The probability that more than 175 cable homes will assess cable firms as providing outstanding or exceptional transmission quality is roughly 0.0287.
What makes probability so special?The word "probability" comes directly from the Latin word "probabilitas," which means "credibility, likelihood," in Old French probability (14th century) (see probable). The word first appeared in mathematics around 1718.
Let X be the proportion of the 300 randomly chosen cable homes that are satisfied or excellent with their provider's transmission quality.
Let p be the probability that a cable household will rate cable firms as providing good or exceptional quality transmission, which in this instance is 53% or 0.53.
Let q represent the likelihood that a cable household does not consider cable companies to be providing good or exceptional quality transmission, which in this instance is 47% or 0.47.
Let 300 * 0.53 = 159, or the mean of the binomial distribution, be denoted by = n * p.
The binomial distribution's standard deviation, = sqrt(n * p * q), is sqrt(300 * 0.53 * 0.47) = 8.38. (rounded to two decimal places).
The binomial distribution can be approximated by the normal distribution:
P(X > 175) = P(Z > (175 - μ) / σ)
where Z is a standard normal variable.
P(Z > (175 - 159) / 8.38) = P(Z > 1.91)
Using a standard normal table or calculator, we can find that P(Z > 1.91) is approximately 0.0287.
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70.61% of 736.97cm
Give your answer rounded to 2 DP.
Answer:
520.37 cm
Step-by-step explanation:
apply equation:
x = 736.97(0.7061) = 520.374517
Notice 70.61% is the same as 0.7061 (just divide by 100)
now you need to round to 2 DP
x ≈ 520.37
so the 70.61% of 736.97cm is 520.37 cm
The length of a rectangle is 11 cm more than twice its width. If the area of the rectangle is 6 cm", what
are the dimensions of the rectangle?
The width of the rectangle is
cm.
ation
The length of the rectangle is
cm
The width of the rectangle is 3/2 cm and the length is 17 cm.
The formula for the area of a rectangle is A = L x W, where A is the area, L is the length, and W is the width. To solve this problem, we can rearrange the formula to solve for W: W = A / L. In this case, A = 6 cm and L = 2W + 11 cm. Substituting these values, we get W = 6 / (2W + 11). We can solve this equation by dividing both sides by 2W to get 1/W = 6 / (2W + 11) * 1/2W. Simplifying, we get 1/W = 3 / (11 + 2W). Subtracting 3/11 from both sides, we get -2/11 W = -3/11. Finally, we can solve for W by dividing both sides by -2/11 to get W = 3/2 cm.
Therefore, the width of the rectangle is 3/2 cm, and the length of the rectangle is 2W + 11 = 11 + 6 = 17 cm.
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Theorem: For any real number x, x+∣x−5∣≥5 In a proof by cases of the theorem
A. x≤0 B. x≤5 C. x<5 D. x<0
The theorem holds for all real numbers x and the other case is that x < 5.
option C.
What is a real number?A real number is a value that represents a quantity along a continuous number line. Real numbers can be either rational or irrational. Rational numbers are numbers that can be expressed as a ratio of two integers, such as 1/2, 3/4, or -7/8.
For the given question, if one of the cases is that x > 5, we can determine the other case by considering the definition of absolute value:
If x > 5, then ∣x-5∣ = x-5 (since x-5 is positive),
so x + ∣x-5∣ = x + (x-5) = 2x - 5
which is clearly greater than or equal to 5.
If x < 5, then ∣x-5∣ = -(x-5) (since x-5 is negative),
so x + ∣x-5∣ = x - (x-5) = 5,
which is also greater than or equal to 5.
Therefore, the theorem holds for all real numbers x.
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The complete question is below:
Theorem: For any real number x, x+∣x−5∣≥5. In a proof by cases of the theorem, there are two cases. One of the cases is that x > 5.
What is the other case?
A. x≤0
B. x≤5
C. x<5
D. x<0
The ratio of 2 institutions is 7 : 3 and their sum is 630. Find the number
the first institution has 441 and the second institution has 189.
We can use algebra to solve the problem. We can start by assigning variables to represent the two institutions:
Let x be the multiplier of the ratio.
Then, we have:
7x is the first institution.
3x is the second institution.
From the problem, we know that the sum of the two institutions is 630:
7x + 3x = 630
Simplifying the left side, we get:
10x = 630
Dividing both sides by 10, we get:
x = 63
Now that we know the value of x, we can find the number of each institution:
First institution = 7x = 7(63) = 441
Second institution = 3x = 3(63) = 189
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Identify the number as prime, composite or neither. If the number is composite, write it as the product of prime factors 360
Step-by-step explanation:
To determine whether 360 is prime, composite, or neither, we need to check if it has any factors other than 1 and itself.
We can start by finding the prime factorization of 360:
First, we can divide 360 by 2 to get 180:
360 ÷ 2 = 180
Next, we can divide 180 by 2 to get 90:
180 ÷ 2 = 90
We can continue dividing by 2 until we can no longer divide evenly:
90 ÷ 2 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5
5 is a prime number, so we have found the prime factorization of 360:
360 = 2 × 2 × 2 × 3 × 3 × 5
Therefore, we can see that 360 is composite because it has more than two factors. We can write it as the product of its prime factors as shown above.
In summary, the number 360 is composite and its prime factorization is:
360 = 2 × 2 × 2 × 3 × 3 × 5
HELP NEEDED QUICK!!
Directions: Calculate the following simple interest problems. Write your answers in the space provided. Use the formula I = P × R × T and round your answers to the nearest cent or the nearest tenth of a percent. Use four decimal places for fractions of time.
(a) I = ?, P = $500, R = 8%, T = 3 months (3/12)
simple interest: $
(b) I = ?, P = $50, R = 12%, T = 1 month (1/12)
simple interest:
cents
(c) I = ?, P = $1,000, R = 18%, T = 24 months (24/12)
simple interest: $
(d) I = ?, P = $600, R = 15%, T = 60 days (60/360)
simple interest: $
(use .1667)
(a) The simplest interest is $12.
(b) The simplest interest is 5 cents.
(c) The simplest interest is $360.
(d) The simplest interest is $15.
What is the interest rate?
In relation to the amount lent, deposited, or borrowed, the amount of interest due each period is expressed as an interest rate. The total interest on a sum lent or borrowed is determined by the principal amount, the interest rate, the frequency of compounding, and the period of time over which it is lent deposited, or borrowed.
The formula of simple interest is I = P × R × T
(a) Given that P = $500, R = 8% = 0.08, T = 3 months = (3/12) years = 1/4 years
The simple interest is
500 × 0.08 × (1/4)
= $12
(b) Given that P = $50, R = 12% = 0.12, T = 1 months = (1/12) years
The simple interest is
50 × 0.12 × (1/12)
=$0.5
= 5 cents
(c) Given that P = $1,000, R = 18% = 0.18, T = 24 months = (24/12) years = 2 years
The simple interest is
1000 × 0.18 × 2
=$360
(d) Given that P = $600, R = 15% = 0.15, T = 60 days = (60/360) years
The simple interest is
600 × 0.15 × (60/360)
=$15
P is principal, R is known as rate of interest.
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Solve for x. Type your answer as a number
The numerical value of x is 3.
What is the numerical value of x?The Midsegment Theorem states that the segment joining the midpoints of two sides of a triangle is parallel to and half the length of the third side.
This simply means that:
The middle segment = half the third side
From the image:
The middle segment = x + 10The third side = x + 23Using the Midsegment Theorem
x + 10 = 1/2 × (x + 23)
Solve for x
Multiply both sides by 2
2( x + 10 ) = 1/2 ×2 (x + 23)
2( x + 10 ) = x + 23
2x + 20 = x + 23
2x - x = 23 - 20
x = 3
Therefore, the value of x is 3.
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A statistics student wants to determine if there is a relationship between a student's number of absences, x, and their
grade point average (GPA), y. The given data lists the number of absences and GPAs for 15 randomly selected
students.
Number of
Absences
GPA
15 1 0
9
12
3
3
2.1 4.3 4.5 3.2 4.0 1.7 3.8 2.9
6
1
3.6
2 7
3.4
2.6
Using technology, the y-intercept is
O4.5, which means a student with no absences has a GPA of 4.5.
O 4.5, which means a student with no absences is predicted to have a GPA of 4.5.
O 3.79, which means a student with no absences is predicted to have a GPA of 3.79.
O 3.79, but it does not make sense to interpret the y-intercept in this context.
0 4
3.1
2.8
9 10
2.8
4.1
Answer: The correct answer is:
The y-intercept is 3.79, which means a student with no absences is predicted to have a GPA of 3.79.
Explanation:
To determine the relationship between the number of absences and the GPA, the student can use linear regression analysis. The regression line can be obtained using software such as Excel or R. The y-intercept of the regression line represents the predicted value of the response variable (GPA) when the predictor variable (number of absences) is zero.
Using technology, the y-intercept for this data set is found to be 3.79. This means that a student with zero absences is predicted to have a GPA of 3.79. Therefore, the correct answer is that the y-intercept is 3.79 and it does make sense to interpret it in this context.
Step-by-step explanation:
Name the type of angle indicated
Answer: Acute
Step-by-step explanation:
Acute - Less than 90 degress
Straight - Exactly 180 degrees
Obtuse - More than 90 degrees
Right - Exactly 90 degrees
A school supplier sells boxes of A4 paper for £4, and offers a £2 discount on any order paid for in advance. Write the formula the supplier would use for calculating what to charge for any order paid in advance. Use n to represent the number of boxes purchased.
When calculating the price of an order that has been paid in advance, the school supplier will use the following formula:
4n - 2
The ordering cost formula is useful for calculating the economic order quantity and gives businesses insight into how
much of an item is necessary to meet customer demand and fulfill sales goals.
These ordering costs can include shipping fees, unexpected transportation costs, inspection fees and other expenses
necessary to acquire inventory products. Essentially, any money your company spends to place and receive inventory
orders accounts for the purchasing and ordering costs.
Where n represents the number of boxes purchased.
The school supplier sells boxes of A4 paper for £4, and a £2 discount is given on any order paid for in advance.
Formula for calculating what to charge for any order paid in advance:
To calculate the price for an order paid in advance, the formula 4n - 2 should be used.
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PLS HELP!!!!!
Find area and perimeter.
Answer:
I think it has an area of 4 and a perimeter of 8, i'm not totally sure but I thought I'd try to help
Answer:
area:4
perimeter:8ft
Step-by-step explanation:
when doing the area, you have to MULTIPLY the length by the width. For example, length:5ft width:7ft so to find the area you have to multiply both and get the answer of 35. so for the sum you have is 2 × 2 = 4
for perimeter, you have to ADD all the sides so if you have a square with all sides of 4 you add them all up which = 16. so for your sum, add them all up = 8ft
Hope it helps I'm not that good at explaining :)
The CPI basket price for two consecutive years in five different economies are given. Determine the rate of inflation for each economy. Then
order the tiles from least to greatest inflation rate.
The greatest inflation rate was 1.78% in year1 and year2
When you have a lot of repetitive calculations to do, it is convenient to let a spreadsheet do it. Copying the given data to the spreadsheet ensures we have made no data entry errors.
The inflation rate is calculated as ...
(year 2 price)/(year 1 price) -1 . . . . . expressed as a percentage
[tex]\frac{74.30}{73.00}=1.0178\\\\\frac{76.015}{75}=1.0135\\\\\frac{89.25}{88}=1.0142[/tex]
The attachment shows the results of this calculation as applied to the economies in the order shown. The least-to-greatest order is shown in the right-most column.
The complete question is-
The CPI basket price for two consecutive years in five different economies are given. Determine the rate of inflation for each economy. Then order the tiles from least to the greatest inflation rate.
Year 1 = $73.00
Year 2 = $74.30
Year 1 = $75.00
Year 2 = $76.15
Year 1 = $88.00
Year 2 = $89.25
Year 1 = $72.50
Year 2 = $73.75
Year 1 = $79.00
Year 2 = $80.25
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prove that the altitude to the base of an icosceles triangle is also the following. The median to the base please dont make it to much of a crazy explanation i need to copy and paste it lol.
We οbserve that the line segment AM frοm vertex A tο midpοint M οf base BC alsο bisects BC, since M is the midpοint οf BC. Therefοre, we have AM = BM = MC = BC/2.
What is Isοsceles triangle?An isοsceles triangle is type οf triangle that has the twο sides οf equal length. In isοsceles triangle, angles οppοsite equal sides are alsο equal in measure. The third side οf isοsceles triangle is called base.
Tο prοve this, we can cοnsider the fοllοwing diagram οf an isοsceles triangle ABC with base BC:
A
/ \
/ \
/ \
/ h \
B------------C
where h is the altitude tο the base BC and M is the midpοint οf the base BC. We want tο shοw that the line segment AM is alsο the median tο the base BC.
First, we οbserve that the triangle ABC is isοsceles, sο the twο legs AB and AC are cοngruent. Therefοre, the altitude h frοm vertex A tο base BC bisects BC, which means that BM = MC = BC/2.
Secοnd, we οbserve that the line segment AM frοm vertex A tο midpοint M οf base BC alsο bisects BC, since M is the midpοint οf BC. Therefοre, we have AM = BM = MC = BC/2.
Thus, we have shοwn that the altitude tο the base and the median tο the base οf an isοsceles triangle are the same line segment, which cοmpletes the prοοf.
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The initial population of a town is 15 000, and it grows with a
doubling time of 10 years. What will the population be in 12 years?
24 years?
The population of the town after 12 years Aand in 24 years will be approximately 34,461 and 79,171 respectively.
What will the population be in 12 years and in 24 years?If the population doubles every 10 years, then we can use the formula for exponential growth to find the population after a certain number of years:
P = P₀ x 2^(t/T)
where:
P₀ = initial population = 15,000
P = population after t years
T = doubling time = 10 years
t = number of years
Using this formula, we can find the population after 12 years:
P = 15,000 × 2^(12/10)
P = 34,461
Therefore, the population of the town after 12 years will be approximately 34,461.
Similarly, we can find the population after 24 years:
P = 15,000 × 2^(24/10)
P = 79,171
Therefore, the population of the town after 24 years will be approximately 79,171.
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What is -37/76 simplified
Answer:
Already in simplest form. -37/76
Step-by-step explanation:
Nothing changes, it's the most simplified it can be.
answer #
you can't simplify the answer
a rectangular pizza, 35 cm by 70 cm, is cut into 24 square pieces. two round pizzas, each cut into 12 slices, also give 24 pieces. so that the pizza slices are the same size, what must be the diameter of the round pizzas? round to the nearest tenth. don't include units.
The diameter of each round pizza should be approximately d ≈ 2r ≈ 39.6
Rounding to the nearest tenth, we get a diameter of 39.6 cm.
The rectangular pizza has an area of:
35 cm x 70 cm = 2450 [tex]cm^2[/tex]
Dividing the area by 24 gives us the area of each square piece:
[tex]2450 cm^2 / 24 = 102.08 cm^2[/tex]
For the round pizzas, each slice is a sector of the circle, and the area of each sector is given by:
[tex]A = (θ/360)\pi r^2[/tex]
where θ is the angle of the sector in degrees, and r is the radius (half the diameter) of the circle.
Since each round pizza is cut into 12 slices, each slice covers an angle of:
θ = 360/12 = 30 degrees
We want the area of each slice to be equal to the area of each square piece from the rectangular pizza, which is 102.08 [tex]cm^2[/tex]. Therefore, we can set up the equation:
[tex](30/360)\pi r^2 = 102.08[/tex]
Simplifying, we get:
[tex]\pi r^2/12 = 102.08[/tex]
[tex]\pi r^2 = 1224.96[/tex]
[tex]r^2[/tex] ≈ 391.2
r ≈ 19.8
Therefore, the diameter of each round pizza should be approximately:
d ≈ 2r ≈ 39.6
Rounding to the nearest tenth, we get a diameter of 39.6 cm.
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The circle graph shows the results of a survey by a bakery on which of their new products 105 customers preferred most. How many customers preferred cake? Round your answer to the nearest whole number.
Answer:
37 customers preferred cake.
Step-by-step explanation:
What is a percentage?A percentage is a ratio or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.
To find out how many customers preferred cake, we need to multiply the total number of customers (105) by the percentage of customers who preferred cake (35%):
(35% = 0.35)
105 × 0.35 = 36.75.Rounding this to the nearest whole number gives us 37. Therefore, approximately 37 customers preferred cake.
Answer:
35% of 105 is 36.75. ( Rounded up 37). So 37 customers preferred cake the most
Philip's meal costs $14.50 at a local restaurant. The server did their job very well and Philip would like to a 20% tip. What amount of money should he leave as a tip?
Answer:
$2.90
Step-by-step explanation:
We know
Philip's meal costs $14.50 at a local restaurant. Philip would like to a 20% tip
20% = 0.2
14.50 x 0.2 = $2.90
So, he should leave $2.90 as a tip.
I need this asap I need to turn it in like an hour 25points
Answer:
c. 36 people
pls mrk me brainliest
Answer:
The answer would indeed be C. 36 people.
Add. Express your answer in standard form. (Highest exponent first and then descending order)
[tex](2x^{4} -5x^{3} -7) + (-5x^{5} -5x^{2} +9x+17)[/tex]
Answer:
The answer would be -5x^5 + 2x^4 - 5x^3 - 5x^2 + 9x + 10.
please help i have until saturday
The distance between the two points from the geometrical formula for that purpose is 6.2.
What is distance between two points in geometry?The distance between two points in geometry is the length of the straight line segment that connects the two points. It is calculated using the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.
Using the formula;
d= √(x2 - x1)^2 + (y2 - y1)^2
d = √(7.5 - 3)^2 + (6.25 - 2)^2
d = √20.25 + 18.06
d = 6.2
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Colby is making a home video consisting of a 5-minute introduction followed by several short skits. Each skit is 6 minutes long. If Colby's video is 143 minutes long, how many skits are in his video?
answer: 23
explanation - 143 - 5 = 138
(total time - the intro)
138 / 6 = 23
(remaining time divided by skit time)
how do you calculate volume
Answer:
Height*width*depth= volume
Points A, B, and C are collinear. Point B is the midpoint of AC. Find the length of AB.
AB = 3x
BC = 4x − 6
Answer:
18 unitsStep-by-step explanation:
As per question, point B is the midpoint of AC.
According to definition of midpoint, AB = BC:
3x = 4x - 64x - 3x = 6x = 6The length of AB is:
AB = 3*6 = 18Answer:
AB = 18
Step-by-step explanation:
To find:-
The length of AB .Answer:-
We are here given that points A , B and C are collinear and B is the midpoint of AC . From the data provided in the question we have;
AB = 3x BC = 4x - 6 .Since B is the midpoint of AC, it will divide AC into two equal parts namely AB and BC. And these parts will be equal to one another. ( By Euclid's first axiom, Things which are half of the same thing are equal to one another.)
So we have;
[tex]\sf:\implies AB = BC \\[/tex]
[tex]\sf:\implies 3x = 4x - 6 \\[/tex]
[tex]\sf:\implies 3x -4x = -6 \\[/tex]
[tex]\sf:\implies -x = -6 \\[/tex]
[tex]\sf:\implies\red{ x = 6} \\[/tex]
Finally plug in the value of x, in the given expression of AB as ,
[tex]\sf:\implies AB = 3(x) \\[/tex]
[tex]\sf:\implies AB = 3(6) \\[/tex]
[tex]\sf:\implies \red{AB = 18} \\[/tex]
Hence the value of AB is 18 .
Find the values of p
for which the integral converges. And evaluate the integral for those values of p
.
a
)
∫
1
0
3
1
x
p
d
x
b
)
∫
[infinity]
e
25
x
(
ln
x
)
p
d
x
a) For the integral ∫01^3 1/x^p dx to converge, p > 0. Evaluating the integral for those values of p gives ∫01^3 1/x^p dx = -1/(p-1).
b) For the integral ∫[infinity]^e 25/x^(lnx)^p dx to converge, p > 1. Evaluating the integral for those values of p gives
∫[infinity]^e 25/x^(lnx)^p dx = -25/(p-1).
Convergence and divergence. The improper integral is said to converge if the limit is both real and a limited integer.
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A desk is on sale for $380, which is 20% off the original price. Which equation can be used to determine the
amount of money saved, s, in dollars, when purchasing this desk on sale?
A s= 0. 2(380)
B
S = (380 = 0. 8) - 380
Cs= (380 = 0. 5) – 380
D
8 = (380 = 0. 8)
The right formula to figure out how much money was saved, s, in dollars when getting this desk on sale is: s = 0.2(380) (380) This calculation accounts for desk being 20% less expensive than it was originally.
which translates to a 20% discount for the consumer. So, we must multiply the original price by the discount %, which in this case is 0.2, in order to determine the amount saved. The equation in Option A that best captures the presented circumstance is accurate. A desk is on sale for $380, which is 20% off the original price. Which equation can be used to determine the amount of money saved, s, in dollars, when purchasing this desk on sale accounts for desk being 20% less expensive than it was originally. The equation in Option A that best captures the presented circumstance is accurate.
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An outdoor racetrack is shaped like an ellipse. The equation of the inner lane is x^2/6241 + y^2/1296=1. Each lane is approximately 1 meter apart. Find the length and width of the second lane, as indicated in the figure. Assume that the center is located at (0,0), that the track is a horizontal ellipse, and that one meter is equivalent to one coordinate unit.
ANSWER CHOICES:
A.
length = 79 m
width = 36 m
B.
length = 81 m
width = 38 m
C.
length = 158 m
width = 72 m
D.
length = 160 m
width = 74 m
The length οf the secοnd lane is apprοximately 160 meters, and the width is apprοximately 74 meters. Sο the cοrrect οptiοn is D.
We can start by nοticing that the given equatiοn [tex]x^2/6241 + y^2/1296 = 1[/tex]is the equatiοn οf an ellipse cantered at the οrigin, with a majοr axis οf length 2a = 279 = 158 and a minοr axis οf length 2b = 236 = 72. This is the equatiοn οf the innermοst lane.
Tο find the equatiοn οf the secοnd lane, we need tο add 1 meter tο bοth sides οf the equatiοn, since each lane is apprοximately 1 meter apart. This gives:
[tex]x^2/6241 + y^2/1296 = 2^2[/tex]
Simplifying, we get:
[tex]x^2/6241 + y^2/1296 = 4[/tex]
This is the equatiοn οf an ellipse with the same center as the first ellipse, but with a majοr axis οf length 2(a+1) = 280 = 160 and a minοr axis οf length 2(b+1) = 237 = 74.
Therefοre, the length οf the secοnd lane is apprοximately 160 meters, and the width is apprοximately 74 meters. Sο the cοrrect οptiοn is D.
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When you are factoring a polynomiat and the signs of the polynomial are as follows: a x 2
+bx⋅c, the factors will have the following signs: a (t)(t) b (x) (+x) one of each d none of the above Question 2 (1 point) Give one of the prime factors of: x 2
−4x+12 a. (x−4) b (x+4) c) (x−6) d (x+6)
However, the response would be (x - 2 + 2i2)(x - 2 - 2i2) if you are searching for factors with real coefficients.
what is polynomial ?A polynomial is a mathematical expression made up of variables, factors, one or more terms, and non-negative integer exponents used in addition, subtraction, multiplication, and multiplication. Any mathematical object, including numbers, variables, and even functions, can be represented by the variables in a polynomial. In the polynomial equation 3x2 + 2x - 5 as an illustration, the coefficients are 3, 2, and -5, the variable is x, and the exponent is 2. This polynomial has the terms 3x2, 2x, and -5, each of which is denoted by a plus or negative sign. Monomials have one term, binomials have two terms, trinomials have three terms, and so on. Polynomials can be categorized based on how many terms they contain.
given
The solution to the first question is "none of the above," as the signs of the terms in a polynomial are not what determine the signs of the factors.
(x - 2i)(x + 2i) is one of the prime factors of x2 - 4x + 12, where I is the imaginary number.
However, the response would be (x - 2 + 2i2)(x - 2 - 2i2) if you are searching for factors with real coefficients.
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A circular fountain has a radius of 11 feet. Find the area in terms of pi
[tex]\mathcal{A} = \pi r^{2} = \pi (11^{2}) = 121 \pi \ ft^{2}[/tex]
Answer:
121 pi divide to 4
Step-by-step explanation:
the answer is 121 pi divide to 4. please see it on the picture.
12 ft by 21 ft rectangle. How much carpeting does she need to buy to cover her entire family room?
Answer:
144 feet²
Step-by-step explanation:
12 x 12 = 144