Answer:
5x³-13x²+24x+12
Step-by-step explanation:
Start by distributing (5x+2) into (x²-3x+6)
It is easiest to start with 5x.
When distributing 5x, your answer should be: 5x³-15x²+30x.
Then, distribute the 2 just as you did for 5x.
Your answer for that should be: 2x²-6x+12
After that, add the like- terms from both answers together.
5x³-15x²+30x+2x²-6x+12
The final answer is then: 5x³-13x²+24x+12
What is the surface area of this design ?
please help!!!!!!!!!!
Answer: 392.
Step-by-step explanation:
A and B are mutually exclusive events. P(A) = 0.20 and P(B) =
0.50.
What is P(A or B)?
A blueprint used a scale of 1.5 cm = 2 m to
represent a grain silo. If the height of the silo in
the drawing was 33 cm, how tall is the actual grain
silo?
Answer: The Silo is 44 meters tall
Step-by-step explanation:
To find the height of the silo, first you have to divide the drawing height (33cm) by 1.5 to get the unit rate. Then multiply the 22 by 2 to get 44 meters (The height of the silo)
What is the M.A.D. (mean absolute deviation) of the following data set?
8 9 9 7 8 6 9 8
The mean absolute deviation is 0.75
How to determine the mean absolute deviationTo calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set
From the information given, we have that the data set is;
8 9 9 7 8 6 9 8
Let's calculate the mean, we get;
Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8
Mean = 64 / 8
Divide the values
Mean = 8
Let's determine the absolute difference, we get;
Absolute differences=
|8 - 8| = 0
|9 - 8| = 1
|9 - 8| = 1
|7 - 8| = 1
|8 - 8| = 0
|6 - 8| = 2
|9 - 8| = 1
|8 - 8| = 0
Find the mean of the absolute differences:
Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8
Absolute difference = 6 / 8 = 0.75
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According to a poll, 80% of Americans report being afflicted by stress. Suppose a random sample of 1,200 Americans is selected. Complete parts (a) through (d) below.
a. What percentage of the sample would we expect to report being afflicted by stress?
The percentage of the sample selected at random that would be expected to be afflicted by stress would also be = 80%
How to calculate the percentage afflicted by stress?The percentage of a data set is when part of the data is represented per 100 with a symbol of %.
It was stated in the question that 80% of Americans report being afflicted by stress.
Therefore when a sample is randomly selected from an American population, the percentage that is expected to be afflicted by stress should also be 80%.
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Part A: Maci made $170 grooming dogs one day with her mobile dog grooming business. She charges $60 per appointment and earned $50 in tips. Write an equation to represent this situation and solve the equation to determine how many appointments Maci had.
Part B: Logan made a profit of $235 as a mobile groomer. He charged $75 per appointment and received $40 in tips, but also had to pay a rental fee for the truck of $10 per appointment. Write an equation to represent this situation and solve the equation to determine how many appointments Logan had.
Maci and 2 appointments and Logan had 3 appointments.
How many appointments did Maci and Logan have?The linear equation that represents the total amount earned by Maci is:
Total amount earned = (amount per appointment x number of appointments) + tips
$170 = ($60 x a) + $50
$170 = $60a + $50
$170 - $50 = $60a
$120 = $60a
a = $120 / $60
a = 2
The linear equation that represents the total amount earned by Logan is:
Profit = total revenue - total cost
Profit = (fee per appointment x number of appointments) + amount received in tips - (rental fee x number of appointments)
$235 = ($75 x a) + $40 - ($10 x a)
$235 = $75a + $40 - $10a
$235 = $65a + $40
$235 - $40 = $65a
$195 = $65a
a = $195 / 65
a = 3
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Identifying the center and radius to graph
Answer:
center is (5/2,2) and the radius is 4
Step-by-step explanation:
Calculate the producers' surplus (in dollars) for the supply equation at the indicated unit price
p.
(Round your answer to the nearest cent.)
p = 7 + 2q1⁄3; p = 20
Answer:
Step-by-step explanation:
Given the equation of the unit price expressed as;
p = 7 + 2q1⁄3, we are to find the value of q when p = 20
20 = 7 + 2q1⁄3
20-7 = 2q/3
13 = 2q/3
Cross multiply
13 * 3 = 2q
39 = 2q
q = 39/2
q = $19.5
Hence the producer surplus is 1950 cents
The probability of a certain flower having eight petals is 0.45. In a randomly selected batch of 240 of these flowers how many would be expected not to have eight petals? i need the answer for high school and i have no idea what the answer could be. ive asked my parents and they don't seem to know
We would expect approximately 132 flowers in the batch to not have eight petals.
What is the probability about?If the probability of a flower having eight petals is 0.45, then the probability of a flower not having eight petals is 1 - 0.45 = 0.55.
So, for we to find the expected number of flowers that do not have eight petals in a randomly selected batch of 240 flowers, we have to multiply the total number of flowers (240) by the probability of a flower not having eight petals (0.55):
Expected number of flowers without eight petals = 240 × 0.55
Expected number of flowers without eight petals = 132
Therefore, we would expect approximately 132 flowers in the batch to not have eight petals.
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Prove that Newton-Raphson method for solving the equation \(x^{k} e^{x} = 0\) (where k is constant) is given by this formula: \(x _{n +1} = \frac{(K-1)x_n + x_n^{2} }{K+x_n}\)
We have proved that the Newton-Raphson iteration formula for solving the equation\(x^k e^x = 0\) is given by \(x_{n+1} = (k - 1) x_n + x_n^2 / k + x_n.\)
To prove that the Newton-Raphson method for solving the equation \(x^k e^x = 0\), where k is a constant, is given by the formula
\(x_{n+1} = (k - 1) x_n + x_n^2 / k + x_n,\)
we can start by considering the iterative process of the Newton-Raphson method.
Given an initial guess \(x_n\), we want to find a better approximation \(x_{n+1}\)that is closer to the root of the equation \(x^k e^x = 0.\)
The Newton-Raphson method involves the following steps:
Calculate the function value \(f(x_n) = x_n^k e^x_n\) and its derivative \(f'(x_n) = k x_n^(k-1) e^x_n.\)
Find the next approximation x_{n+1} by using the formula:
\(x_{n+1} = x_n - f(x_n) / f'(x_n)\)
Let's apply these steps to our equation \(x^k e^x = 0\):
Calculate the function value and its derivative:
\(f(x_n) = x_n^k e^x_n\\f'(x_n) = k x_n^(k-1) e^x_n\)
Find the next approximation x_{n+1} using the formula:
\(x_{n+1} = x_n - f(x_n) / f'(x_n)\)
Substituting the function value and its derivative:
\(x_{n+1} = x_n - (x_n^k e^x_n) / (k x_n^(k-1) e^x_n)\\= x_n - (x_n^k / k)\)
Simplifying the expression by combining like terms:
\(x_{n+1} = x_n - (x_n^k / k)\\= x_n - x_n^k / k\\= (k - 1) x_n + x_n^2 / k + x_n\)
Therefore, we have proved that the Newton-Raphson iteration formula for solving the equation\(x^k e^x = 0\) is given by \(x_{n+1} = (k - 1) x_n + x_n^2 / k + x_n.\)
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Ribbon wands are made from strips of ribbon tied to sticks. Connie has 84 feet of red ribbon, 48 feet of blue ribbon, and 72 feet of white ribbon. She wants to cut the ribbons into equal lengths that are as long as possible so that no ribbon is wasted
How many pieces of each color will she have?
Answer
Connie can cut the ribbon into 12 foot pieces.
Step-by-step explanation:
For these problems we should find the GCF, which is 12.
10. Elvira has 3 caps: one red, one green, and one blue. She also has two green 1-shirts, one blue I-shirt
and 3 black T-shirts. Elvira considers it a faux pas to ever be seen wearing blue and green at the same
time. What is the probability that Elvira will commit a fashion faux pas, if she randomly reaches into
her dresser and selects a cap and a T-shirt?
Answer:
i would help you but i dont know thw ansewer
Step-by-step explanation:
PLEASE HELP ME QUICKLY!! The graph shows the number of eggs a farmer collected from each chicken pen one morning. How many more eggs were collected from pen 3 than from pen 2 & 5? (Each egg = 5 eggs)
Answer:
Pen 2 = 5 eggs
Pen 3 = 25 eggs
Pen 5 = 10 eggs
It is asking how many MORE eggs does pen 3 have from BOTH pens 2 and 5. Add 2 and 5. But remember one egg = 5 eggs so as stated in the beginning pen 2 has 1 egg which equals 5 eggs and pen 5 has 2 eggs which equals 10.
5 + 10 is?
15, exactly. So how many more eggs does pen 3 have? 15 + one more egg is 20 and pen 3 has 25 which is more than 20 so let’s add another egg which again equals 5.
Now we have 25 eggs, the exact amount pen 3 has. The answer is 2 more eggs/10 more eggs.
Step-by-step explanation:
Are there any linear quantities in the chart shown? And if so, what is the slope of said pairs?
The chart does not represent a linear quantity
How to determine if there are linear quantities in the chart shown?From the chart, we have the following coordinates
(x, y) = (0.10, 0.14), (0.50, 0.32), (1.00, 0.46), (1.70, 0.59) and (2.00, 0.63)
To determine if the chart is a linear quantity, we simply calculate the slope using the coordinates.
The slope is calculated as:
m = (y2 - y1)/(x2 - x1)
So, we have:
m = (0.32 - 0.14)/(0.50 - 0.10) = 0.45
m = (0.46 - 0.32)/(1.00 - 0.50) = 0.28
In the above computations, the calculated slopes are not equal
Hence, the chart does not represent a linear quantity
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A father is four times as old as his son. In two years the will have been five times as old as his son was two years ago. How old is the father?
Answer:
Q13)A man is four times as old as his son. After 20 years, he will be twice as old as his son at that time. Find their present ages. Present age of the father is = 4 x = 4 × 10 = 40 4x=4\times10=40 4x=4×10=40 years.
-1/3 = r -3/4 what is r?
Answer:
5/12 = r
Step-by-step explanation:
-1/3 = r - 3/4
+3/4 +3/4
5/12 = r
Alaina evaluated 17/18+1/20 and got an answer of 18/38. Which statement is true about her answer?
1. Her answer is not correct because when you add fractions, the sum is always greater than 1.
2. Her answer is correct because all the fractions are less than 1.
3. Her answer is not correct because the sum cannot be less than either addend.
4. Her answer is correct because 17+1=18 and 18+20=38.
Answer:
I think it's 3. cuz 17 cannot be divided by 18
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 13 , 17 , 21 , . . . 13,17,21,... Find the 43rd term. Find the 43rd term.
Answer:
a₄₃ = 181
Step-by-step explanation:
there is a common difference between consecutive terms, that is
17 - 13 = 21 - 17 = 4
this indicates the sequence is arithmetic with nth term
\(a_{n}\) = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 13 and d = 4 , then
a₄₃ = 13 + (42 × 4) = 13 + 168 = 181
Please solve this
∫ (log(1 + x ^ 2))/((x + 1) ^ 2) dx
The final result of the integral is:
∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,
where Li(x) is the logarithmic integral function and C is the constant of integration.
We have,
To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.
Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:
∫ (log(1 + (u-1)²) / u²) du.
Expanding the numerator, we have:
∫ (log(1 + u² - 2u + 1) / u²) du
= ∫ (log(u² - 2u + 2) / u²) du.
Now, let's split the logarithm using the properties of logarithms:
∫ (log(u² - 2u + 2) - log(u²)) / u² du
= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.
We can simplify the second integral:
∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.
Using the power rule for integration, we can integrate both terms:
∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.
Now, let's focus on the second integral:
∫ (log(u) / u³) du.
This integral does not have a simple closed-form solution in terms of elementary functions.
It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).
Therefore,
The final result of the integral is:
∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,
where Li(x) is the logarithmic integral function and C is the constant of integration.
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Trent buys a new smartphone. The total cost is $599.40, but he pays in equal monthly payments of $33.30. How many months will it take Trent to pay off the smartphone?
how many months?
At 3:30 p.m., Berto’s train was 34 miles past the egg farm, traveling at an average speed of 85 miles per hour. At the same time on a nearby track, Eduardo’s train was traveling at an average speed of 110 miles per hour and had 12 miles to go before it reached the egg farm. To the nearest hundredth of an hour, after how much time will the trains meet up?
E=egg farm
x=distantce between the Berto´s trains and the meeting point.
t=time where the trains meet up
⇒110 miles/h ⇒85miles/h
[---------------------------E----------------------]-------------------------------------X
[............12 miles.......][........34 miles.....][------------ x ----------------------]
distance between Berto´s train and Eduardo´s train=
=12 miles+34 miles=46 miles.
S=d/t ⇒d=S*t
S=seed
d=distance
T=time
Eduardo´s train;
46 miles+x=t*110 miles/h ⇒x=t*110 miles/h-46 miles (1)
Berto´s train;
x=t*85 miles/h (2)
With the equations (1) and (2) we suggest this system equations:
x=t* 110 miles/h-46 miles
x=t*85 miles/h
we solve this system equiations :
t*110 miles/h-46 miles=t*85 miles/h
110t miles/h-85t miles/h=46 miles
25 t miles/h=46 miles
t=46 miles/25 miles/h=1,84 hour (≈1 hour, 50 minutes, 24 seconds)
x=t*85 miles/h=156,4 miles
Solution: 1,84 hour
Answer:
1.84
Step-by-step explanation:
I did it on edge it was correct
what is the value of x?
please help!!
Answer: 20
Step-by-step explanation:
y = 2x + 4
4y - 8x = 16
Answer: Infinitely many solutions
Step-by-step explanation:
Solve by Substitution :
Solve equation [2] for the variable y
y = 2x + 4
Plug this in for variable y in equation [1]
4•(2x+4) - 8x = 16
0 = 0 => Infinitely many solutions
Please make me brainliest!
Solve the following system of linear equations by substitution and determine whether the system has one solution, no solution, or an infinite number of solutions. If theSystem has one solution, find the solution5x+y=-28- 7x - 4y =8Answer
Given the equation system
\(\begin{gathered} 1)5x+y=-28 \\ 2)-7x-4y=8 \end{gathered}\)First, write the first equation for y
\(\begin{gathered} 5x+y=-28 \\ y=-28-5x \end{gathered}\)Second, replace the expression in the second equation, that way you'll determine one expression with one unknown
\(-7x-4(-28-5x)=8\)Now you can solve for x
Start solving the multiplication on the parenthesis term by applying the distributive propperty of multiplications
\(\begin{gathered} -7x+(-4\cdot-28)+(-4\cdot-5x)=8 \\ -7x+112+20x=8 \end{gathered}\)Order the like terms and simplify
\(\begin{gathered} -7x+20x+112=8 \\ 13x+112=8 \end{gathered}\)Pass "112" to the other side of the equation by performing the opposite operation, that is to subtract the number from both sides of the equation
\(\begin{gathered} 13x=8-112 \\ 13x=-104 \end{gathered}\)Divide both sides by 13 to reach the value of x
\(\begin{gathered} \frac{13x}{13}=-\frac{104}{13} \\ x=-8 \end{gathered}\)Finally, replace the value of x in the first equation to determine the value of y
\(\begin{gathered} y=-28-5x \\ y=-28-5(-8) \\ y=12 \end{gathered}\)The equation system has one solution for x=-8 and y=12
help me on this one more time for 60 points
Answer:
Your answer is X = 7
Step-by-step explanation:
50, 60, 72, ...
Find the 8th term.
5^{x+1}-5^{x+2}=-2500. Find x
Answer:
x is 3
Step-by-step explanation:
\( {5}^{(x + 1)} - {5}^{(x + 2)} = - 2500 \\ \)
divide all sides by -1:
\( {5}^{(x + 2)} - 5 {}^{(x + 1)} = 2500\)
from law of indices:
\(( {5}^{x} . {5}^{2} ) - ( {5}^{x} . {5}^{1} ) = 2500\)
factorise out 5^x:
\( {5}^{x} ( {5}^{2} - {5}^{1} ) = 2500 \\ {5}^{x} (20) = 2500 \\ {5}^{x} = 125 \\ {5}^{x} = {5}^{3} \\ x = 3\)
Guys help me on this one please…
Answer: 6. 35 hours
7. 741 Miles
8. 1.5 or 1.54
Step-by-step explanation:
6. 142.20/6=23.7
829.50/23.7=35
7. 117/3=39
39x19=741
8.19/12.35=1.538
What is the reference angle for 289°?
Answer:
71º
Step-by-step explanation:
360 - 289 = 71º
Find the surface area of a cylinder pls
The total surface area of the cylinder is 157 square feet.
Given the radius of the cylinder = 4 inches
height of the cylinder = 9 inches
Total surface area is calculated by the formula:
A = 2πr² + 2πh
A = 2 × 3.14 × 4² + 2 × 3.14 × 9
or, A = 157 square feet.
Therefore the total surface area of the cylinder is 157 square feet.
The surface area of a solid item is a measurement of the total volume that the surface of the thing occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more complicated than the definition of arc length for one-dimensional curves.
The definition of surface area for polyhedral (i.e., particles with flat polygonal faces), where the surface area is equal to the sum of the areas of its faces. When smooth surfaces, like spheres, are represented as parametric surfaces, their surface area can be calculated.
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