Answer:
width = 6k², length = 5k + 1
Step-by-step explanation:
Given
A = 30k³ + 6k² ← factor out 6k² from each term
= 6k²(5k + 1)
Since area = width × length , then
width = 6k² and length = 5k + 1
Answer:
30k³ + 6k²
= 6k²(5k + 1)
because the width is equal to the greatest common monomial factor of 30k³ and 6k²
=> the width = 6k²
=> the length = 6k²(5k+1)/6k² = 5k + 1
Step-by-step explanation:
which sum is equivalent to 7/9 + 5/6?
Answer:
The Answer is 29/18 and in mixed form it is 1 11/18
Step-by-step explanation:
Steps for adding fractions
Find the least common denominator or LCM of the two denominators:
LCM of 9 and 6 is 18
Next, find the equivalent fraction of both fractional numbers with denominator 18
For the 1st fraction, since 9 × 2 = 18,
7
9
=
7 × 2
9 × 2
=
14
18
Likewise, for the 2nd fraction, since 6 × 3 = 18,
5
6
=
5 × 3
6 × 3
=
15
18
Add the two like fractions:
14
18
+
15
18
=
14 + 15
18
= 29/18
So, 7/9 + 5/6 = 29/18
In mixed form: 1 11/18
What is 8,743 divided by 4
Answer:
2185 \(\frac{3}{4}\)
Step-by-step explanation:
Question:
What is 8,743 divided by 4?
Explanation:
Heya, I heard you need help! Well, let me explain for ya! c:
Step 1: Divide.
- First, you would write down the division problem using long division, let me show you how:
1. Write it down in long division form.
2. 4 can go into 8 2 times, so subtract that by 8 to get a difference of 0.
3. Subtract 8 by 8 and get a difference of 0.
4. 4 cannot go into 0, so bring down the 7.
5. 4 goes into 7 1 time, so you would subtract 7 by 4 to get a difference of 3.
6. 4 cannot go into 3, so bring down the 4.
7. 4 goes into 34 8 times, so you would subtract 34 by 32 to get a difference of 2.
8. 4 does not go into 2, so bring down the 3.
9. 4 goes into 23 5 times, so you subtract 23 by 20 to get a difference of 3.
10. 4 does not go into 3, so you bring down an imaginary 0 and add a decimal on the left of the 3 in 8743.
11. 4 goes into 30 7 times as 7 times 4 is 28, so subtract 30 by 28 to get a difference of 2.
12. Finally, you bring down another 0 as 4 cannot go into 2. Then, you subtract 20 by 20 to get 0.
- Your quotient is 2185.75.
Step 2: Converting to a mixed number.
- This is the easiest part. All you have to do is convert 75/100 into simplest form as 75/100 is the decimal in fraction form. This will get you 3/4.
- Then, you would write 2185 \(\frac{3}{4}\).
Therefore, your answer is 2185 \(\frac{3}{4}\)
Also, sorry about that book for a math problem.
Hope that helped! If you have anymore questions, just comment down and I will try my best to help you! Au revoir!
~ Sienna
How do you find the domain?
The domain of a function is the set of numbers that can go into a given function.
The set of input values (x) for which a function generates an output value is known as the domain of the function (y).
we can write \(y = f(x).\)
domain is the full set of x-values that can be plugged into a function to produce a y-value.
The most effective approach to finding a domain will depend on the type of function.
The domain is expressed using an open bracket or parenthesis, the domain's two endpoints separated by a comma, and then a closed bracket or parenthesis.
To find domain of function we should know the property of that function like what the function can take inside it.
Like if we consider square root function \(\sqrt{x}\) so inside root negative numbers are not allowed so value of x should be positive means x>=0
So domain of square root function [0, ∞).
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Evaluate the expression p 3 2 q 4 1 3r 4 2 for p 5 6, q 5 2, and r 5 4. Show your work.
Answer:
206
Step-by-step explanation:
p³ - q^4 + 3r ÷ 2
(6)³ - (2)^4 + 3(4) ÷ 2
216 - 16 + 12 ÷ 2
216 - 16 + 6
200 + 6
206
I hope this helps!
Determine which regions contain cube roots of −1. Check all that apply.
on real axis
on imaginary axis
quadrant 1
quadrant 2
quadrant 3
quadrant 4
cube roots of -1 lies in the region given in the best options are A. on real axis, B. quadrant 1, F. quadrant 4.
What is cube roots of -1?
Cube roots of -1 mean "finding solution of the equation z³ = -1 since the equation is of order 3, the equation has 3 roots in complex field."
According to the question,
Cube roots of -1 can written as \((-1)^\frac{1}{3}\)
First, write the given number in polar form
\(x = ( cos 0 - i sin 0)^\frac{1}{3}\)
Add 2kπ to the argument
\(x = (cos2k\pi - i sin 2k\pi )^\frac{1}{3}\)
Apply De Moivre's theorem
\((cos\alpha - i sin\alpha) = cosn\alpha + i sin\alpha\)
x = \(\frac{2k\pi }{3} - i sin\frac{2k\pi }{3}\)
Put k = 0,1,2..., (n-1) [sin (-θ) = -sin θ, cos(-θ) = cos θ]
The three roots are
cos 0 - sin 0, cos \(\frac{2\pi }{3}\), \(i sin\frac{2\pi }{3}\) , cos \(\frac{4\pi }{3}\), \(i\)sin\(\frac{4\pi }{3}\)
-1, \(-\frac{1}{2} ,- i \frac{\sqrt{3} }{2}, -\frac{1}{2} , +\frac{\sqrt{3} }{2}\) , are the three roots of cube roots of -1
It can be seen that the three roots lies in the regions of real axis, quadrant 1 and quadrant 4.
Hence, cube roots of -1 lies in the region given in the best options are A. on real axis, B. quadrant 1, F. quadrant 4.
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Solve the system of linear equations by graphing.
y equals negative one half times x plus 2
y equals one half times x minus 1
negative 3 comma one half
one half comma 3
one half comma negative 3
3 comma one half
Answer:
Give brainliest to the other person they deserve it
Step-by-step explanation:
a professor at a local university noted that the exam grades of her students were normally distributed with a mean of 65 and a standard deviation of 18. according to the professor's grading scheme only the top 12.3 percent of her students receive grades of a. what is the minimum score needed to receive a grade of a?
The minimum score needed to receive a grade of A is approximately 86.06.
To find the minimum score needed to receive a grade of A, we need to determine the cutoff point that corresponds to the top 12.3 percent of students in a normal distribution with a mean of 65 and a standard deviation of 18.
First, we need to find the z-score associated with the top 12.3 percent.
The z-score represents the number of standard deviations a data point is from the mean.
Using a standard normal distribution table or a calculator, we can find the z-score that corresponds to the top 12.3 percent.
The z-score is approximately 1.17.
Next, we can use the formula for z-score conversion to find the corresponding score value:
z = (x - μ) / σ
Rearranging the formula to solve for x (the score):
x = z * σ + μ
Plugging in the values:
x = 1.17 * 18 + 65
x ≈ 86.06
Therefore, the minimum score needed to receive a grade of A is approximately 86.06.
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candice scored 74 on an exam that had normally distributed results with a mean of 66 and a standard deviation of 4. erin scored 58 on an exam that had normally distributed results with a mean of 42 and a standard deviation of 7. who scored better?
Candice's z-score is lower than Erin's z-score, this means that Candice performed better relative to the rest of her peers than Erin did relative to hers. Therefore, Candice scored better on the exam than Erin did.
To explain, we can use the concept of z-scores, which allow us to compare scores from different normal distributions. The z-score for Candice's score of 74 is calculated as: z = (74 - 66) / 4 = 2
This means that Candice's score is two standard deviations above the mean for her exam. The z-score for Erin's score of 58 is calculated as: z = (58 - 42) / 7 = 2.29
This means that Erin's score is 2.29 standard deviations above the mean for her exam. Hence, Candice scored better on the exam.
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Can anyone help me with this?
Answer:
Step-by-step explanation:
The average of a sample of high daily temperature in a desert is 114 degrees F, a sample standard deviation or 5 degrees F, and 26 days were sampled. What is the 90% confidence interval for the average temperature? Please state your answer in a complete sentence, using language relevant to this question.
In a sample of 26 days from the desert, the average of the high daily temperature is 114 degrees F, and the sample standard deviation is 5 degrees F.
To determine the 90% confidence interval for the average temperature, we can use the t-distribution as follows:To find the critical value of t, we can use the t-table. Since our sample has n = 26, the degrees of freedom (df) are n - 1 = 25. At a confidence level of 90%, with 25 degrees of freedom, the critical t-value is 1.708.The standard error of the mean is calculated as s / sqrt(n), where s is the sample standard deviation and n is the sample size. Therefore, the 90% confidence interval for the average temperature is (114 - 1.67, 114 + 1.67), or (112.33, 115.67) degrees F.
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11) Forty percent of the homes constructed in the Quail Creek area include a security system. Three homes are selected at random: 1. What is the probability all three of the selected homes have a security system? 2. What is the probability none of the three selected homes have a security system? 3. Did you assume the events to be dependent or independent?
Answer:
1) Pr(all three) = 0.064
2) Pr(none) = 0.216
3) Independent event
Step-by-step explanation:
Let Probability of homes constructed in the Quail Creek area with a security system = Pr (security)
Where Pr = probability
This is a binomial distribution problem. There ate only two outcomes in this distribution: a success and a failure
Where p = success, q = failure
For n trials,
Pr(X = x) = n!/[(n-x)!x!] × p^x × q^(n-x)
Pr (security) = 40% = 0.4
p = 0.4
q = 1-p = 1-0.4 = 0.6
Numbers selected at random = n = 3
See attachment for more details on the workings.
1) Probability all three of the selected homes have a security system = Pr(all three)
Pr(all three) = 1× (0.4)³ (0.6)^0 = 0.4³
= 0.4×0.4×0.4
Pr(all three) = 0.064
2) Probability none of the three selected homes have a security system
= Pr(none)
Pr(none) = 1 × (0.4)^0 × (0.6)³
= 0.6³ = 0.6×0.6×0.6
Pr(none) = 0.216
3) The events were assumed to be independent as the selection of one house doesn't affect the outcome of the selection of another.
which of the following would be a correct interpretation of a 99% confidence interval such as 4.15.6? question content area bottom part 1 choose the correct answer below. a. it means that 99% of sample means fall between 4.1 and 5.6. b. we are 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of . c. there is a 99% chance that will fall between 4.1 and 5.6. d. it means that 99% of a
We are 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of mu.
The correct interpretation of a 99% confidence interval is that we are 99% confident that the true population mean falls in it.
The probability that it contains the true population mean is 99%.
Given 99% confidence interval : 4.1 < μ < 5.6
Then, the correct interpretation is we are 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of mu.
Hence the answer is We are 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of mu.
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Down the street, Smiley Face Foods has 24 pound watermelons on sale for $3.99. What is the unit rate for watermelon at this store? Which store has the better deal on watermelon?
Answer:
1 pound of watermelon is approximately $0.17 ($0.16625).You must've forgot to add the rest of the problem because there is no other store included
Step-by-step explanation:
CAN SOMEONE HELP ME #faqgeometry
18. 19.20. 21.
Answer:
Yes
Step-by-step explanation:
So I assume the question is asking if the lines AC and DF are parallel and they are because if you graphed it out you would see the lines would never touch (Basically what a parellel line is).
Counting jails and prisons, approximately how many citizens are incarcerated? a. 1 million b. 2.3 million c. 3 million d. 4.3 million.
In September 2021, the approximate number of citizens incarcerated in jails and prisons is around 2.3 million.
It is important to note that this figure can vary over time due to changes in policies, criminal justice reforms, and other factors. The incarcerated population includes individuals who have been convicted of crimes and are serving their sentences, as well as those who are awaiting trial or have been sentenced but not yet transferred to a correctional facility.
These numbers can vary between different countries and jurisdictions. To obtain the most accurate and up-to-date information on current incarceration rates, it is advisable to refer to official sources such as the U.S. Bureau of Justice Statistics or relevant governmental organizations in your country.
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maria has books that she wants to arrange in piles. the books have different thicknesses. this line plot shows the thickness of each book. she piles the four thinnest books on top of each other. how thick is the pile?
Once we have identified these lines, we can add up their corresponding thickness values to find the thickness of the pile.
Therefore, the answer to the question is dependent on the specific thickness values of the four thinnest books on the line plot.
Maria has books of varying thicknesses, and a line plot has been provided to show the thickness of each book.
The question asks how thick the pile of the four thinnest books will be when they are stacked on top of each other.
To determine the thickness of the pile, we will need to find the total thickness of the four thinnest books on the line plot. We can do this by adding up the thicknesses of each of these four books.
Then, we will have the total thickness of the pile.
To make sure we have the correct four books, we will need to start from the left side of the line plot and select the four shortest lines.
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if h(z)=2z2-5z+7, find h(3c)
Answer: h(3c) = 18c2 - 15c + 7
Step-by-step explanation:
h(z) = 2z2 - 5z + 7
To find h(3c), replace each z with 3c.
h(3c) = 2(3c)2 - 5(3c) + 7
Now just simplify.
h(3c) = 2(9c2) - 5(3c) + 7
h(3c) = 18c2 - 15c + 7
See attachment for math work and answer.
Plz help me
will give the brainliest!
Urgent!!!
Please answer correctly
Please help me!!
Step-by-step explanation:
1-a ,2-c,3_d
i thibk is you're answer
the clock is showing 8:00 am. what is the angle of the hour hand starting at 12 going counterclockwise to 8 in radian?
The angle between two pointers say, no. 12 and no. 8 in a clock is 120° or 2.094 radians.
According to given question, we can say clock is showing 8:00 am. At 8'o clock the two pointers will just touch the no. 12 and no. 8. In a clock at the centre angle 360° must be divided into 12 equal or similar sections. The value of angle for each section in clock is 360° / 12 = 30° .
The counting of angle is always anti clock wise direction so , at 12 the two pointers postion is 360° .. As time passes the angle0 reduces each section ( 1 hour ) by 30° ..as every hours one pointers remains at no. 12 ..
At 8'o clock 8 such sections reduced .
Now, the angle between two pointers is 360° - 8× 30 = 360° - 240° = 120°..
Using the formula for reducing degree to radians , 1 degree = π / 180° radians
=> 120 ° × π / 180° radians = 2.094 radians .
Thus, the angle between two pointers no. 12 and no. 8 is 2.094 radians.
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find two consecutive natural numbers whose sum is 23
Answer:
Step-by-step explanation:
11 and 12
find the value of the expression 0.01y^4 if y=3
Answer:
0.81
Step-by-step explanation:
\(0.01 \times {3}^{4} = 0.01 \times 81 = 0.81\)
an oil storage tank can be described as the volume generated by revolving the area bounded by about the x-axis. find the volume of the tank (in cubic meters). round to four decimal places.
The volume of the tank can be found using the given information as:\(Volume=\int\limits^b_a {\pi f(x)^2} \, dx\)
How to find the volume of the tank?Assuming that the area bounded is given by a function f(x), the volume of the oil storage tank can be calculated using the formula for the volume of a solid of revolution:
\(Volume=\int\limits^b_a {\pi f(x)^2} \, dx\)
where a and b are the limits of integration. In this case, the axis of revolution is the x-axis, so we are revolving the area about the x-axis.
Therefore, the volume of the tank can be found using the given information as:
\(Volume=\int\limits^b_a {\pi f(x)^2} \, dx\)
We need more information about the function f(x) or a curve that bounds the area in order to find the limits of integration and calculate the volume.
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Find the absolute (i.e., global) maximum and absolute minimum values of the function f(x) = 8x/6х + 4 on the interval (1,5) Absolute maximum = Absolute minimum =
The absolute maximum value is 20/17, which occurs at x = 5, and the absolute minimum value is 4/5, which occurs at x = 1.
To find the absolute maximum and minimum values of the function f(x) = 8x/(6x + 4) on the interval (1, 5), we need to find the critical points of the function within the interval and evaluate the function at those points, as well as at the endpoints of the interval.
First, let's find the derivative of the function:
f(x) = 8x/(6x + 4)
f'(x) = [8(6x + 4) - 8x(6)] / (6x + 4)^2
f'(x) = [8(2)] / (6x + 4)^2
f'(x) = 16 / (6x + 4)^2
The critical points occur when f'(x) = 0 or is undefined. However, since f'(x) is always positive on the interval (1, 5), there are no critical points within the interval.
Next, let's evaluate the function at the endpoints of the interval:
f(1) = 8(1)/(6(1) + 4) = 8/10 = 4/5
f(5) = 8(5)/(6(5) + 4) = 40/34 = 20/17
Finally, we need to determine which of these values is the absolute maximum and which is the absolute minimum.
Since f(x) is always positive on the interval (1, 5), the function can never be less than 0. Therefore, the absolute minimum value is the smallest value of f(x) on the interval, which occurs at x = 5, where f(5) = 20/17.
To find the absolute maximum value, we compare the values of f(1), f(5), and the maximum value of f(x) as x approaches the endpoints of the interval. We can use the fact that the function is continuous on the closed interval [1, 5] to find the maximum value.
As x approaches 1, we have:
f(x) = 8x/(6x + 4) → 8/10 = 4/5
As x approaches 5, we have:
f(x) = 8x/(6x + 4) → 40/34 = 20/17
Therefore, the absolute maximum value is 20/17, which occurs at x = 5, and the absolute minimum value is 4/5, which occurs at x = 1.
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A market stall has 13 bags of apples, and 11 loose apples on display. In
total there are 141 apples at the stall. How many apples are in each bag?
Answer:
10 apples
Step-by-step explanation:
141-11 is 130. it says there are 11 loose apples on display. in total, there are 130 apples in the bag
we know that there are 13 bags of apples. so 130/13 is 10. there are 10 apples in each bag
What is the slope for the graph shown? Leave he answer as a fraction and simplify if necessary
Answer:
Slope 1/3
Step-by-step explanation:
Hope this helps! Please let me know if you need more help or think my answer is incorrect. Brainliest would be MUCH appreciated. Have a wonderful day!
Answer:
slope = \(\frac{1}{3}\)
Step-by-step explanation:
calculate the slope m using the slope formula
m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)
with (x₁, y₁ ) = (3, - 1) and (x₂, y₂ ) = (9, 1) ← 2 points on the line
m = \(\frac{1-(-1)}{9-3}\) = \(\frac{1+1}{6}\) = \(\frac{2}{6}\) = \(\frac{1}{3}\)
5. Suppose X 1and X 2are random variables with mean 10,20 respectively, and SDs 2, 3 respectively.
Let T=11X 1−2X2
Find the mean and SD of T when X 1and X 2are independent.
Find the mean and SD of T when X1and X 2 have correlation of
−0.76
In the case that X1and X 2 are independent, normally distributed
variables, find P(T>30)
The mean of T is -10 and the standard deviation of T is √425 when X1 and X2 are independent.
To find the mean of T, we can use the properties of expected values. Since T = 11X1 - 2X2, the mean of T can be calculated as follows: E(T) = E(11X1) - E(2X2) = 11E(X1) - 2E(X2) = 11(10) - 2(20) = -10. To find the standard deviation of T, we need to consider the variances and covariance of X1 and X2. Since X1 and X2 are independent, the covariance between them is zero. Therefore, Var(T) = Var(11X1) + Var(-2X2) = 11^2Var(X1) + (-2)^2Var(X2) = 121(2^2) + 4(3^2) = 484 + 36 = 520. Thus, the standard deviation of T is √520, which simplifies to approximately √425. When X1 and X2 have a correlation of -0.76, the mean and standard deviation of T remain the same as in the case of independent variables. To calculate the probability P(T > 30) when X1 and X2 are independent, normally distributed variables, we need to convert T into a standard normal distribution. We can do this by subtracting the mean of T from 30 and dividing by the standard deviation of T. This gives us (30 - (-10))/√425, which simplifies to approximately 6.16. We can then look up the corresponding probability from the standard normal distribution table or use statistical software to find P(T > 30). The probability will be the area under the standard normal curve to the right of 6.16.
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A dozen eggs cost 1.50$. How much will 18 eggs cost at the same rate?
Answer:
$2.25
Step-by-step explanation:
A dozen = 12 eggs = $1.50
1 egg = 1.5 / 12 = 0.125
18 eggs = 0.125 * 18
= $2.25 = 1 1/2 dozen
HURRY!!!!!
What is the solution to -2(8x - 4) < 2x + 5?
O x> 1 / 2
0 x < 1/16
O x>6
O x < 6
Answer:
O x>6Step-by-step explanation:
Answer:
C. O×>6
Hope this helps:)
A tunnel is constructed with a semielliptical arch. The width of the tunnel is 70 feet, and the maximum height at the center of the tunnel is 20 feet. What is the height of the tunnel 10 feet from the edge? round your answer to the hundredths place.
Considering the equation of an ellipse, it is found that the height of the tunnel 10 feet from the edge is of 14 feet.
The following is the equation for a horizontal ellipse of center with coordinates (h,k):
(x - h)²/a² + (y - k)²/b² = 1.
In relation to this issue, we have that:
The origin is where the center is.
Since the major axis is 70, 2a = 70 and a = 35.
The maximum height is 20, therefore b is equal to 20.
As a result, the ellipse's equation is as follows:
x²/35² + y²/20² = 1.
It is determined that x = 25 when the tunnel is 10 feet from the edge since 35 – 10 = 25; therefore, the height y is calculated as follows:
25²/35² + y²/20² = 1
0.51 + y²/20² = 1
y²/20² = 0.49
y² = 20² x 0.49
y =√(20² x 0.49)
y = 14 feet.
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i need help with this
Answer:
I believe it's the third option
I could be wrong, so sorry if it's not correct.
Step-by-step explanation: