how do i simplify 6⁴ 6⁸ please help its dou today
Answers
Answer: 6^12 (or 2176782336)
When you multiply exponents with the same base, you add the exponents together. (e.g., x^m · x^n = x^m+n)
6^4 · 6^8 = 6^4+8 = 6^12
Related Questions
A bird sanctuary initially contains 1500 birds. Each year, 15% of the birds fly away, so the sanctuary is restocked with 60 new birds. Write a recursive rule for the number of birds an of birds at the start of the nth year A1=____. An=____
Answers
Answer:
\(A_1 = 1500\\A_n = A_{n-1} - 15\%\cdot A_{n-1} + 60\)
Step-by-step explanation:
We just put the task description into the answer :)
The last line can also be shortened to:
\(A_n = 85\%\cdot A_{n-1} + 60\)
or
\(A_n = 0.85A_{n-1} + 60\)
How do you write 0.53 as a whole number
Answers
Answer:
Step-by-step explanation:
0.53 cannot be written as a whole number, but it can be written as the ratio 53/100, which is the ratio of two whole numbers (53 and 100).
Source:trust me bro
Show that if y(t) satisfies y'' – ty = 0, then y( - t) satisfies y'' + ty = 0. The first derivative of y( – t) is ____, and the second derivative of y( - t) is ____. How does this help to complete the proof? Choose the correct answer below. A. Since each derivative of y( – t) is the opposite of each derivative of y(t), the equations y'' – ty = 0 and y'' + ty = 0 are equivalent and are both satisfied by y(t) and y-t). B. Since y(t) is odd, y( -t) = -y(t). Using this and the second derivative above gives the equation y'' + ty = 0. C. Replacing t with - t in the equation y'' – ty = 0 gives the same equation, y'' – ty = 0.
D. Replacing t with-t in the equation y'' - ty = 0 gives y''(-t)-(-t)y( – t) = 0, or y'' + ty = 0.
Answers
The correct answer is: A. Since each derivative of y( – t) is the opposite of each derivative of y(t), the equations y'' – ty = 0 and y'' + ty = 0 are equivalent and are both satisfied by y(t) and y(-t). To show that if y(t) satisfies y'' - ty = 0, then y(-t) satisfies y'' + ty = 0, we will find the first and second derivatives of y(-t) and plug them into the equation.
First derivative of y(-t): Let's denote y(-t) as u(t). Then, u(t) = y(-t), and the first derivative u'(t) = -y'(t).
Second derivative of y(-t): Taking the derivative of u'(t) gives us u''(t) = -y''(t).
Now, let's plug these derivatives into the equation: u''(t) + tu(t) = -y''(t) + t*y(-t) = 0.
Since y(t) satisfies y'' - ty = 0, we can replace y''(t) with t*y(t) in the equation: - (t*y(t)) + t*y(-t) = 0.
This simplifies to: y'' + ty = 0, which is satisfied by y(-t).
Therefore, the correct answer is: A. Since each derivative of y( – t) is the opposite of each derivative of y(t), the equations y'' – ty = 0 and y'' + ty = 0 are equivalent and are both satisfied by y(t) and y(-t).
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Given points A(-1,4) and B(x,7), determine the value(s) of x if AB=5cm
Answers
The value of x is either 3 or -5 based on the distance formula.
What is a co-ordinate system?
In pure mathematics, a coordinate system could be a system that uses one or additional numbers, or coordinates, to uniquely confirm the position of the points or different geometric components on a manifold like euclidean space.
Main body:
according to question
Given points A(-1,4) and B(x,7)
Also AB = 5 cm
Formula of distance = \(\sqrt{(y1-y2)^{2}+(x1 -x2)^{2} }\)
here by using points ,
5 = \(\sqrt{(x+1)^{2} +(7-4)^{2} }\)
taking square on both side ,'
25 = \((x+1)^{2} +3^{2}\)
25-9 = (x+1)²
16 = (x+1)²
taking square root on both sides,
x+1= ±4
x = 4-1 = 3 or x = -4-1 = -5
Hence value of x is either 3 or -5.
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gradient descent algorithm given a continuous and differentiable function f : r n → r, the gradient of f at any point ⃗x, ∇f(⃗x), is orthogon
Answers
The gradient descent algorithm is an iterative optimization algorithm commonly used to find the minimum of a function.
At each iteration, the algorithm updates the current point in the direction opposite to the gradient of the function evaluated at that point. The gradient of a function measures the rate of change of the function with respect to each variable.
In the context of the gradient descent algorithm, the gradient of a function at a point is orthogonal to the level set of the function at that point. This means that the gradient vector points in the direction of steepest ascent, while the level set represents the set of points where the function has the same value. Orthogonality between the gradient and the level set implies that moving in the direction of the negative gradient will lead to a decrease in the function's value.
By updating the current point in the direction of the negative gradient, the gradient descent algorithm efficiently moves towards the minimum of the function. The algorithm iteratively performs this update until it converges to a local minimum.
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find value of x round answer to nearest tenth
Answers
Answer:
14
Step-by-step explanation:
19^2 = y^2+ 17^2
y = 8.5
by figure
x = 31 - 2*y
x = 14
1.2 mi =
ft someone pls tell me I have a test tomorrow!!
Answers
Answer: 6336 ft.
Step-by-step explanation:
If you were asking what 1.2 miles equals in feet, your answer would be 6336 feet. Good luck on your test tomorrow!
Answer:
6336 feet
Step-by-step explanation:
each mile has 5280 feet. Simply multiply 1.2 by 5280 to get your answer
The Internal Revenue Service estimates that 8% of all taxpayers filling out forms make mistakes.
An IRS employee randomly selects and checks 10 forms for mistakes. What is the probability that exactly one has an error?
The same IRS employee announces at lunch one day that she is going to check 25 randomly selected forms after lunch.
Calculate the mean and the standard deviation of the number of forms with mistakes she should expect to find.
The IRS employee checked 25 randomly selected forms and didn't find any mistakes. Does this provide convincing evidence to cause her supervisor to believe that she is missing mistakes? Explain.
Answers
Probability of exactly one error in 10 forms: Use binomial distribution with n = 10 and p = 0.08..Mean and standard deviation of forms with mistakes: Calculate using expected value and standard deviation formulas for a binomial distribution.
To calculate the probability that exactly one form has an error out of 10 randomly selected forms, we use the binomial probability formula: P(X = k) = (n C k) * p^k * (1-p)^(n-k), where n is the number of trials, p is the probability of success, and k is the number of successes. In this case, n = 10, p = 0.08, and k = 1. Plugging in these values, we can calculate the probability as P(X = 1) = (10 C 1) * (0.08)^1 * (1-0.08)^(10-1).
The mean (expected value) of the number of forms with mistakes can be calculated as μ = n * p, where n is the number of trials and p is the probability of success. In this case, n = 25 and p = 0.08. The standard deviation can be calculated as σ = sqrt(n * p * (1-p)), where sqrt represents the square root. Plugging in the values, we can calculate the mean and standard deviation.
Finding no mistakes in 25 randomly selected forms does not provide strong evidence to conclude that the employee is missing mistakes. The probability of not finding any mistakes in 25 forms can be calculated using the binomial distribution with parameters n = 25 and p = 0.08. If the actual proportion of mistakes is 8%, it is possible to observe a sample without mistakes due to random chance. To draw a more reliable conclusion, a larger sample size or additional evidence would be needed.
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What is the volume of the cylinder in terms of pi 2 m 6m
Answers
Answer:
6πm³
Step-by-step explanation:
To work out the volume of a cylinder, use the formula πr²h
Next, substitute the known values into the equation (remember that the radius is half of the diameter):
volume = π × 1² × 6
The volume of the cylinder is 6πm³
Hope this helps!
Events D and E are independent, with P(D)- 0.6 and P(D and E) - 0.18. Which of the following is true? A. P(E)- 0.12 B. P(E) = 0.4 C. P(D or E)-0.28 D. P(D or E) 0.72 E. P(D or E)-0.9
Answers
The correct statement is: A. P(E) = 0.3. The probability of event E, denoted as P(E), is equal to 0.3.
To determine the correct answer, let's analyze the given information.
We know that events D and E are independent, which means that the occurrence of one event does not affect the probability of the other event happening.
Given:
P(D) = 0.6
P(D and E) = 0.18
Since events D and E are independent, the probability of both events occurring (P(D and E)) can be calculated as the product of their individual probabilities:
P(D and E) = P(D) * P(E)
Substituting the given values:
0.18 = 0.6 * P(E)
To find the value of P(E), we can rearrange the equation:
P(E) = 0.18 / 0.6
P(E) = 0.3
Therefore, the correct answer is A. P(E) = 0.3.
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Which of the following is a right Riemann sum for arctan(1 + xdx? k=1 © ( aretan (1 + 4) :) į (aretan (4+4) ) ©Ë (arctan ( 1 + **) :) © (aretan (2 + %). :) arctan 1+ .
Answers
The right Riemann sum for arctan(1 + xdx) is Σ[arctan(1 + iΔx)]Δx, where i ranges from 1 to n and Δx is the width of each subinterval. The correct answer among the options provided is (arctan(1 + Δx) + arctan(1 + 2Δx) + ... + arctan(1 + nΔx))Δx.
In a right Riemann sum, the function is evaluated at the right endpoint of each subinterval. Therefore, we add up the values of arctan(1 + iΔx) at the endpoints of the subintervals, where i ranges from 1 to n. The width of each subinterval is Δx, so we multiply the sum by Δx to get the approximate value of the integral.
The provided expression (arctan(1 + Δx) + arctan(1 + 2Δx) + ... + arctan(1 + nΔx))Δx satisfies the conditions of a right Riemann sum, where the function is evaluated at the right endpoint of each subinterval. Therefore, this is the correct option among the given choices.
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dilate the figure with the origin as the center of dilation
Answers
Explanation
In this case as the factor of dilation is 2.5 and the point (0,0) each coordinate is multiplied by 2.5.
Answer
Carl is planning out his route for an upcoming race. He uses negative numbers to represent points before the finish line and positive numbers to represent points past the finish line. On Carl's map, the last water station is at − 27 1 4 −27 4 1 minus, 27, start fraction, 1, divided by, 4, end fraction meters, and his family is watching him at 9 1 2 9 2 1 9, start fraction, 1, divided by, 2, end fraction meters. What does 0 00 meters represent?
Answers
Answer:
0 represents the start point
Step-by-step explanation:
Given
\(Before\ Finish\ Line = -27\frac{1}{4}\)
\(After\ Finish\ Line = 9\frac{1}{2}\)
Required
What does 0 represents
In a race; there's always a starting point, irrespective of the current position of the racer.
This position is always at the 0 point.
Hence:
The 0 meters represents the start point
Answer:
The finish line
John has taken six quizzes in his statistics class. His
scores on these quizzes are listed below.
71, 75, 76, 80, 85, 87
He finds that the mean is 79.0 and the median is 78.0
for these six quiz scores. If John earns a 100% on the
next exam, what will the new mean and median be?
O The new mean will be 82.0 and the new median will
be 78.0.
O The new mean will be 82.0 and the new median will
be 80.0.
O The new mean will be 89.5 and the new median will
be 78.0.
O The new mean will be 89.5 and the new median will
be 80.0
Answers
Answer:
The new mean will be 82.0 and the new median will be 80.0.
Step-by-step explanation:
To find the mean, we must divide the sum of terms by the number of terms.
71+75+76+80+85+87+100 = 574Divide 574 by 7 because there are 7 quiz scores574 ÷ 7 = 82The new mean is 82
To find the median, we need to find the middle number of the set
Order the numbers up: 71, 75, 76, 80, 85, 87, 10080 is in the middleThe new median is 80
Two right ide if a right triangle meaure 2 unit and 4 unit. What i the area of the quare that hare a ide with the third ide of the triangle?
Answers
The area of the third side of the triangle is either 20 square unit or 12 square units.
Triangle:
in math, triangle refers a simple closed curve made of three line segments and it has three vertices, three sides and three angles.
Given,
Two sides of a right triangle measure 2 units and 4 units.
And we need to find the area of the square that shares a side with the third side of the triangle
Let us consider is Two sides of a right triangle measure 2 units and 4 units.
Here if sides are perpendicular sides, then by using Pythagorean theorem
=> third side² = 2² + 4²
When we simplify this one, then we get,
=> third side² = 4 + 16
So, the third side² = 20
Then the area of the square that shares a side with the third side of the triangle = third side² = 20 sq units
Similarly, if 4 units is hypotenuse side, then by using Pythagorean theorem, the third side is calculated as,
=> third side² = 4² - 2²
And when we simplify this one, then we get,
=> third side² = 16 - 4
Therefore, the third side² = 12
And the area of the square that shares a side with the third side of the triangle = third side² = 12 sq units
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what is 7/30 as a decimal
Answers
Answer: 7/30 as a decimal is 0.23333333333333
Hope this helps!
salesperson works 40 hours per week at a job where he has two options for being paid. Option A is an hourly wage of $23. Option B is a commission rate of 10% on weekly sales. How much does he need to sell this week to earn the same amount with the two options?
Answers
Michaela drops a ball vertically from a height of 80 feet. The peak height after each bounce is half the previous height.
How far does the ball travel from the time she drops it until it reaches the peak height after the 5th bounce?
O 155 ft
O 230 ft
O 232.5 ft
O 312.5 ft
Answers
Answer:
232.5 ft
Step-by-step explanation:
Bounce
1
2
3
4
5
80 + 40X2 + 20 x 2 + 10 x 2 + 5 x 2 + 2.5 = 232.5 ft
A set of data has a mean of 12 and a standard deviation of 3. A data point of the set has a z-score of 1. 3. What does a z-score of 1. 3 mean?.
Answers
Answer:
cccccccccccccccccccc
Step-by-step explanation:
cccccccccccccccccccccccc
Find matrix M such that M × [3 -2 , 6 -8 ] = [-2 16]
Answers
The matrix M is: M = [2/9 -8/27 , 4/9 -8/27 ]
Let's say that M is a 2 x 2 matrix that satisfies M × [3 -2 , 6 -8 ] = [-2 16]. This means that the product of matrix M and matrix [3 -2 , 6 -8 ] will give us the result matrix [-2 16]. We know that the product of two matrices is equal to the sum of the products of their corresponding elements. We can use this knowledge to solve for the unknown elements in matrix M. Let us assume that M = [a b , c d] so that we can solve for its elements.
a(3) + b(6) = -2 ... (1) c(3) + d(6) = 16 ... (2) a(-2) + b(-8) = -2 ... (3) c(-2) + d(-8) = 16 ...
(4)Simplifying equations (1) to (4), we get:
3a + 6b = -2 ... (5) 3c + 6d = 16 ... (6) -2a - 8b = -2 ... (7) -2c - 8d = 16 ... (8)
Solving for a, b, c, and d, we get:a = 2/9 b = -8/27 c = 4/9 d = -8/27.
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Reyna has 5 coins worth 10 cents each and 4 coins worth 25 cents each. If she chooses two of these coins at
random, what is the probability that the two coins together will be worth 50 cents?
A- 4/27
B- 5/18
C- 20/81
D- 1/6
Answers
Answer:
B-5/18
Step-by-step explanation:
There are two cases where Reyna can choose two coins that add up to 50 cents:
Case 1: She chooses two of the 5-cent coins. There are 5 choose 2 ways she can do this, or 10 ways.
Case 2: She chooses one 5-cent coin and one 25-cent coin. There are 5 x 4 = 20 ways she can choose one of the 5-cent coins and one of the 25-cent coins.
The total number of ways she can choose any two coins out of the nine coins is 9 choose 2, or 36 ways.
Therefore, the probability of choosing two coins that add up to 50 cents is (10 + 20)/36, which simplifies to 5/18.
So the answer is (B) 5/18.
community college faculty is negotiating a new contract with the school board. The distribution of faculty salaries is skewed right by several faculty members who make over $100,000 per year. If the faculty impression that they deserve higher sales should they a r e the meanor median of their current salaries? A. The faculty should use the mean to make their argument. The mean will be higher than the median since the mean is influenced by the few extremely high res.B. The faculty should use the mean to make o rgument. The man will be lower than the median since it will be henced by the few high salariesC. The faculty should use the median to make their argument. The median will be higher than the mean since the media is unced by the high e s D. The faculty should use the median to make their argument. The median will be lower than me since the means i nced by the extremely histories
Answers
Option D. The faculty should use the median to make their argument. The median will be lower than the mean since the mean is influenced by the few extremely high salaries.
Mean is the average of any data set whereas the median is the middle value we get after arranging the data in ascending order.
So for example, if the salaries of any 5 faculty members are as follows:
$10,000 , $50,000 , $80,000 , $150,000 , $160,000
Mean= (10,000+50,000+80,000+150,000+160,000) / 5
Mean= $90,000
Median= (5+1) / 2
Median= 6/2
Median= 3rd value
As the data is already arranged in ascending order, Median is $80,000
Hence, if the faculty want to give the community the impression that they deserve higher salaries, they should advertise the median of their current salaries.
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Please help me :(((((
Answers
question 3: -2
question 4: 0
Ordered pairs in a graph go in the sequence of (x, y)
What is the answer please show the work
Answers
it is 30 because it says 1 and 20 soooooo
Answer (20 years worth): $18,080.63
simplify the expression:
(x^3y^n/z^m+1)^k
Answers
There are four blood types, and not all are equally likely
to be in blood banks. In a certain blood bank, 49% of
donations are type O blood, 27% of donations are type
A blood, 20% of donations are type B blood, and 4%
of donations are type AB blood. A blood bank wants to
know how many donations will be required, on
average, to achieve at least one of each of the blood
types.
is it appropriate to use the geometric distribution to calculate probabilities in the situation?
Answers
Answer:
D
Step-by-step explanation:
ed
Selection of raffle tickets from a large bowl is an example ofSimple probabilitySampling without replacementSubjective probabilityNone of the above
Answers
Selecting raffle tickets from a large bowl is an example of probability sampling without replacement.
Probability sampling is a method of selecting a subset of individuals from a larger population in a way that each individual in the population has a known and non-zero probability of being selected for the sample.
Sampling without replacement means that once an individual is selected for the sample, they are removed from the population and cannot be selected again. This is in contrast to sampling with replacement, where an individual can be selected multiple times for the sample.
In the case of selecting raffle tickets from a large bowl, each ticket has a known and non-zero probability of being selected for the sample, and once a ticket is selected, it is removed from the bowl and cannot be selected again. Therefore, this is an example of probability sampling without replacement.
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Describe the relationship between a circumference of a circle and its diameter.
Group of answer choices
The circumference is half the length of the diameter.
The diameter is about 3.14 times greater than the circumference.
The circumference is about 3.14 times greater than its diameter.
The circumference is twice the length of its diameter.
which option do i pick! help
Answers
Answer:
i wish i knew
Step-by-step explanation:
points
The relationship between a circumference of a circle and its diameter is given by the circumference is about 3.14 times greater than its diameter.
What is the circumference of a circle?
The distance along a circle's perimeter is referred to as its circumference. In other words, the circumference of a circle is equal to the length of a straight line formed by opening up the circle. It is given by
C = 2πr
where r is the radius of the circle.
The diameter is equal to two times the radius
i.e. d = 2r ................. (1)
and the circumference of a circle is C = 2πr ................ (2)
From equations (1) and (2), we get
C = πd
where the value of π = 3.14 called constant
So, the required answer is circumference is about 3.14 times greater than its diameter.
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the tortoise and the hare are running a 1 km race. after running comfortably for 7 s, the hare is so far ahead that he decides to take a nap under a tree, 100 m away from the finish line. if the tortoise is moving constantly at a speed of 0.27 m/s, and the maximum speed of the hare is 15 m/s, how long can the hare afford to nap if he does not want to lose the race?
Answers
The hare can afford to nap for a maximum time of 3,690 seconds without losing the race if his speed is 15 m/s.
After running for 7 seconds, the hare has covered a distance of:
\(distance = speed \times time\\distance = 15 \times 7\\\)
distance = 105m
The hare is now 895 m away from the starting line and 100 m away from the finish line.
The hare needs to cover a distance of 100 m to reach the finish line, while the tortoise needs to cover a distance of 895 m.
calculate the time it would take the tortoise to reach the finish line:
\(time = \frac{100}{0.27}\) = 3704 seconds
The maximum speed of the hare is 15 m/s, which means the time it would take the hare to cover the distance is:
\(time = \frac{100}{15}\) = 6.67 seconds
so, the time hare have to nap so that he does not lose race = 3704 - (7+6.67) ≅3690 seconds
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Samantha invented a new outdoor game
Answers
The maximum distance between the base of pole A and the base of pole B is 8 ft.
Height of the building A =3 ft
Height of the building B =7 ft
Length of the rope = 9 ft
Suppose the maximum distance between the base of pole A and the base of pole B is x ft.
Find the attached diagram to visualize the given situation better.
What is Pythagoras' theorem?The square on the hypotenuse is equal to the sum of the squares on the other two sides.
Using the Pythagoras' theorem
\(9^{2} =4^{2} +x^{2}\)
\(x^{2} =9^{2} -4^{2}\)
\(x^{2} =81-16\)
\(x=\sqrt{65}\)
x ≈8 ft.
Therefore, the maximum distance between the base of pole A and the base of pole B is 8 ft.
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