6 to the negative 3rd power times 6 to the 2nd power times 6 to the 5th power times 6
Answers
The value of 6 to the negative 3rd power times 6 to the 2nd power times 6 to the 5th power times 6 is 6^5.
What is an exponent?The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
Based on the information given, the numbers will be expressed as:
6^-3 × 6^2 × 6^5 × 6
= 6^5
It's important to note that they've the same base. Therefore, the powers will be added thus:
= -3 + 2 + 5 + 1
= 5
This gives 6^5. This illustrates the concept of exponents.
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Related Questions
The diameter of the sphere is 12.8 cm calculate the value 3.14
Answers
what is needed to be calculated please tell
what is 4 1/5+1 2/5 add and subtract mixed numbers no regrouping
Answers
Answer:
5 3/5 or 5.6
Step-by-step explanation:
Answer:
5 & 3/5
Step-by-step explanation:
4 plus 1 = 5
Since the fractions have the same denominator, this is easy. 1/5 + 2/5 = 3/5.
5 + 3/5 = 5 & 3/5
Which description is paired with its correct expression?
four less than the quotient of a number cubed and seven, increased by three; 4-2+3
five times the difference of a number squared and six; 5(6-n²)
nine more than the quotient of six and a number cubed, decreased by four; 8+²-4
9+
O twice the difference of nine and a number squared; 2(9-n²)
Answers
The correct pairings are:
a) Four less than the quotient of a number cubed and seven, increased by three: (n³/7) - 4 + 3
b) Five times the difference of a number squared and six: 5(n² - 6)
c) Nine more than the quotient of six and a number cubed, decreased by four: (6/n³) + 9 - 4
d) O twice the difference of nine and a number squared: 2(9 - n²)
The correct pairings of descriptions and expressions are as follows:
Four less than the quotient of a number cubed and seven, increased by three: (n³/7) - 4 + 3
This expression represents taking a number, cubing it, dividing the result by seven, subtracting four, and then adding three.
Five times the difference of a number squared and six: 5(n² - 6)
This expression represents taking a number, squaring it, subtracting six, and then multiplying the result by five.
Nine more than the quotient of six and a number cubed, decreased by four: (6/n³) + 9 - 4
This expression represents taking the cube of a number, dividing six by the cube, adding nine, and then subtracting four.
O twice the difference of nine and a number squared: 2(9 - n²)
This expression represents taking a number, squaring it, subtracting it from nine, and then multiplying the result by two.
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In this Exploration we will use a situation modeled by an exponential function to investigate the rate of change of that function. There will be two different types of rate of change examined, the average rate of change of the function and the instantaneous rate of change of the function. The average rate of change of a function gives information about how the dependent variable of the function changes with respect to the independent variable between two independent values of the function. This can be expressed as the average rate of change off, which is the quantity
f(x)-f(c)/x-c
where x is an independent value of choice and c is a particular value of interest in the domain of f . In what context have you encountered expression (1) in past mathematics classes? 1. What do the average rates of change found in Exercise 3 represent with respect to the rim of the tire and its proximity to the street? 2. We want to find out how fast the rim of the tire is approaching the street at the instant t=3sec. Discuss how using the average rate of change is an approximation but not exact at the instant t=3sec
Answers
1. The average rates of change found in Exercise 3 represent the average speed at which the rim of the tire is moving
towards or away from the street between two specific time intervals.
2. The instantaneous rate of change, which is typically found by taking the derivative of the function and evaluating it at the desired point (t=3 sec in this case).
In past mathematics classes, you may have encountered expression (1) in the context of finding the slope of a secant
line between two points on a curve, which represents the average rate of change of a function.
1. The average rates of change found in Exercise 3 represent the average speed at which the rim of the tire is moving
towards or away from the street between two specific time intervals.
2. Using the average rate of change is an approximation but not exact at the instant t=3sec because it considers the
change over an interval of time rather than at a specific instant.
To find the exact rate at which the rim of the tire is
approaching the street at t=3 sec, we need to calculate the instantaneous rate of change, which is typically found by
taking the derivative of the function and evaluating it at the desired point (t=3 sec in this case).
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3. There are five different tables in the class and five students. Each table can be occupied by only onestudent. Their
studying year consists of 200 days. As a small prank on their teacher students would like to sit in a new way every
day, so there are no two days during their studying year such that all students are occupying the same tables.
They would like to see whether this is possible. How many ways are there for them to sit in the class?
Answers
There are 3,125 different places to sit if they don't mind sharing s desk sometimes and there are 120 different places to sit, if they all sit on separate tables.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given that there are five different tables in the class and five students
Each table can be occupied by only one student
There are 200 days of studying years.
As a small prank on their teacher students would like to sit in a new way every day, so there are no two days during their studying year such that all students are occupying the same tables.
5×4×3×2×1 = 120
There are 120 different places to sit, if they all sit on separate tables.
5×5×5×5×5 = 3,125
There are 3,125 different places to sit if they don't mind sharing s desk sometimes.
Hence, there are 120 different places to sit, if they all sit on separate tables and there are 3,125 different places to sit if they don't mind sharing s desk sometimes.
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Which algebraic expression is equivalent to the expression below?
14x + 4- 6x
A. 4(x + 1)
B. 4(2x + 1)
C. 4(2x - 1)
D..8(x + 1)
Answers
Answer:
4(2x + 1)
Step-by-step explanation:
14x + 4 - 6x
Rearrange the expression with like terms together
14x - 6x + 4
8x + 4
Factorize the expression
4(2x + 1)
Find the inversion point of the given point (4, 5) with respect to the circle x² + y² - 4x - 6y - 3 = 0. Also, show in the graph.
Answers
The inversion point of (4, 5) with respect to the circle x² + y² - 4x - 6y - 3 = 0 is (6, 7).
Finding the inversion pointTo find the inversion point of the given point (4, 5) with respect to the circle x² + y² - 4x - 6y - 3 = 0, we need to follow these steps:
Step 1: Write the equation of the given circle in standard form by completing the square for x and y: (x - 2)² + (y - 3)² = 16.
Step 2: Find the radius of the circle by taking the square root of the constant term: r = √16 = 4.
Step 3: Find the distance between the given point (4, 5) and the center of the circle (2, 3) using the distance formula: d = √[(4 - 2)² + (5 - 3)²] = √8.
Step 4: Use the formula for inversion point to find the coordinates of the inversion point (x', y'): (x', y') = (h + r²/d² * (x - h), k + r²/d² * (y - k)), where (h, k) is the center of the circle and r is the radius.
Plugging in the values, we get: (x', y') = (2 + 4²/8 * (4 - 2), 3 + 4²/8 * (5 - 3)) = (6, 7).
Therefore, the inversion point of the given point (4, 5) with respect to the circle x² + y² - 4x - 6y - 3 = 0 is (6, 7).
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Hi i would like some help with this asap
Answers
The constant of variation for the given graph is 1/4.
What is Slope?Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.
Slope can also be defined as the tangent of the angle that the line is making with the positive X axis.
Given that the equation of the line in the graph is a direct variation equation.
Direct variation equations are of the form,
y = k x, where k is a constant number called constant of variation.
We have to find the value of k.
y = k x is an equation in slope intercept form where k is the slope and the value of y intercept is 0, since the line passes through origin (0, 0).
It is enough to find the slope of the given line.
Take two points from the graph, let it be (4, 1) and (-4, -1).
Slope = (-1 - 1) / (-4 - 4) = -2 / -8 = 1/4
The value of k is 1/4.
Hence the value of constant of variation is 1/4.
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In order to evaluate the performance of the artificial pancreas, a researcher randomly draw 5 rats as a control group, and draw other 5 rats as a treatment group. The control group did not receive the artificial pancreas, the treatment group did. The research wanted to compare the blood-sugar readings for the treatment group with those of the control group. The treatment group has a sample mean blood-sugar reading Y = 400 unit and a standard deviation Si = 80 unit. The control group has a sample mean blood-sugar reading Y, = 200 unit and a standard deviation S2 = 50 unit. Assume the population variances are not equal, calculate the standard error for the difference of the sample means Ý -Y (Round to three decimal places)
Answers
Answer: 42.190
Step-by-step explanation:
From the question, the population variances are not equal. The calculation has been attached in the picture below.
The answer is 42.190 to 3 decimal places.
Use the area to find the radius. If you could include steps that’ll be very helpful :)
Answers
Answer:
Radius = 13 m
Step-by-step explanation:
Formula for area of circle is given as:
\(A = \pi {r}^{2} \\ \\ \therefore \: 169\pi \: = \pi {r}^{2} \\ \\ \therefore \: {r}^{2} = \frac{169\pi }{\pi} \\ \\ \therefore \: {r}^{2} = 169 \\ \\ \therefore \: {r} = \pm \sqrt{169} \\ \\\therefore \: r = \pm \: 13 \: m \\ \\ \because \: radius \: of \: a \: circle \: can \: not \: be \: a \: negative \: \\quantity \\ \\ \huge \red{ \boxed{\therefore \: r = 13 \: m }}\)
1.7 Basil Yamey is setting up a new business. Before selling anything, he bought a van for £9,000; a
transportable market stall for £1,800; a computer for £280; and an inventory of goods for £11,200. Fie
did not pay in full for his inventory of goods and still owes £5,000 for them. Fie borrowed £8,000 from
Luca Pacioli. After the eventsjust described, and before trading starts, he has £900 cash in hand and
£6,300 in the bank. Calculate the amount of his capital.
Answers
Answer:
the amount of Basil Yamey's capital is £16,480.
Step-by-step explanation:
To calculate Basil Yamey's capital, we need to add up the value of his assets and subtract his liabilities.
The value of his assets is:
Van: £9,000
Market stall: £1,800
Computer: £280
Inventory of goods: £11,200
Cash in hand: £900
Money in the bank: £6,300
Total value of assets = £9,000 + £1,800 + £280 + £11,200 + £900 + £6,300 = £29,480
His liabilities are:
Amount still owed for inventory of goods: £5,000
Amount borrowed from Luca Pacioli: £8,000
Total liabilities = £5,000 + £8,000 = £13,000
Therefore, Basil Yamey's capital is:
Capital = Total value of assets - Total liabilities
Capital = £29,480 - £13,000 = £16,480
So the amount of Basil Yamey's capital is £16,480.
Answer:
Basil Yamey's capital is the total amount of money that he has invested in his business. This can be calculated as the sum of the cost of the assets that he has purchased, minus any outstanding debts, plus any cash or cash equivalents he has on hand.
The cost of the assets that Basil has purchased is:
£9,000 (van) + £1,800 (market stall) + £280 (computer) + £11,200 (inventory) = £21,280
He still owes £5,000 for the inventory, so the total cost of the assets minus the outstanding debt is:
£21,280 - £5,000 = £16,280
He borrowed £8,000, so the total amount of his capital is:
£16,280 + £8,000 = £24,280
He also has cash on hand and in the bank:
£900 (cash) + £6,300 (bank balance) = £7,200
So, Basil Yamey's total capital is £24,280 + £7,200 = £31,480.
An airplane travels 550 miles from North Carolina to Tennessee in 90 minutes. At this rate, how many minutes will it take the airplane to travel 6,600 miles?
Answers
Answer:
It will take 1,080 min or 18 hours
Step-by-step explanation:
Here is why, since 6600 miles is 12 times farther than 550 miles you'd multiply the time it took to go 550 miles by 12 too
A consumer group has determined that the distribution of life spans for gas ovens has a mean of 15.0 years and a standard deviation of 4.2 years. The distribution of life spans for electric ovens has a mean of 13.4 years and a standard deviation of 3.7 years. Both distributions are moderately skewed to the right. Suppose we take a simple random sample of 35 gas ovens and a second simple random sample of 40 electric ovens. Suppose we take a simple random sample of 35 gas ovens and a second SRS of 40 electric ovens. Which of the following best describes the sampling distribution of barXG - bar XE, the difference in mean life span of gas and electric ovens?
A. Mean = 1.6 years, standard deviation = 7.9 years, shape: moderately right-skewed.
B. Mean = 1.6 years, standard deviation = 0.92 years, shape: approximately Normal.
C. Mean = 1.6 years, standard deviation = 0.92 years, shape: moderately right skewed.
D. Mean = 1.6 years, standard deviation = 0.40 years, shape: approximately Normal.
E. Mean = 1.6 years, standard deviation = 0.40 years, shape: moderately right skewed.
Answers
Answer:
B. Mean = 1.6 years, standard deviation = 0.92 years, shape: approximately Normal.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction of normal variables:
When we subtract normal variables, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.
35 gas ovens
A consumer group has determined that the distribution of life spans for gas ovens has a mean of 15.0 years and a standard deviation of 4.2 years. This means that:
\(\mu_G = 15, \sigma_G = 4.2, n = 35, s_G = \frac{4.2}{\sqrt{35}} = 0.71\)
40 electric ovens.
The distribution of life spans for electric ovens has a mean of 13.4 years and a standard deviation of 3.7 years.
\(\mu_E = 13.4, \sigma_E = 3.7, n = 40, s_E = \frac{3.7}{\sqrt{40}} = 0.585\)
Which of the following best describes the sampling distribution of barXG - bar XE, the difference in mean life span of gas and electric ovens?
By the Central Limit Theorem, the shape is approximately normal.
Mean: \(\mu = \mu_G - \mu_E = 15 - 13.4 = 1.6\)
Standard deviation:
\(s = \sqrt{s_G^2+s_E^2} = \sqrt{(0.71)^2+(0.585)^2} = 0.92\)
So the correct answer is given by option b.
Write a recursive formula for
Answers
Answer:
\(a(1) = 144\)
\(a(n) = 144{( - \frac{1}{6} )}^{n - 1} \)
\(a(n) = - \frac{1}{6} a(n - 1)\)
25/8 in decimal form
Answers
Answer:
3.125
Step-by-step explanation:
Answer:
25/8 in a decimal form is
Step-by-step explanation:
3.125
Which is true of a population in a statistical survey? Check all that apply.
A population can only be a group of people.
O Apopulation can be a group of objects or events.
O Apopulation can only be a particular event.
O Apopulation must be the target of the survey question.
O Apopulation must be very small.
Answers
Answer:
A population can be a group of objects or events.
A population must be the target of the survey question.
Step-by-step explanation:
I had the same question.
Baby otters born 3/4 of a month early at birth of the week was 78 kg which is 9/10 kg less than the average weight of a newborn otter in the aquarium. What is the average weight of a newborn otter?
Answers
Answer:
Step-by-step explanation:
Baby otter is 9/10 kg less than the average.
PLS HELP WILL GIVE BRAINLIEST IF CORRECT (NO LINKS)
Find the measure of arc BC.
Answers
Answer: A 129
Step-by-step explanation:
Because the 2 chords are the same (lines in the circle), the 2 arcs are the same create an equation that makes them equal
3x+24 = 4x -11 >bring x to one side by subtracting both sides by 3x
24 = x -11 > add both sides by 11
35 = x
Now that we have solved for x you need to plug that back into the equation for BC
BC= 4x-11
BC = 4(35) - 11
BC = 140 - 11
BC = 129 >A
The short run is defined as a period of time where
Select one:
a. some of a firm's inputs are fixed
b. only a small number of firms can enter or exit the industry.
c. the firm always breaks even (earns zero profit).
d. all inputs can be changed, but only for a little while and then must be changed back to their original levels.
Answers
Answer:
q
Step-by-step explanation:
a q q q q q q q q q q qq q qq q q q q q qa q q q q q q q q q q q
What is the answer to 36/(9-4)??
Answers
Answer:
36/(9-4)=7.2
Step-by-step explanation:
You first have to subtract 4 from 9, because it is in the parentheses. The answer is 5, so you have 36/5, which equals 7.2
Answer:
36/5
Step-by-step explanation:
\(\frac{36}{9-4}\\\\\)
Subtract the numbers
\(9-4=5\\\\=\frac{36}{5}\)
What percent of 48 is 20?
Pleaseee
Answers
Answer:
41.6666% is a required percent of 48 is 20
20/48×100%=41.6666%
Use the Factor Theorem to determine whether x-c is a factor of f(x).
f(x)=x^3+4x^2-10x+12; x+6
A. Yes
B. No
Answers
x+6 is a factor of the polynomial, so it is Yes.
What is a Polynomial?Polynomials are algebraic expressions that consist of variables and coefficients.
Any Algebraic expression with degree of it variable grater than 1 is a polynomial.
The degree of the highest variable determines the number of factors that polynomial will have. For example a quadratic expression has two factors.
If x +6 is a factor of the polynomial, x^3+4x^2-10x+12;
Then x = -6.
Using factor theorem,
For x +6 to be a factor, the f(-6) = 0
Substituting x = -6 into the equation,
\((-6)^{3}\) + \(4(-6)^{2}\) -10(-6) + 12 = 0
In conclusion, x+6 is a factor of the polynomial
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prove that, given a nonnegative integer , there is a unique nonnegative integer such that m^2 < sqrt n < (m 1)^2
Answers
It is proved that m = √n.
To prove that given a nonnegative integer n, there is a unique nonnegative integer m, we just need to take the square root of the given equation:
m^2 ≤ n < (m + 1)^2.
So, after taking the square root, it will be:
m ≤ √n < m + 1
From that we can see m = √n is the unique m.
What is a nonnegative integer?A nonnegative integer is an integer which is either positive or zero. It is the union of the natural numbers and the number zero. Occasionally, it is referred to as Z*, and it can be described as the set {0, 1, 2, 3, 4, 5, …}. In other words, nonnegative integers are integers that are not negative.
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Although part of your question is missing, you might be referring to this full question: Prove that given a nonnegative integer n, there is a unique nonnegative integer m such that m^2 ≤ n < (m+1)^2.
Which of the following sentences show correct verb tense usage? Check all that apply. When the facilitator announced a bathroom break, the seminar participants took out their iPhones and begun checking their messages a The overall outlook is favorable, so I wrote to the board chair to inform him. She has wrote him an e-mail
Answers
The sentence which show correct verb tense usage is The overall outlook is favorable.
Verbs are a necessary component of communication in every language, including English, without which it would be difficult to convey what the subject is doing. All acts, including those motivated by sentiments and emotions, are included.
Verbs exist in a variety of forms and kinds so they can function in many ways to convey the whole meaning. Let's have a look at how different dictionaries define the word "verb" before we examine the many kinds of verbs and their forms.
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Solve y = ax² + c for x.
O x
x= ± √ay-c
O
O
x = ±₁
X=
X=
у-с
a
y
y + c
a
Answers
In the quadratic equation y = a\(x^{2}\) + c ,the value of x = ± \(\sqrt \frac{y-c}{a}\)
A quadratic equation is any equation containing one term wherein the unknown is squared and no term wherein it's far raised to a higher power.
A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0, in which a and b are the coefficients, x is the variable, and c is the constant term.
To find the value of x
Assuming \(a\neq o\)
First, subtract c from both the sides to get:
\(y-c=ax^{2}\)
then, divide both sides by \(a\) and transpose to get:
\(x^{2} =\frac{y-c}{a}\)
So, \(x\) must be a square root of \(\frac{y-c}{a}\) and we can deduce:
\(x=\) ± \(\sqrt \frac{y-c}{a}\)
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PLEASE HELP THIS IS DUE & I DON'T UNDERSTAND AND FEEL LIKE GARBAGE: On the coordinate plane shown, each grid unit represents 10 feet. Polygon QRST has vertices Q(10, 20), R(−10, 20), S(−10, −10), and T(10, −10), and represents the floor plan of a room. Find the perimeter and area of the room.
The perimeter of the room is
feet. The area of the room is
square feet.
Answers
Answer:
perimeter is the length of all sides added together, since this a square and one side is 20 length, all sides must be 20 length. 20 + 20 + 20 + 20 = 80
The area is the length times width. 20 * 20 is 400.
Step-by-step explanation:
Dan had sixteen dimes and thirty-seven pennies in his bank. His dad borrowed nineteen pennies from Dan. How many pennies does he have now ?
Answers
Answer:
if he had 37 pennies and his dad borrowed 19 it means that he has 18 pennies left.
Which velocity vs. time graph corresponds to the data represented by the position vs. time graph?
A graph with horizontal axis time (seconds) and vertical axis position (meters). A line runs straight upward from 0 seconds 0 minutes.
A graph labeled velocity versus time with horizontal axis time (seconds) and vertical axis velocity (meters per second). A straight line begins at 0 seconds 10 meters per second and runs to 5 seconds 2 meters per second.
Answers
Answer: Its D Hope I Helped !!
Step-by-step explanation:
Mark Me Brainliest If you would
Answer:
b
Step-by-step explanation:
If my dot plot is not skewed or symmetrical which measure of variability should I use? (15 data points) PLEASE HELP THE ASSIGNMENT IS DUE TONIGHT!
these are the data points: 5,6,7,7,7,8,8,9,9,9,9,9,10,10,11
I also need the best measure of center!
Answers
If the data is not skewed, then the mean is the best measure of center.
This then also includes the standard deviation because the standard deviation relies on the mean.
To get the mean, add up the data values:
5+6+7+7+7+8+8+9+9+9+9+9+10+10+11 = 124
Then divide by the sample size n = 15
124/n = 124/15 = 8.267 approximately
Once you determine the mean, you can then determine the standard deviation which involves a bit more complicated steps. The rough outline is:
Subtract each data value from the mean. So right off the bat, we can see how important the mean is when it comes to calculating the standard deviation.Square those differences from step one.Add up the squares to get the Sum of the Squared Errors (SSE)Divide the SSE by n-1 to get the sample variance, or divide by n to get the population variance. It will depend on context which version you go for.Apply the square root to the variance to get the standard deviation.Once again, step 1 shows how critical the mean is to finding the standard deviation. The standard deviation measures how far each value is from the mean on average. In other words, it's like a measure of the average distance from the mean.
Use of spreadsheet software is strongly recommended to keep track of everything. You can also use a standard calculator to compute the standard deviation. There are also tons of free online calculators that can help out with that as well.
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If the data was skewed to one side, then the median is the better measure of center because it is not affected by outliers. The IQR (interquartile range) is used instead of the standard deviation for skewed distributions.
Which expression have a quotient of 3/4?
Answers
Answer:
we need answers please
Step-by-step explanation:
Answer:
Step-by-step explanation: