Answer:a^2/b
Step-by-step explanation:
(a^6b^−3)1^/3
a^6 ^ 1/3 b ^ -3 ^ 1/3
using the power of power rule we can multiply the exponents
a ^ (6*1/3) b ^ (-3* 1/3)
a^ 2 b ^ -1
the negative exponent flips it from the numerator to the denominator
a^2* 1/ b^1
a^2/b
Answer:
A. -18b^-4
second answer is B. -18/b^-4
Step-by-step explanation:
A wall of a building is made from blocks that are each 1 cubic foot. The wall is 6 feet high and 6 feet wide. A window is made by removing some blocks as shown below. The window is 2 feet high by 2 feet wide. Suppose the wall is expanded to be 12 feet high by 12 feet wide, and the window is expanded to be 4 feet high by 4 feet wide. How will this change the volume of the wall?
Answer:
This will increase the volume of the wall by 104 cubic feet
This will increase the volume of the wall by 104 cubic feet
i copied that dude above me so i dont expect any stars or thanks i mainly did this so he can get brainlyest
A media personality argues that global temperatures are not rising because every year an increase is reported such as 0.09 degrees Celsius. The difference from the previous year is less than the margin of error of about 0.13 degrees C, so that difference should be ignored. What is the best counterargument?
The media personality's argument is flawed because they are basing their conclusion on a single year's data and ignoring the overall trend of increasing global temperatures. To counter this argument, one can make the following points:
1. While it is true that the annual increase in temperature may be less than the margin of error, the trend of increasing temperatures over several decades cannot be ignored. The margin of error is a statistical concept that takes into account the uncertainty in the measurement, but it does not negate the overall trend.
2. Global temperature records show that the Earth's temperature has been steadily rising over the past century, with the 10 warmest years on record occurring since 2005. This trend cannot be explained by natural variability alone and is consistent with the effects of human-caused climate change.
3. The consequences of rising global temperatures, such as melting glaciers, rising sea levels, and more frequent extreme weather events, are already being felt around the world. Ignoring this trend could have devastating consequences for future generations.
In summary, the media personality's argument is based on a flawed understanding of statistics and ignores the overall trend of increasing global temperatures. The best counterargument is to highlight the overwhelming evidence of climate change and its potential consequences.
i dont understand this
We can Add 7 black beads to make ratio 3 : 1.
Since we can only change the number of black beads, decide how many black beads you will add based on how many white beads there are.
There are three white beads in the picture.
Total beads we will have (b meaning black)b : 3
Ratio black : white beads 3 : 1
Use the common ratio, which is a number that both sides of the original ratio multiply by to get to the new ratio.
Find common ratio by dividing total by ratio white beads: 3/1 = 3
Multiply ratio black beads by common ratio. 3 X 3 = 9
We need 9 black beads in total.
Check answer
9 : 3
Both sides divisible by 3; reduce ratio
= 3 : 1
Which is Correct ratio
Hence, There will be a total of 9 black beads, but we already have 2 black beads:
(9 total) - (2 original) = (7 to add)
Therefore , we need to add 7 black beads.
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solue for &
X(3 + X) = 3x + x²
we have
\(g(x)=x^2-3x-10\)\(g\mleft(x+3\mright)=x^2+bx-c\)Solve for b and c
step 1
Find out g(x+3)
\(g(x+3)=(x+3)^2-3(x+3)-10\)simplify
\(g(x+3)=x^2+6x+9^{}-3x-3-10\)combine like terms
\(g(x+3)=x^2+3x-4\)equate with the given expression
\(x^2+3x-4=x^2+bx-c\)b=3
c=4
3x=bx -------> b=3
-4=-c ------> c=4
f(3/4) if f(x)= 2x +1/4
Answer:
\(\boxed{f\left(\frac{3}{4} \right) = \frac{7}{4}}\)
.
Step-by-step explanation:
\(f(x) = 2x + \frac{1}{4}\)
.
\(f\left(\frac{3}{4} \right) = 2(\frac{3}{4} ) + \frac{1}{4}\)
\(f\left(\frac{3}{4} \right) = \frac{6}{4} + \frac{1}{4}\)
\(f\left(\frac{3}{4} \right) = \frac{6 + 1}{4}\)
\(f\left(\frac{3}{4} \right) = \frac{7}{4}\)
The base of S is a circular disk with radius 3r. Parallel cross-sections perpendicular to the base are isosceles triangles with height 4h and unequal side in the base. (a) Set up an integral for the volume of S. (b) By interpreting the integral as an area, find the volume V of S.
The given integral is equivalent to finding the area under the curve of (1/2)b(x)h(x) from 0 to 3r, we can evaluate it using calculus to obtain the volume V of S.
Let x be the distance from the center of the circular base to the vertex of the isosceles triangle. Then the radius of the cross-section at height y is r(y) = 3r - (3r/4h)y. The length of the unequal side of the isosceles triangle is l(y) = 2x, and the height is h(y) = 4h - y.
The area of the cross-section is:
A(y) = 1/2 * l(y) * h(y) = x(y) * (4h - y)
We can use the Pythagorean theorem to relate x, y, and r:
\(x^2 + (4h - y)^2 = r(y)^2\)
Solving for x, we get:
x(y) = \(sqrt(r(y)^2 - (4h - y)^2)\)
Substituting r(y) = 3r - (3r/4h)y, we get:
x(y) = \(sqrt((3r - (3r/4h)y)^2 - (4h - y)^2)\)
Now we can set up the integral for the volume of S:
V = ∫[0,4h] A(y) dy
= ∫[0,4h] x(y) * (4h - y) dy
= \(∫[0,4h] sqrt((3r - (3r/4h)y)^2 - (4h - y)^2) * (4h - y) dy\)
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How does the value of the digit 3 in the number 63,297 compare to the value of the digit of 3 in the number 60,325? Be sure to include what you know about place value in your answer.
The solution is, the value of the digit 3 in the number 63,297 compare to the value of the digit of 3 in the number 60,325 is 2700.
Here, we have,
given that,
the value of the digit 3 in the number 63,297 compare to the value of the digit of 3 in the number 60,325.
we have,
The value of the digit 3 in the number 63,297 is 3,000 while the value of the digit 3 in the number 60,325 is 300.
we know,
the value of the digit 3 in the number 63,297 = 3000
the value of the digit 3 in the number 60,325 = 300
so, we get,
The difference between value of the digit 3 in the number 63,297 and the value of the digit 3 in the number 60,325 will be:
= 3000 - 300
= 2700
Hence, the value of the digit 3 in the number 63,297 compare to the value of the digit of 3 in the number 60,325 is 2700.
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Two students are interested in whether or not there is variation in their test scores for math class. There are 15 total math tests they have taken so far. The first student’s grades have a standard deviation of 38.1. The second student’s grades have a standard deviation of 22.5. The second student thinks his scores are lower.
State the null and alternative hypotheses. (fill in <,≤, >, ≥, =)
a) H0: σ1 _____ σ2
b) Ha: σ1 ______ σ2
c) What is the F-statistic?
d) What is the p-value?
e) At the 5% significance level, do we reject or fail to reject the null hypothesis?
f) There (is or is not) ________enough evidence to say that the variance of the grades for the first student is higher than the variance in the grades for the second student
To compare variance of math test scores between two students, null hypothesis is that variances are equal and alternative hypothesis is that variance of first student's grades is higher.
Calculate F-statistic and p-value to reject or fail to reject null hypothesis at 5% significance level. If null hypothesis is rejected and p-value is less than 0.05, conclude that variance of first student's grades is higher.
a) H0: σ1 = σ2
b) Ha: σ1 > σ2
c) The F-statistic would be calculated by taking the ratio of the variance of the first student's grades (σ1²) to the variance of the second student's grades (σ2²).
d) The p-value is the probability of obtaining a result as extreme as the one observed, given that the null hypothesis is true. To determine the p-value, you would need to perform a statistical test such as an F-test or Levine's test.
e) At the 5% significance level, you would reject the null hypothesis if the p-value is less than 0.05. If the p-value is greater than 0.05, you would fail to reject the null hypothesis.
f) There is enough evidence to say that the variance of the grades for the first student is higher than the variance in the grades for the second student if the p-value is less than 0.05 and the null hypothesis is rejected. If the p-value is greater than 0.05 or the null hypothesis is not rejected, then there is not enough evidence to make this conclusion.
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Help !!!!!!!!!!!!!!!!!!!!!
Answer:
6
1+6
2+5
3+4
4+3
5+2
6+1
hope it helps
18. Find the present value of a deferred annuity of ₱ 30,000.00 at the end of every year for 10 years. The first payment of a mother will be done at the end of the second year, and the money is compounded at 3% annually. a. ₱ 244,354.12 b. ₱ 248,452.51 c. ₱ 278,520.14 d. ₱ 291,245.18
Answer:
₱ 248,452.51
Step-by-step explanation:
₱ 248,452.51
Determine the interval(s)
on which the given function is-decreasing.
A function assigns the values. The interval for which the given function will be decreasing is (-∞, -1)∪(0,∞).
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The interval for which the given function will be decreasing is from point A to point B, and then from point C to point D. Therefore, the interval will be (-∞, -1) and (0,∞). Hence, The interval for which the given function will be decreasing is (-∞, -1)∪(0,∞).
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Convert 0.622 0.622 to a fraction in simplest form and a percent.
Answer: 311/500 and 62.22%
Step-by-step explanation:
Fraction: 0.622 = 622/1000 = 311/500
Percent: 0.6222 = 62.22 % (Move decimal 2 places down)
The decimal 0.622 in the form of simplest fraction as 311/500 and in percent is 62.2%.
To convert 0.622 to a fraction in simplest form, write it as follows:
0.622 = 622/1000
Now, simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
622/1000 = (311 × 2)/(500 × 2)
= 311/500
So, 0.622, when expressed as a fraction in simplest form, is 311/500.
To convert 0.622 to a percent, multiply it by 100:
0.622 × 100 = 62.2%
Therefore, 0.622 is equivalent to 311/500 or 62.2%.
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CAN SOMEONE PLEASE HELP ME ASAP
(wrong answers will be reported )
The inequality is solved and the number is x ≥ 12
Given data ,
Let the number be represented as x
Now , sum of three times a number and -4 is at least twice the number plus 8
And , 3x - 4 ≥ 2x + 8
To solve for "x", we can start by isolating the "x" term on one side of the inequality
3x - 4 ≥ 2x + 8
Subtract 2x from both sides , we get
3x - 2x - 4 ≥ 2x - 2x + 8
x - 4 ≥ 8
Add 4 to both sides , we get
x - 4 + 4 ≥ 8 + 4
x ≥ 12
Hence , the inequality is x ≥ 12
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Two hundred sixty students were surveyed on whether they prefer apple juice or orange juice. A table of relative frequencies is shown. How many more girls prefer apple juice than boys?
Answer:
91
Step-by-step explanation:
the solution to a system of linear equations is (0,4) one of the linear equations in the system is Y=8x+4
What is 6721 x 381 divided by 14 + 84
Answer: 26129.6
Step-by-step explanation:
6721 x 381 = 2560701
14 + 84 = 98
2560701 / 98 = 26129.6
Find the remainder when the sum of the six smallest primes is divided by the seventh.
Answer:
7
Step-by-step explanation:
Six smallest prime numbers: 2, 3, 5, 7, 11, 13
Sum: 41
Seventh smallest prime number: 17
41/17 = 2 R7
Answer:
7
Step-by-step explanation:
The first 7 prime numbers are ...
2, 3, 5, 7, 11, 13, 17
The sum of the first 6 is ...
(2 +3 +5 +7 +11 +13) = 41
Dividing this sum by 17 gives ...
41/17 = 2 r 7
The remainder is 7.
Gabriella has a salt shaker in the shape of a right circular cylinder with a radius of 5 cm and a height of 12 cm. What is the volume of this salt shaker?
Answer:
I mean 60 that is V= H×radius
Answer:
The volume of the cylinder is \(300\pi \text{ cm}^3\)
Step-by-step explanation:
Volume of a right circular cylinder: \(V=\pi r^2 h\)
r = radius
h = height (both measured in the same units!)
\(r=5\text{ cm}, \, h=12\text{ cm}\)
Substitute those values into the formula.
\(V=\pi (5^2)(12) = \pi (25)(12) = 300\pi \text{ cm}^3\)
That is an exact answer. If you need an approximation, use something like 3.14 or 3.1416 .
Negative numbers do not have square roots that are real numbers
Answer:
Negative numbers don't have real square roots since a square is either positive or 0. The square roots of numbers that are not a perfect square are members of the irrational numbers. This means that they can't be written as the quotient of two integers.
513.4497 rounded to the hundredths place
Answer:
513.45
Step-by-step explanation:
use intelligence
If a/b and x/y represent rational expressions and b0 and y0, what is true of their product? Select three options.
The product is equivalent to ay/bx
The product is a rational expression.
The product is equivalent to a/y(x/b)
The product is the ratio of ax and by.
The product is equivalent to ax/b(y)
Answer:
It’s the 2nd,3rd,and 4th
Step-by-step explanation:
I just took the quiz
Answer:
2,3,4
Step-by-step explanation:
I need help with this
Answer:
The solution for problem a is cross multiplication
5×500=2500 and 15×x=15× so 15×=2500
divide both sides by the coefficient 15. 15x ÷15=×
divide 2500 by 15=500
x=500/3= approximately 166.7
Solution for b:
This one's easy!!
10/20=x/500
cross multiply
10×500=5000
20×X=20x
now we have the equation. 20x=5000
stay with me. I hope this makes sense ^_^
divide both sides by the coefficient 20
20x÷20=x
5000÷20=250
x=250
a is true
i hope this helps ;)
This shows a function. F(x)=4x^3+8 which statement describes f(X)? A. The function does not have an inverse function because F(x) fails the vertical line test. B. The function does not have an inverse function because f(x) fails the horizontal line test. C. The function has an inverse function because f(x) passes the vertical line test. D. The function has an inverse function because f(x) passes the horizontal line test
Answer:
Step-by-step explanation:
The statement that describes the function f(x) = 4x^3 + 8 is:
A. The function does not have an inverse function because f(x) fails the vertical line test.
To see why this is the correct answer, let's first define what the vertical line test and the horizontal line test are.
Vertical line test: A function passes the vertical line test if any vertical line intersects the graph of the function at most once. This means that no two points on the graph have the same x-coordinate.
Horizontal line test: A function passes the horizontal line test if any horizontal line intersects the graph of the function at most once. This means that no two points on the graph have the same y-coordinate.
Now, let's look at the function f(x) = 4x^3 + 8. We can graph this function by plotting points or by using a graphing calculator. The graph of the function looks like a curve that goes up and to the right.
If we draw a vertical line anywhere on the graph, we can see that it intersects the graph at most once, which means that f(x) passes the vertical line test. However, if we draw a horizontal line on the graph, we can see that it intersects the graph at more than one point. This means that f(x) fails the horizontal line test.
The fact that f(x) fails the horizontal line test tells us that there are some values of y that correspond to more than one value of x. This means that f(x) is not a one-to-one function, and therefore it does not have an inverse function.
Therefore, the correct statement that describes the function f(x) is:
A. The function does not have an inverse function because f(x) fails the vertical line test.
simplify using distributive law ;
1.) X n ( X n Y )
2.) ( X n Y ) u ( X n Y )
Answer:
X n Y , X n Y
Step-by-step explanation:
1) Use Associative law:
X n (X n Y) = (X n X) n Y
Idempotent law:
= X n Y
2) it is in the 'distributed' form, thus we need to reverse the distribution,
akin to 'factorization':
(X n Y) u (X n Y) = (X n (Y u Y))
which can be further simplified using idempotent law:
= X n Y
Perform the following mathematical operation, and report the answer to the appropriate number of significant figures.
1204.2 + 4.72613 = [?]
The answer is not 1208.92613 / 1200
Answer:
1,208.92613
Step-by-step explanation:
this is the answer
A convex lens with focal length f centimeters will project the image of an object on a
point behind the lens. If an object is placed a distance of p centimeters from the lens,
then the distance q centimeters of the image from the lens is related to p and f by the
lens equation: 1/p+1/q=1/f
A. If the focal length of the convex lens is supposed to be 5 cm, and if the image is
formed 7 cm from the lens, find the distance from the lens to the object, p. (It’s not necessary to simplify your answer.)
B. Find an expression that gives q as a function of p, assuming that the focal length is a constant of 5 centimeters.
C. Sketch a graph of q as a function of p (i.e., q(p)), assuming that the focal length is a
constant of 5 centimeters. Show any important features of the graph.
D. Find limq(p) as p approaches infinity and limq(p) as p approaches 5from the positive side. What do these limits represent physically? What must
happen to the distance of the image and the object?
Answer:
A. Using the lens equation, 1/p + 1/q = 1/f, and substituting f = 5 cm and q = 7 cm, we can solve for p:
1/p + 1/7 = 1/5
Multiplying both sides by 35p, we get:
35 + 5p = 7p
Simplifying and rearranging, we get:
2p = 35
Therefore, the distance from the lens to the object, p, is:
p = 35/2 cm
B. Solving the lens equation, 1/p + 1/q = 1/f, for q, we get:
1/q = 1/f - 1/p
Substituting f = 5 cm, we get:
1/q = 1/5 - 1/p
Multiplying both sides by 5qp, we get:
5p = qp - 5q
Simplifying and rearranging, we get:
q = 5p / (p - 5)
Therefore, the expression that gives q as a function of p is:
q = 5p / (p - 5)
C. Here is a sketch of the graph of q(p):
The graph is a hyperbola with vertical asymptote at p = 5 and horizontal asymptote at q = 5. The image distance q is positive for object distances p greater than 5, which corresponds to a real image. The image distance q is negative for object distances p less than 5, which corresponds to a virtual image.
D. Taking the limit of q as p approaches infinity, we get:
lim q(p) = 5
This represents the horizontal asymptote of the graph. As the object distance becomes very large, the image distance approaches the focal length of the lens, which is 5 cm.
Taking the limit of q as p approaches 5 from the positive side, we get:
lim q(p) = -infinity
This represents the vertical asymptote of the graph. As the object distance approaches the focal length of the lens, the image distance becomes infinitely large, indicating that the lens is no longer able to form a real image.
In order for the lens to form a real image, the object distance p must be greater than the focal length f. When the object distance is less than the focal length, the lens forms a virtual image.
Which equation represents a population of 210 animals that decreases at an annual rate of 14%
Answer:
The equation i.e. used to denote the population after x years is:
P(x) = 490(1 + 0.200 to the power of x
Step-by-step explanation:
This problem could be modeled with the help of a exponential function.
The exponential function is given by:
P(x) = ab to the power of x
where a is the initial value.
and b=1+r where r is the rate of increase or decrease.
Here the initial population of the animals are given by: 490
i.e. a=490
Also, the rate of increase is: 20%
i.e. r=20%
i.e. r=0.20
Hence, the population function i.e. the population of the animals after x years is:
P(x) = 490(1 + 0.200 to the power of x
So for this, we will be using exponential form, which is y = ab^x (a = initial value, b = growth/decay).
Since we start off with 210 animals, that is our a variable.
Next, since this is *decreasing* by 14%, you are to subtract 0.14 (14% in decimal form) from 1 to get 0.86. That will be your b variable.
Putting everything together, your equation is y = 210(0.86)^x
Question Number 7 of 10 - 8th Grade Math
Which graph shows only a translation?
The graph that shows only a translation is (c)
How to determine the graph that shows only a translation?From the question, we have the following parameters that can be used in our computation:
The list of options
The general rule of translation it that
The image and the preimage have the same orientationThe image and the preimage have the same side lengthsThe image and the preimage have the same angle measuresUsing the above as a guide, we have the following:
the graph that shows only a translation is (c)
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Answer two questions about Systems A and B:
System A:
8x - 3y = 0
2x + 7y = 3
System B:
8x – 3y = 0
8x + 28y = 12
1) How can we get System B from System A?
2) Based on the Previous answer are the systems equivalent? In other words do they have the same solution?
Answer: 1) A
2) yes
Step-by-step explanation:
Answer:
a and yes
Step-by-step explanation:
Solve the problem by using addition, subtraction, multiplication, or division. First use front end rounding to estimate the answer. Then find the exact answer.
The foggiest place in a certain country is City A. It is foggy there an average of days each year. How many days is it not foggy each year? Find the estimated and the exact number of days.
The notion of an equation in algebra is a statistical statement that demonstrates the equality of two mathematical expressions.
For the stated question;
Use addition, subtraction, multiplication, or division to find the solution. To first estimate the response, use front end rounding. Find the precise response next. City A is located in the nation with the most haze. how many days a year are clear of fog.365 days are included in a year.
There are 256 days a year on average when it is foggy.
Determine the approximate number of clear days by using the formula:
We round the figures.
To the nearest tens, 365 days
= 370 days
The nearest tenth of 256 days
= 260 days
370 - 260 days, then
= 110 days
The precise number of days without fog is =
= 365 − 256
= 109
Thus, the precise number of days without fog is found as 109 days.
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The complete question is -
Solve the problem by using addition, subtraction, multiplication, or division. First use front end rounding to estimate the answer. Then find the exact answer. The foggiest place in a certain country is City A. It is foggy there an average of 256days each year. How many days is it not foggy each year? Find the estimated and the exact number of days.