs. Reid's situation:
[tex]\[ n = 9 \] \[ k = 3 \][/tex]
So we plug these values into the formula:
[tex]\[ C(9, 3) = \frac{9!}{3!(9-3)!} \][/tex]
Calculating the factorials:
[tex]\[ 9! = 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 \] \[ 3! = 3 \times 2 \times 1 \] \[ (9-3)! = 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 \][/tex]
Now we simplify the expression by canceling out the common terms in the numerator and the denominator:
[tex]\[ C(9, 3) = \frac{9 \times 8 \times 7 \times 6!}{3! \times 6!} \] \[ C(9, 3) = \frac{9 \times 8 \times 7}{3 \times 2 \times 1} \][/tex]
Divide out the common factors:
[tex]\[ C(9, 3) = \frac{9}{3} \times \frac{8}{2} \times \frac{7}{1} \] \[ C(9, 3) = 3 \times 4 \times 7 \][/tex]
Now we multiply the remaining numbers [tex]\[ C(9, 3) = 3 \times 4 \times 7 = 84 \][/tex]
Therefore, Mrs. Reid can choose 3 books to bring on the trip in 84 different ways.
What is the length of each side of a cube if its surface area is 486 in2?
Jill bought items costing $3.45 , $ 1.99, $6.59 , and $ 12.98 . she used a coupon worth $2. 50. if jill had $ 50.00 when she went into the store , how much did she have when she left
Does this figure have rotational symmetry?
A) No, pentagons cannot be rotated.
B) No, it has five lines of symmetry.
C) Yes, it has five lines of symmetry.
D) No, it only looks the same if it is rotated 360°.
More than half of which climate type averages between 40 and 59 inches of precipitation a year?
Simplify the expression, if possible. (if the expression cannot be simplified, enter the given expression.) (k − 5)13 (k − 5)
Is the probability of contamination more than twice the mean of 14.4 unusual, or can it be considered typical variation? explain?
To determine if a probability of contamination more than twice the mean of 14.4 is unusual, the standard deviation must be considered. In a normal distribution, occurrences more than two standard deviations from the mean are typically unusual.
Whether a probability of contamination more than twice the mean of 14.4 is unusual or not depends on the standard deviation of the data. In a typical normal distribution, values more than two standard deviations away from the mean could be considered unusual. Considering a mean of 14.4, if the standard deviation is small, then a value twice as large would likely be an outlier. However, if the standard deviation is large, such a value could fall within the realm of normal variation.
To ascertain if a value is unusual, one would compare it to the range defined by a certain number of standard deviations from the mean. A common rule of thumb is the empirical rule, which states that for a normally distributed dataset, roughly 68% of data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.
In this context, if a probability of contamination is more than twice the mean (greater than 28.8), and assuming a normal distribution, it would be considered unusual if it falls outside of two standard deviations from the mean.
Find the slope of the line.
We can use the points (-4, -1) and (0, -2) to solve.
Slope formula: y2-y1/x2-x1
= -2-(-1)/0-(-4)
= -1/4
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What is the reciprocal of each mixed number? Drag and drop the answer into the box to match each number.
10 1/3
2 2/3
5 1/3.
Answer:
10 1/3 = 3 /31. 2 2/3 = 3/8. 5 1/3 = 3/16.
Step-by-step explanation:
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Hey Yo I needs some Help
Answer:
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Step-by-step explanation:
THE FUNCTION ARCSINE CAN ALSO BE DEFINED AS?
If the top of a set of characters is chopped off, then line spacing may be set to ____.
Erica sells magazine subscriptions and makes a flat rate of $5.35 for each subscription see cells if Erica man $42.80 on Monday $64.20 on Tuesday and $74.90 on Wednesday how many subscriptions did she sell in three days
C—34. Subscriptions
evaluate the expression if a=3 and b=5
4(a+2b)
30 POINTS!!
Find the measure of angle B in isosceles triangle ABC.
3 angles inside a triangle = 180 degrees
since the 2 sides are equal
angle B and C are the same
180 - 50 = 130 degrees
130 / 2 =65
Angle B is 65 degrees
Force equals mass times acceleration. If m represents mass and a represents acceleration, Which function f represents Force?
A. F=ma
B. F=m+a
C. F= m exponent a
D. F=m/a
Calculus: Help ASAP
Evaluate the integral of the quotient of the secant squared of x and the square root of the quantity 1 plus tangent x, dx.
Answer:
[tex]2\sqrt{1+tan(x)} +C[/tex]
Step-by-step explanation:
To start solving this you need to use substitution. I let u = 1+tan(x). Next you need to find du/dx, which is sec^2(x) using trigonometric properties. Solve for dx and get dx = du / sec^2(x). Next put the new dx back in. This gives you integral sec^2(x) / sqrt u * du / sec^2(x). The sec^2(x) cancels and the new expression is integral 1/sqrt u * du, which can be simplified to integral u^-1/2 * du. You then take the integral and get 2u^1/2. Lastly, substitute the original u back in and get 2 sqrt 1+tan(x) + C.
A certain mutual fund has net assets of $1,359,600. One share of this fund has a net asset value of $11.33. How many shares make up the fund?
Answer:
B
Step-by-step explanation:
5(1+4m)=2(3+10m)
Please help. Show work please
ALGEBRAAA
1. What is the average rate of change? How do you find it?
2. Whats the difference between recursive and explicit formulas?
1. The average rate of change is the slope of a line to find it divide the vertical change by the horizontal change
2. recursive is a formula to calculate the next term, depending on what the previous term was
Explicit is a formula to calculate any term depending on the term number
A function is given. Determine the average rate of change of the function between the given values of the variable.
h(t) = t2^2+ 2t; t = −1, t = 4
in a experiment investigating the growth of spores in varying soil conditions a certain spore colony grew an average of 3 times larger during each 24 hours period.if the colony contained 50 spores at the beginning of the experiment how many spores were there at the end of the 4th day?
Given that the certain type of spore colony having 50 spores and a rate of growth of 3 times in 24 hour or one day period, it would grow to (3 times 50) 150 spores at the end of the first day, (3 times 150) 450 in the 2nd day, (3 times 450) 1350 in the third day, and (3 times 1350) 4050 spores at the end of the fourth day.
The spore colony, which triples in size each day, will contain 4050 spores at the end of the 4th day starting from an initial count of 50 spores.
This question involves exponential growth, where the size of the spore colony triples every day.
To solve this, we will calculate the number of spores at the end of each day:
Initial spores= 50
End of Day 1,
50 * 3 = 150
End of Day 2,
150 * 3 = 450
End of Day 3,
450 * 3 = 1350
End of Day 4,
1350 * 3 = 4050
Therefore, at the end of the 4th day, the spore colony would contain 4050 spores.