The solution to the given problem of equation comes out to be quotient : x² +x+6+2/(x+2) and remainder is 2.
We have to find the remainder and quotient
Given : synthetic division for
x³ + 3x² + 8x + 14
------------------------
x + 2
Write the problem in synthetic division format
-2 | 1 3 8 14
-2 -2
------------------------
1 1 6
Carry down the leading coefficient, unchanged, to below the division symbol
-2 | 1 3 8 14
-2 -2
---------------------------
1 1 6
Multiply the carry - down value by the zero of the denominator, and carry the result up into the next column:
1(-2)=-2
-2 | 1 3 8 14
-2 - 2
------------------
1 1 6
=> We get:
As x² +x+6+ 2/(x+2)
and remainder is 2
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Translation
AABC is translated 4 units to the right and 5 units down. Answer the questions to
find the coordinates of A after the translation.
1. Give the rule for translating a point 4 units right and 5 units down. (2 points)
(x,y) → (x
y
)
The rule for this translation. and the coordinates of the image point are (x, y) = (x + 4, y - 5); (7, -6)
a, Write the rule for this translation.From the question, we have the following parameters that can be used in our computation:
translated to the right 4 units and down t units
Mathematically, this can be expressed as
(x, y) = (x + 4, y - 5)
b. What are the coordinates of the image point?Given that
A = (3, -1)
And, we have
(x, y) = (x + 4, y - 5)
This means that
A' = (3 + 4, -1 - 5)
Evaluate
A' = (7, -6)
So, the image point is A' = (7, -6)
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Question
ABC is translated 4 units to the right and 5 units down. Answer the questions to find the coordinates of A after the translation.
A = (3, –1)
BC is tangent to circle A at point B. DC=9 and BC=15. find the radius of the circle.
Suppose that the average number of friends users have is normally distributed with a mean of 130 and a standard deviation of about 49. Assume eighteen individuals are randomly chosen.
Answer the following questions. Round all answers to 4 decimal places where possible.
What is the distribution of
X? X ~ N( , )
For the group of 18, find the probability that the average number of friends is less than 135.
Find the first quartile for the average number of friends.
For part b), is the assumption that the distribution is normal necessary? No or Yes
(a) The distribution of X is X ~ N(130, 49)
(b) The probability that the average number of friends is less than 135 is 0.610
(c) The first quartile for the average number of friends is 96.925
(d) The assumption of normal distribution is necessary
(a) What is the distribution of X?Given that
Mean = 130
Standard deviation = 49
The distribution of X is represented as
X ~ N(Mean , Standard deviation)
So, we have
X ~ N(130, 49)
(b) The probability that the average is less than 135.The z-score is calculated as
z = (x - Mean)/Standard deviation
So, we have
z = (135 - 130)/18
Evaluate
z = 0.278
So, we have
P = P(z < 0.278)
Evaluate
P = 0.60949
Approximate
P = 0.610
(c) Finding the first quartileThis is calculated as
Q₁ = Mean - 0.675 * Standard deviation
So, we have
Q₁ = 130 - 0.675 * 49
Evaluate
Q₁ = 96.925
Hence, the first quartile for the average friends for this sample size is 96.925
(d) Is the assumption necessaryYes, the assumption is necessary
This is because
The distribution has a sample size greater than 25 as required by the central limit theorem
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Evaluate the following question given below
The solution is, simplification of the expression is; 71.19.
Here, we have,
the given expression is:
(5/2)^4/2 * (3/2)^6
=(5/2)^2 * (3/2)^6
as we know that, 4/2 = 2.
now, we have,
(5/2)^2 * (3/2)^6
=5²/2² ^ 3⁶/2⁶
= 5² * 3⁶ / 2² * 2⁶
=5² * 3⁶ / 2 ^ (2+6)
=5² * 3⁶ / 2 ^8
=25 * 729/ 256
=18225/ 256
=71.19
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All one question. An electrical firm manufactures light bulbs that have a claimed lifetime with a mean of 1000 hours and a well-established standard deviation of 150 hours. Bulb life is approximately normally distributed.
a) The null hypothesis: H0: μ >= 1000
alternate hypothesis Ha: μ < 1000
b) The value of the test statistic is -3.12.
a) The null hypothesis, denoted by H0, is a statement of no difference or no effect. The alternate hypothesis, denoted by Ha, is a statement of a difference or effect that we want to test.
In this case, the null hypothesis would be that the average bulb life is greater than or equal to 1000 hours:
H0: μ >= 1000
The alternate hypothesis would be that the average bulb life is less than 1000 hours:
Ha: μ < 1000
where μ is the population mean bulb life.
b) To calculate the test statistic, we need to use the formula:
t = (x - μ) / (s / √(n))
where x is the sample mean, μ is the hypothesized population mean (under the null hypothesis), s is the sample standard deviation, and n is the sample size.
Substituting the given values, we get:
t = (950 - 1000) / (160 / √(30))
t = -3.12
Therefore, the value of the test statistic is -3.12.
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The owner of a pet shop predicts that 10 out of 20 new puppies are male. He randomly selects 10 of the puppies, and notes that all 10 are male. Which of the following conclusions BEST supports his findings?
Select one:
a.
All 20 puppies are male.
b.
Less than 10 of the puppies are male.
c.
More than 10 of the puppies are male.
d.
10 of the puppies are male and 10 are female.
10. Given ADEF, find m/E.
Round your answer to the nearest hundredth of a degree.
E
6
D
4
Find the missing degree E>
After considering all the given data we conclude that the measure of m∠E is 54.46° under the condition that ADEF is a right angled triangle.
We already know that ADEF is a right angled triangle having sides EF = 6 and FD = 4, we can apply the Pythagorean theorem to evaluate the length of the hypotenuse AD.
AD = √(6² + 4²)
= √52)
≈ 7.21
Now we can apply the sine function to find the measure of angle E.
sin(E) = opposite/hypotenuse = EF/AD
E = arcsin(EF/AD)
≈ 54.46°
Therefore, m∠E ≈ 54.46°.
The Pythagorean Theorem is considered a fundamental relation in the context of Euclidean geometry comparing the three sides of a right triangle.
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M- What is the exponent for
X in the problem below:
Xy³z²
Step-by-step explanation:
x y^3 z^2 = x^1 y^3 z^2
the x exponent is '1'
what is the surface area of the cylinder with height 7in and radius 2in? round your answer to the nearest tenth
Answer:
113.1 in²
Step-by-step explanation:
A = 2πrh + 2πr²
r = 2 in
h = 7 in
A = 2π(2)(7) + 2π2² = 113.1 in²
A 12-sided die is rolled. The set of equally likely outcomes is (1,2,3,4,5,6,7,8,9,10,11,12). Find the probability of rolling a 7.
←
The probability of rolling a 7 is
(Type an integer or a simplified fraction.)
Ans4863
Step-by-step explanation:
What is the magnitude of -10 + 24¡?
The magnitude of the complex number -10 + 24i is 26.
We have,
Complex numbers can be represented as a combination of a real number and an imaginary number, in the form a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square root of -1.
Now,
To find the magnitude of a complex number, we take the square root of the sum of the squares of its real and imaginary parts.
For -10 + 24i, the real part is -10 and the imaginary part is 24.
So the magnitude:
| -10 + 24i | = √((-10)^2 + (24)^2) = √(100 + 576) = √676 = 26
Therefore,
The magnitude of -10 + 24i is 26.
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Sanjay tried to find the median from the following dot plot, which shows how far he went on his recent walks. However, he made a mistake.
Answer:
Do you wish for the mistake to be pointed out? If so, can you please provide the dot plot so I can answer this question?
Step-by-step explanation:
If a trader Gaines 15% interest by selling an article for 1560.00 what is the cost price for the article
$1356.52 is the cost price of the article.
To find the cost price of the article, we can utilize the concept of calculating the original amount based on a percentage increase.
Let's assume the cost price of the article is "x" dollars.
The trader gained a 15% interest, which means the selling price is 115% of the cost price. In other words, the selling price is 115% of "x".
To calculate the selling price, we can set up the following equation:
115% of x = 1560
To convert the percentage to a decimal, we divide it by 100:
1.15 * x = 1560
Now we can solve for x by dividing both sides of the equation by 1.15:
x = 1560 / 1.15
Using a calculator, we find:
x ≈ 1356.52
Therefore, the approximate cost price of the article is $1356.52.
This means that the trader purchased the article for around $1356.52 and then sold it for $1560.00, resulting in a 15% gain.
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Use a number line to illustrate:
1.) p – q
p + (-q)
If the equation is true: p – q = p + (-q)
The illustration of p - q and p + (-q) using a number line is added as an attachment
Illustrating the expression using a number lineFrom the question, we have the following parameters that can be used in our computation:
p - q
Also, we have
p + (-q)
The above expressions mean that
To add two numbers (positive and negative), we can start from a point p, and then count backwards on the number line in q terms
Using the above as a guide, we have the following:
The illustration using a number line is added as an attachment
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The function f(x) is defined as f(x) = 1/x + 5x3, Find the value of f(2).
The value of f(2) is 40.5
The given function is f(x) = 1/x + 5[tex]x^3[/tex], and we need to find the value of f(2).
To do this, we substitute x=2 into the function and simplify:
f(2) = 1/2 + 5([tex]2^3[/tex])
= 1/2 + 5(8)
= 1/2 + 40
= 40.5
Therefore, the value of f(2) is 40.5.
The function f(x) has two parts: 1/x and 5[tex]x^3[/tex]. The first part of the function, 1/x, is a decreasing function that approaches zero as x gets larger. The second part of the function, 5[tex]x^3[/tex], is an increasing function that grows rapidly as x gets larger.
When we substitute x=2 in the function f(x), we get f(2) = 1/2 + 5([tex]2^3[/tex]) = 40.5. This means that at x=2, the value of the function is 40.5.
This result tells us that the function f(x) has a positive value at x=2. Moreover, since the second part of the function grows faster than the first part, the value of the function f(x) will increase as x gets larger. This means that as x increases, the value of f(x) will increase more and more rapidly.
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A new car is purchased for $41, 000 and over time its value depreciates by one half every 3 years. What is the value of the car 4 years after it was purchased, to the nearest hundred dollars?
The value of the car 4 years after it was purchased is $16,270.86.
What is the value of the car after 4 years?
Depreciation is when the value of an asset declines with the passage of time as a result of wear and tear.
The equation that would be used to determine the value of car with the passage of time would be an exponential equation.
Value of the car after t years = [tex]p(1 -r)^{\frac{t}{3}[/tex]
Where:
p = purchase price of the car r = rate of depreciation t = number of yearsValue of the car after 4 years = [tex]41,000(1 -0.5)^{\frac{4}{3}[/tex] = $16,270.86
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Find the formula for the Riemann sum obtained by dividing the interval [0, 1] into n equal
subintervals and using the right endpoint for each c. Then take the limit of these sums as n → ∞
to calculate the area under the curve f(x) = 21x + 21x³ over [0, 1].
The area under the curve over [0, 1] is…..
The area under the curve over [0, 1] is 15.75.
How to solveTo find the Riemann sum, divide [0, 1] into n equal subintervals of width Δx = 1/n.
Using the right endpoint, c = iΔx = i/n. The Riemann sum is:
Σ[f(c)Δx] = Σ[(21(i/n) + 21(i/n)³)(1/n)] from i=1 to n.
To find the area under the curve, take the limit as n→∞:
Area = lim(n→∞) Σ[(21(i/n) + 21(i/n)³)(1/n)].
Find the answer by using the method of definite integration.
Area = ∫(21x + 21x³)dx from 0 to 1 = [10.5x² + 5.25x⁴] from 0 to 1 = 10.5(1)² + 5.25(1)⁴ - 0 = 15.75.
The area under the curve over [0, 1] is 15.75.
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How much kinetic energy does i-6 kg bowling ball have when it's rolling at 60 mph 7.1 m/s then when it's rolling at 14 mph 6.2 m per second??
What is the slope of line represented by 5x-12y=24
Answer:
5/12
Step-by-step explanation:
add 12 y to both sides:
5x = 24 + 12y
subtract 24 from both sides:
12y = 5x - 24
divide all by 12:
y = (5/12)x - 2.
slope is the number in front of x.
slope is (5/12).
A plane leaves an airport and flies 19 km east then 24 km south. How far is the plane from the airport?
Answer: 30.6 km away
Step-by-step explanation:
The main thing this problem requires is Pythagoras' theorem. So set the problem up by marking the airport as (0,0) on a graph. Then move 19 units to the right, and 24 units down and make a point. Now you have the two short lengths of a right-angle triangle, so all that's left is to solve for the hypotenuse. So using the formula [tex]a^{2} + b^{2} = c^{2}[/tex] you would end up with [tex]19^{2} + 24^{2} =c^{2}[/tex]. Then you get: 361+576=[tex]c^{2}[/tex]
solve for c and you get about 30.6 km!
Hope this helps!
-b-
Note: Figure is not drawn to scale.
If a = 5m, b = 8 m, c = 8 m, and d = 2 m, what is the perimeter of the swimming pool?
OA.
21 m
OB.
32 m
29 m
34 m
OC.
OD.
6 of 10 Answered
Reset
Submit
Session Timer: 78:05
O Search
C
After considering the given data we conclude that the perimeter of the given swimming pool is 23 meters which is Option A.
The perimeter of a rectangle is evaluated by adding up all its sides. For the given case, we possess a rectangle with sides
a = 5m,
b = 8m,
c = 8m and
d = 2m.
Perimeter regarding the swimming pool is evaluated as
a + b + c + d
= 5m + 8m + 8m + 2m
= 23 meters
Hence the option regarding the question which satisfy the perimeter is Option A.
Perimeter the counted measurement regarding the distance around the outside of a two-dimensional shape. In this system the length of the outline or boundary of any two-dimensional geometric shape is defined as perimeter .
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The complete question is
If a = 5m, b = 8 m, c = 8 m, and d = 2 m, what is the perimeter of the swimming pool?
A.23 m
B. 32 m
C.29 m
D.34 m
Solve the inequality. Graph the solution on the number line and then give the answer in interval notation.
Answer:
[-infinity, 4]
Step-by-step explanation:
-9x + 3 >= -33
-9x >= -36
x<=4 (sign switched because of dividing both sides by a negative integer in an inequality)
Therefore, x is less than or equal to 4
[ - infinity, 4]
Gabe has eight dollars the game at the arcade cost 2$ dollars instead of one dollar write ordered pairs to represent the amount of money left after playing different numbers of games.
The ordered pairs representing the amount of money left after playing variable number of games is :
(Number of games played, Amount of money left)
(0, 8)
(1, 6)
(2, 4)
(3, 2)
(4, 0)
Ordered pairsOrdered pairs gives a tabular description of data as the values of two or more variables change.
Here, the amount Gabe has before playing a game is $8 and the cost per game is $2 .
Hence, the amount he has left decreases by $2 for every increase in number of games played.
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Chau is cooking a roast. The table below gives the temperature of the roast (in degrees Celsius), at a few times (in minutes) after he removed it from the oven.
Time
(minutes) Temperature
0 184.3
20 140.3
30 109.3
50 51.3
60 28.3
(a) Find the average rate of change for the temperature from 0 minutes to 20 minutes.
(b) Find the average rate of change for the temperature from 30 minutes to 60 minutes.
a. The average rate of change for the temperature from 0 minutes to 20 minutes is 2.2.
b. The average rate of change for the temperature from 30 minutes to 60 minutes is 2.7.
How to determine the average rate of change?In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this mathematical expression:
Average rate of change = [f(b) - f(a)]/(b - a)
Next, we would determine the average rate of change of the function g(t) over the interval [0, 20]:
a = 20; f(a) = 140.3
b = 0; f(b) = 184.3
By substituting the given parameters into the average rate of change formula, we have the following;
Average rate of change = (184.3 - 140.3)/(20 - 0)
Average rate of change = 44/20
Average rate of change = 2.2
Part b.
a = 30; f(a) = 109.3
b = 60; f(b) = 28.3
By substituting the given parameters into the average rate of change formula, we have the following;
Average rate of change = (109.3 - 28.3)/(60 - 30)
Average rate of change = 81/30
Average rate of change = 2.7
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I need help with this quickly of 100 students,27 are taking caculus,26 are taking french and 13 are doing both. If a student is picked at random,what is the prob that the student is taking calculus OR french? Put the aneswer in decimal form rounded to two decimal places.
The required probability that a student is taking calculus or French, rounded to two decimal places, is 0.40.
The probability that a student is taking calculus or French is calculated by adding the number of students taking calculus and the number of students taking French and then subtracting the number of students taking both calculus and French. This gives us the number of students taking either calculus or French. We then divide this number by the total number of students, which is 100.
The number of students taking calculus is 27.The number of students taking French is 26.The number of students taking both calculus and French is 13.So, the number of students taking either calculus or French is 27 + 26 - 13 = 40.
The probability that a student is taking either calculus or French is 40 / 100 = 0.40 = 40%.
Therefore, the probability that a student is taking calculus or French, rounded to two decimal places, is 0.40.
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A toy company sells 3-packs of sphere-shaped bouncy balls. If the company ships the three bouncy balls in a cylindrical container like the one shown, about how much empty space will there be in the container? Use 3.14 for pi and round to the nearest whole number.
The 3 cylinders are 3cm.
Please explain how you got your answer so I can learn to do it on my own next time! Thank you.
There will be about 21 cm³ of empty space in the cylindrical container.
How to explain the volumeThe formula for the volume of a sphere is V = (4/3)πr³ where r is the radius of the sphere. Since the diameter of each bouncy ball is 3 cm, the radius is 1.5 cm.
V = (4/3)π(1.5)³
= 14.13 cm³
The volume of three bouncy balls is 3 times this amount:
= 3 × 14.13
= 42.39 cm³
Since the diameter of each cylinder is 3 cm, the radius is 1.5 cm. We also know that the height of the cylinder is 9 cm, since each cylinder is 3 cm tall and there are three cylinders stacked on top of each other.
= π(1.5)^2(9)
= 63.62 cm³
Empty space = Vcontainer - Vtotal
= 63.62 - 42.39
= 21.23 cm³
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Find the perimeter of a field that has length 2/x+1 and width 5/x^2-1
The perimeter of the field is 4x + 6/(x + 1)(x - 1).
Given that a field has a width of 5/x²-1 and the length is 2/x+1,
We need to find the perimeter,
A field is basically a rectangle, so to find the perimeter of our field we are using the formula for the perimeter of a rectangle,
Perimeter of a rectangle = 2(l+w)
= 2(5/x²-1+2/x+1)
= 2((2(x-1)+5)/(x + 1)(x - 1)
= 4x + 6/(x + 1)(x - 1)
Hence the perimeter of the field is 4x + 6/(x + 1)(x - 1).
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the capacity of P vessel is 12l and that of Q vessel is 18l. Write the capacities of different vessels which completely fill P vessel with exact number of filling.
i) The capacities of different vessels which completely fill P vessel with exact number of fillings are:
One vessel of 12 ITwo vessels of 6 I eachThree vessels of 4 I eachFour vessels of 3 I eachSix vessels of 2 I eachTwelve vessels of 1 I eachHow to explain the information(ii) The capacities of different vessels which completely fill Q vessel with exact number of fillings are:
One vessel of 18 I
Two vessels of 9 I each
Three vessels of 6 I each
Six vessels of 3 I each
Nine vessels of 2 I each
Eighteen vessels of 1 I each
(iii) The common capacities of vessels which completely fill P as well as Q vessels with exact number of fillings are:
Two vessels of 6 I each
Three vessels of 4 I each
Six vessels of 2 I each
Twelve vessels of 1 I each
(iv) The greatest capacity of vessel that completely fills P as well as Q vessels with exact number of fillings is 6 I.
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Find the inverse of this function: f(n)= -4/N-1 -1
a) f^-1(n)= 4/-n-1
b) f^-1(n)= 4/-n-1 +1
c) f^-1(n)= -4/n+3 +1
d) f^-1(n)= 2/n+1 +1
Thank you!!!!!!!! <3
Answer:
The correct answer is b) f^-1(n)= 4/-n-1 +1.
b
Step-by-step explanation:
I think parentheses are missing :
y = -4/(n-1) - 1 switch n and y then solve for y
n = -4/(y-1) - 1 add 1 to both sides of the equation
n+1 = - 4/(y-1) multiply through by y -1
(y-1)(n+1) = - 4 divide through by (n+1)
y -1 = - 4/ (n+1) add 1 to both sides
y = - 4/ (n+1 ) + 1 <=====this is the inverse function y = -4/(n-1) -1
equivalent to 4 / (-1-n) + 1 by putting the ' - ' in the denominator
just needs to be solved can't figure it out thanks
1. The balances for each type of investment at the end of the third year are:
Treasury bond: $13,964.18CD: $3,429.57Stock plan: $9,973.02Savings account: $6,783.622. The total gain from all of the investments combined is $4,150.39.
How to calculate the valuea. Treasury bond:
Balance = Principal * (1 + (interest rate/100))^time
Balance = $12,000.00 * (1 + (5.35%/100))³
Balance = $13,964.18
CD:
Balance = Principal * (1 + (interest rate/100))^time
Balance = $3,000.00 * (1 + (4.75%/100))³
Balance = $3,429.57
Stock plan:
Principal = 0.3 * $30,000.00 = $9,000.00
Year 1: Increase of 9%, so balance = $9,000.00 * (1 + (9%/100)) = $9,810.00
Year 2: Decrease of 5%, so balance = $9,810.00 * (1 - (5%/100)) = $9,319.50
Year 3: Increase of 7%, so balance = $9,319.50 * (1 + (7%/100)) = $9,973.02
Savings account:
Balance = Principal * (1 + (interest rate/100))^time
Balance = $6,000.00 * (1 + (3.90%/100))³
Balance = $6,783.62
b. Treasury bond: Gain = $13,964.18 - $12,000.00 = $1,964.18
CD: Gain = $3,429.57 - $3,000.00 = $429.57
Stock plan: Gain = $9,973.02 - $9,000.00 = $973.02
Savings account: Gain = $6,783.62 - $6,000.00 = $783.62
Total gain from all investments combined = $1,964.18 + $429.57 + $973.02 + $783.62 = $4,150.39
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You saved $30,000.00 and want to diversify your monies. You invest 40% in a Treasury bond for 3 years at 5.35% APR compounded annually. You
place 10% in a CD at 4.75% APR for 3 years compounded annually. 30% you invest in a stock plan and the remainder is in a savings account at
3.90% APR compounded annually. The stock plan increases 9% the first year, decreases in value by 5% the second year, and increases by 7% the
third year.
1. What are the balances for each type of investment at the end of the third year?
2. What is your total gain from all of the investments combined?