Answer
-25x² + 100x - 412
Step-by-step explanation
Given the division:
\((-25x^3-1648-12x)\div(x+4)\)Reordering the terms in the dividend:
\((-25x^3-12x-1648)\div(x+4)\)Completing the terms in the dividend:
\((-25x^3+0x^2-12x-1648)\div(x+4)\)The synthetic division is calculated as follows:
The degree of the quotient is one less than the degree of the dividend (which is 3). Then the degree of the quotient will be 2. Using the coefficients obtained in the synthetic division, the result of the division is:
\(-25x^2+100x-412\)
a bus arrives at 2:30 p.m. in Sydney if it left port if it left port Macquarie at 6.15 a.m the trip took
Answer:
Step-by-step explanation
Left at 6:15 am
How many hours until 2:15pm? 8 hours
How many minutes from 2:15 until 2:30? 15
So it took 8 hours and 15 minutes
10. If eight men can dig 10 ditches in an hour. How many men would be
required to dig 16 ditches?
Answer:
12.8
Step-by-step explanation:
they can dig at a rate of 1.25
Find the volume of a sphere with a surface
area of 16 square feet. Round your answer
to the nearest hundredth.
The volume is about
cubic feet.
The approximate volume of the sphere is 6.01 ft³.
What is the volume of the sphere?A sphere is simply a three-dimensional geometric object that is perfectly symmetrical in all directions.
The volume of a sphere is expressed as:
Volume = (4/3)πr³
Where r is the radius of the sphere and π is the mathematical constant pi (approximately equal to 3.14).
Given that the surface area of the sphere is 16 square feet.
First, we determine the radius r:
Surface area = 4πr²
Hence
16 = 4πr²
Dividing both sides by 4π, we get:
r² = 16/4πr
r = √( 16/4πr )
r = 1.128 ft
Plugging in the value of r that we just found, we get:
Volume = (4/3)πr³
Volume = (4/3) × 3.14 × (1.128 ft)³
Volume = 6.01 ft³
Therefore, teh volume is 6.01 ft³.
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The area of a triangle is 30sq. the perimeter of the triangle is 10in. write an inequality that represents the missing side of the triangle.
Is it supposed to be 30 divided by 10?
HELP
Nico did 78 sit-ups in 2 minutes.
What is the Unit Rate?
sit-ups per minute
At this rate, how many sit-ups can Nico do in 5 minutes?
78 sit ups in 2 minutes
so
= 78 : 2 sits in 1 minute = 39 sits up per minute
x 5 = 195 sit ups in 5 minutes
Answer: 39 situps per time
Step-by-step explanation:
Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes, and one vertex in the plane.
The volume of the largest rectangular box in the first octant with three faces in the coordinate planes, and one vertex in the plane is V = xyz, where x, y, and z are the lengths of the sides of the rectangular box.
To find the largest volume, we need to maximize x, y, and z. Since we have three faces in the coordinate planes, one vertex will be at the origin (0, 0, 0). The other two vertices will lie on the coordinate axes.
Let's assume the vertex on the x-axis is (x, 0, 0), and the vertex on the y-axis is (0, y, 0). The third vertex on the z-axis will be (0, 0, z). Since the box is in the first octant, all the coordinates must be positive.
To maximize the volume, we need to find the maximum values for x, y, and z within the constraints. The maximum values occur when the box touches the coordinate planes. Therefore, the maximum values are x = y = z.
Substituting these values into the volume formula, we get V = xyz = x³. Therefore, the volume of the largest rectangular box is V = x³.
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What is the maximum volume of a rectangular box situated in the first octant, with three of its faces lying on the coordinate planes, and one of its vertices located in the plane?
Two times a number plus one is at least seven
Answer:
x ≥ 3
Step-by-step explanation:
Sentence to Algebra:Two times a number = 2x
Plus one = + 1
At least 7 = ≥ 7
Algebraic Equation: 2x + 1 ≥ 7
Solve for x:2x + 1 ≥ 7 \(\longmapsto\) Subtract 1 from both sides
2x + 1 - 1 ≥ 7 - 1
2x ≥ 6 \(\longmapsto\) Divide both sides by 2
2x ÷ 2 ≥ 6 ÷ 2
x ≥ 3
-Chetan k
plz help me! Brainlist! Thx! :)
Answer:
1: 6 5/6
Step-by-step explanation:
Write the equation in point-slope
form of a line that passes through
(1, -3) with a slope of 4.
Answer:
b
Step-by-step explanation:
determine which equations have the same solution set as startfraction 2 over 3 endfraction minus x plus startfraction 1 over 6 endfraction equals 6 x. – x
The equation 2/3 - x + 1/6 = 6x - x has the same solution set as the equation x = 5/36.
To determine which equations have the same solution set as the given equation, let's simplify and rearrange the terms.
Starting with the given equation:
2/3 - x + 1/6 = 6x - x
We can simplify the left side by finding a common denominator for 2/3 and 1/6, which is 6:
(4/6) - x + (1/6) = 6x - x
Combining like terms on the left side gives us:
(5/6) - x = 6x - x
Further simplifying, we can combine the x terms on the right side:
(5/6) - x = 5x
To isolate the x term on one side, we can add x to both sides:
(5/6) = 6x
Next, we can divide both sides by 6 to solve for x:
5/36 = x
Therefore, the equation 2/3 - x + 1/6 = 6x - x has the same solution set as the equation x = 5/36. Any equation that simplifies and rearranges to x = 5/36 will also have the same solution set as the given equation.
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Indicate whether the line on the graph is a function
The line on the graph is a function
How to determine if the line is a function?The given parameter is the graph
From the graph, we can see that the curve or the line is a quadratic function
As a general rule, all lines represented by a quadratic function are functions
This implies that the line is a function
It should be noted that:
Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
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the total cost of the tiles is £68 plus VAT
the rate of VAT is 20%
(b) work out 20% of £52
Answer:
a) 81-6
b) 10.4
Step-by-step explanation:
a) assuming that the VAT is 20% of the 68 pounds,
you calculate 120% of 68 (convert percentage to decimal)
= 1,20 * 68 = 81.6 pounds
or
calculate 20% of 68 pounds and add the answer to 68 pounds:
(0.2 * 68) + 68 = 81.6 pounds
b) 20% of 52
first convert the percentage to decimals:
0.2 * 52 = 10.4 pounds
Help please I don’t understand
Answer:
oye me puedes ayudar a mi tarea
es del cuento el príncipe feliz
What is the value of y?
Answer:
60
Step-by-step explanation:
60+60+y=180 (angle sum property )
120+y=180
y=180-120
y=60
Which of the following expressions is equal to =
Answer:
4th option
Step-by-step explanation:
Remember the Quotient Rule:
\(\frac{x^{m} }{x^{n} } =x^{m-n}\)
6-2 = 4
So it is the last option
1+1= (WILL GET BRAINLIST TO ANWSER FIRST)
Answer:
2
Step-by-step explanation:
one cookie plus one cookie is two cookies
A sociologist claims the probability that a person picked at random in Grant Park in Chicago is visiting the area is 0.44. You want to test to see if the proportion different from this value.
To test the hypothesis that the proportion is different from the given value, a random sample of 15 people is collected.
• If the number of people in the sample that are visiting the area is anywhere from 6 to 9 (inclusive) , we will not reject the null hypothesis that p = 0.44.
• Otherwise, we will conclude that p 0.44.Round all answers to 4 decimals.1. Calculate a = P(Type I Error) assuming that p = 0.44. Use the Binomial Distribution.
2. Calculate B = P(Type II Error) for the alternative p = 0.31. Use the Binomial Distribution.
3. Find the power of the test for the alternative p = 0.31. Use the Binomial Distribution.
1. The probability of making a Type I error is 0.1118.
To calculate the probability of Type I error, we need to assume that the null hypothesis is true.
In this case, the null hypothesis is that the proportion of people visiting Grant Park is 0.44.
Therefore, we can use a binomial distribution with n = 15 and p = 0.44 to calculate the probability of observing a sample proportion outside of the acceptance region (6 to 9).
The probability of observing 0 to 5 people visiting the area is:
P(X ≤ 5) = Σ P(X = k), k=0 to 5
= binom.cdf(5, 15, 0.44)
= 0.0566
The probability of observing 10 to 15 people visiting the area is:
P(X ≥ 10) = Σ P(X = k), k=10 to 15
= 1 - binom.cdf(9, 15, 0.44)
= 0.0552
The probability of observing a sample proportion outside of the acceptance region is:
a = P(Type I Error) = P(X ≤ 5 or X ≥ 10)
= P(X ≤ 5) + P(X ≥ 10)
= 0.0566 + 0.0552
= 0.1118
Therefore, the probability of making a Type I error is 0.1118.
2.The probability of making a Type II error is 0.5144.
To calculate the probability of Type II error, we need to assume that the alternative hypothesis is true. In this case, the alternative hypothesis is that the proportion of people visiting Grant Park is 0.31.
Therefore, we can use a binomial distribution with n = 15 and p = 0.31 to calculate the probability of observing a sample proportion within the acceptance region (6 to 9).
The probability of observing 6 to 9 people visiting the area is:
P(6 ≤ X ≤ 9) = Σ P(X = k), k=6 to 9
= binom.cdf(9, 15, 0.31) - binom.cdf(5, 15, 0.31)
= 0.5144
The probability of observing a sample proportion within the acceptance region is:
B = P(Type II Error) = P(6 ≤ X ≤ 9)
= 0.5144
Therefore, the probability of making a Type II error is 0.5144.
3. The power of the test is 0.4856.
The power of the test is the probability of rejecting the null hypothesis when the alternative hypothesis is true. In this case, the alternative hypothesis is that the proportion of people visiting Grant Park is 0.31.
Therefore, we can use a binomial distribution with n = 15 and p = 0.31 to calculate the probability of observing a sample proportion outside of the acceptance region (6 to 9).
The probability of observing 0 to 5 people or 10 to 15 people visiting the area is:
P(X ≤ 5 or X ≥ 10) = P(X ≤ 5) + P(X ≥ 10)
= binom.cdf(5, 15, 0.31) + (1 - binom.cdf(9, 15, 0.31))
= 0.0201
The power of the test is:
Power = 1 - P(Type II Error)
= 1 - P(6 ≤ X ≤ 9)
= 1 - 0.5144
= 0.4856
Therefore, the power of the test is 0.4856.
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For the function below find a) the critical numbers; b) the open intervals where the function is increasing, and c) the open intervals where it is decreasing f(x)=8x³-42x-48x + 4 a) Find the critical number(s). Select the correct choice below and, if necessary fill in the answer box to complete your choice. A. The critical number(s) is/are (Type an integer or a simplified fraction. Use a comma to separate answers as needed
A) Function is increasing on (-∞, -1) and (7/2, ∞), and decreasing on (-1, 7/2).
b) The local minimum value of f is; 5608/2197 at x = -42/13, and the local maximum value of f is 139/8 at x = 7/2.
(a) To determine the intervals on which f is increasing or decreasing, we need to determine the critical points and then check the sign of the derivative on the intervals between them.
f(x)=8x³-42x-48x + 4
f'(x) = 24x² - 90
Setting f'(x) = 0, we get
24x² - 90 = 0
24x² = 90
x =± √3.75
So, the critical points are;
x = -1 and x = 7/2.
We can test the sign of f'(x) on the intervals as; (-∞, -1), (-1, 7/2), and (7/2, ∞).
f'(-2) = 72 > 0, so f is increasing on (-∞, -1).
f'(-1/2) = -25 < 0, so f is decreasing on (-1, 7/2).
f'(4) = 72 > 0, so f is increasing on (7/2, ∞).
Therefore, f is increasing on (-∞, -1) and (7/2, ∞), and decreasing on (-1, 7/2).
(b) To determine the local maximum and minimum values of f, we need to look at the critical points and the endpoints of the interval (-1, 7/2).
f(-1) = -49
f(7/2) = 139/8
f(-42/13) = 5608/2197
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If a" = 6", then n logax = m logb x
.
Answer:
If students understand the basic proof on general laws of logarithm then it will be easie. ... loga (MN) = x + y = loga M + loga N [putting the values of x and y] ... a on both sides of the change of base rule formula [loga M = logb M × loga
Step-by-step explanation:
yall i think i got this wrong
even if it is to anyone who needs it just copy it lol
find value of x
x+28+4x-3
Over the last 40 years, the percentage of the Americans who are White has decreased steadily. a. TRUEb. FALSE
The statement is true as over the last 40 years, the percentage of Americans who identify as White has been decreasing steadily.
This trend can be attributed to several factors,
Changing Demographics,
The United States has experienced significant demographic shifts in recent decades.
There has been an increase in immigration from non-European countries, resulting in a more diverse population.
Birth rates among minority populations, such as Hispanic, Asian, and African American communities,
Have been higher compared to the White population.
Multiracial Identification,
With increased recognition and acceptance of multiracial identities,
More individuals are choosing to identify with multiple racial backgrounds rather than solely as White.
This shift in self-identification contributes to the decline in the percentage of Americans identifying as solely White.
Generational Changes,
Younger generations, such as millennials and Generation Z, are more racially and ethnically diverse compared to older generations.
As younger individuals enter adulthood and the workforce, they contribute to the overall demographic changes in the country.
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the united nations stores data about energy production from animal waste and the use around the world. the following data set gives information for converting animal waste into electricity. country or area commodity - transaction year quantity unit united states animal waste - transformation in electricity 2014 171907 terajoules united states animal waste - transformation in electricity 2013 149233 terajoules united states animal waste - transformation in electricity 2012 104847 terajoules united states animal waste - transformation in electricity 2011 141347 terajoules united states animal waste - transformation in electricity 2003 185912 terajoules united states animal waste - transformation in electricity 2002 197120 terajoules united states animal waste - transformation in electricity 2001 104725 terajoules united states animal waste - transformation in electricity 2000 126745 terajoules united states animal waste - transformation in electricity 1999 133206 terajoules united states animal waste - transformation in electricity 1998 224425 terajoules united states animal waste - transformation in electricity 1997 129113 terajoules united states animal waste - transformation in electricity 1996 5274 terajoules united states animal waste - transformation in electricity 1993 21748 terajoules united states animal waste - transformation in electricity 1992 242924 terajoules united states animal waste - transformation in electricity 1991 210448 terajoules united states animal waste - transformation in electricity 1990 215437 terajoules what is the slope of the linear equation of the entire data set? round to nearest hundredth. provide your answer below:
The slope of the linear equation of the entire data set is -720.98
1. Bring data in to excel sheet
2.Select both x and y variable and insert scatter plot chart. Select any data point in the chart and add trend line. In the format trend line option choose "Linear" and also select "Display an equation on chart" & "Display R-squared value on chart"
To find: What is the slope of the linear equation of the entire data set? Round to nearest hundredth.
Regression equation : y = -720.98x + 15,90,277.32
Slope = -720.98 (Round to nearest hundredth.)
Intercept = 15,90,277.32
So, the slope of the linear equation of the entire data set is -720.98
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En un puesto de verduras se han vendido 2 kg de naranjas y 5 kilos
de peras por $4.400 y 4 kilos de naranjas y 2 kilos de peras por
$ 4.000 ¿Calcula el precio de cada producto?
PLANTEA:
Answer:
i don't speak spanish bro sorry
The sum of the first n terms of an arithmetic sequence is given by Sn= n^2-2n. What is the first term and the common difference?
The given formula for the sum of the first n terms of an arithmetic sequence is Sn = n^2 - 2n. To determine the first term and the common difference of the arithmetic sequence, we can analyze the given formula.
The sum of an arithmetic sequence is given by the formula Sn = (n/2)(2a + (n-1)d), where a is the first term, d is the common difference, and n is the number of terms.
Comparing the given formula Sn = n^2 - 2n with the formula Sn = (n/2)(2a + (n-1)d), we can see that n^2 - 2n is equivalent to (n/2)(2a + (n-1)d). By equating the corresponding terms, we have the following equations:
n = n/2 (for the first term)
-2 = 2a + (n-1)d
From the first equation, we find that n = 2. Substituting this value of n into the second equation, we have -2 = 2a + (2-1)d, which simplifies to -2 = 2a + d. Therefore, the first term of the arithmetic sequence is a = -1, and the common difference is d = -3.
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Harpreet took out a payday loan of $500.00. He had to repay $540.00 within 7 days.
A) What was the daily interest on the loan
B) What was the annual interest?
Answer:
a) 1,14%
b) 317%
Step-by-step explanation
J = C . i . t
540 - 500 = 500 . i . 7
40 = 500 . 7 . i
i = 0,0114 = 1,14% within day
-------------------------------------------
J = 500 . 0,0114 . 365 = 2085,71
2085,71 - 500 = 500 . i . 1
1585,71 = 500 . i
i = 3,17 = 317% annual
Find the value of y when the arithmetic mean of 3y+1 and 4y +9 is 2y+11. with solution please:)
\(We \: \: \: \: know \\ mean \: \: = \frac{sum \: \: \: of \: \: \: the \: \: \: terms}{number \: \: \: of \: \: \: terms} \\ \)
\(Given \: \: \: here \: \: the \: \: \: mean \\ of \: \: \: 3y + 1 \: \: \: and \: \: \: 4y + 9 \: \: \: is \: \: \: 2y + 11.\)
\(Therefore \\ \frac{(3y + 1) + (4y + 9)}{2} = 2y + 11 \\ = > \frac{7y + 10}{2} = 2y + 11 \\ = > 7y + 10 = 2(2y + 11) \\ = > 7y + 10 = 4y + 22 \\ = > 7y - 4y = 22 - 10 \\ = > 3y = 12 \\ = > y = \frac{12}{3} \\ = > y = 4\)
\(Your \: \: \: answer \: \: \: is \: \: \: 4.\)
Plzzzzz answer ASAP help meh
Answer:
1= 8
3= 12
5= 16
7= 20
9= 24
Step-by-step explanation:
1+3=4x2=8
3+3=6x2=12
5+3=8x2=16
9+3=12x2=24
ANSWER:1=8
3=12
5=16
7=20
9=24
step -by - step explanation: 1+3=4×2=8
3+3=6×2=12
5+3=8×2=16
9+3=12×2=24
If f(x) = 3x-6 and g(x) = 1/3x+1, then (g(f))^-1 (x) equals.
1-x
1/3(3x-1)
(x+1)
(x-1)
We need to find the inverse of the function gof (x). First we need to find the composite function gof (x) which is given by:
\(g(f(x)) = g(3x - 6)\)
= \((1/3)(3x - 6) + 1\)
= x - 1 + 1
= x
Thus,
gof (x) = x.
Now we need to find the inverse of the function gof (x) to obtain
\((gof)^-1 (x).\)
We have gof (x) = x
which implies\((gof)^-1 (x)\)
= gof (x)^-1
= x^-1
= 1/x,
x ≠ 0
Therefore,
\((gof)^-1 (x) = 1/x\)
which is option (3) (x+1) since 1/x can be written as 1/(x+1-1), where (x+1-1) is the denominator of 1/x.
Hence, the correct option is (3).
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To find (g(f))^-1 (x), substitute the expression for f(x) into g(x) and simplify. The composition of g(f) is x and its inverse is also x. Therefore, (g(f))^-1 (x) equals x.
Explanation:To find (g(f))^-1 (x), we need to first find the composition of g(f) and then find its inverse. Start by substituting the expression for f(x) into g(x): g(f(x)) = g(3x-6) = \frac{1}{3}(3x-6) + 1 = x - 1 + 1 = x. So, g(f(x)) = x. Now, to find the inverse of g(f), we switch the x and y variables and solve for y: y = x. Therefore, (g(f))^-1 (x) = x.
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even though emilio writes neatly and legibly, it takes him a very long time to write a few sentences. which strategy may help emilio to write more fluently?
One strategy that may help Emilio write more fluently is practicing speed writing or shorthand techniques.
Practicing speed writing or shorthand techniques can help Emilio increase his writing speed without sacrificing legibility. Speed writing involves using abbreviations, symbols, and shortcuts to represent words or phrases, allowing for faster transcription of thoughts onto paper.
Shorthand systems, such as Gregg shorthand or Pitman shorthand, provide structured methods for condensing words and phrases into simplified symbols.
By learning and practicing speed writing or shorthand techniques, Emilio can improve his writing efficiency and reduce the time it takes to write a few sentences. This strategy allows him to maintain neatness while increasing his writing speed, enabling him to express his thoughts more fluently.
With regular practice and familiarity, Emilio will become more comfortable with the shorthand system and experience a significant improvement in his writing speed and fluency.
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If f(x)=square root of x +3/square root of x, then f'4=
f'(4) = 5/32. This means that at x = 4, the slope of the tangent line to the curve y = f(x) is 5/32.
To find f'(4), we first need to find the derivative of the given function f(x). We can use the quotient rule to do this:
f(x) = sqrt(x) + 3/sqrt(x)
\(f'(x) = (1/2)x^(-1/2) - 3/2x^(-3/2)\)
Now we can substitute x = 4 to find f'(4):
\(f'(4) = (1/2)4^(-1/2) - 3/24^(-3/2)\)
f'(4) = (1/2)(1/2) - 3/2(1/16)
f'(4) = 1/4 - 3/32
f'(4) = 5/32
Therefore, This also means that the rate of change of f(x) at x = 4 is 5/32, which is the instantaneous rate of change or the derivative of the function at that point.
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