Answer:
To divide polynomials, we need to use polynomial long division. First, we divide the first term of the dividend by the first term of the divisor to get the first term of the quotient, which we write above the division bar. In this case, the first term of the dividend is 2x² and the first term of the divisor is x, so the first term of the quotient is 2x. We then multiply the divisor by the quotient and subtract it from the dividend to get the remainder.
Here's how the long division would look:
2x² + 15x + 20
===
x + 5
2x
_______
15x - 10x
15x + 20 - 10x - 20
___________
5x - 20
After we perform the polynomial long division, we get the quotient 2x + 5 and the remainder -20. Therefore, the final result of the division is:
(2x² + 15x + 20) ÷ (x + 5) = 2x + 5 + (-20)/(x + 5)
Note that the remainder -20 is written as a fraction with the divisor x + 5 in the denominator. This is the correct way to write the remainder because it tells us that the remainder has a degree that is one less than the degree of the divisor. In this case, the degree of the divisor is 1, so the degree of the remainder is 0.
What is the median of the data set?
41,14,28,34,93,45,10,16,19,54,67
A. 41
B. 34
C.38
D.45
Answer: 34
Step-by-step explanation:
How do you find the roots of a polynomial using synthetic division?
Synthetic division is a yet another way to divide a polynomial by the factor, where k is a constant.
What is a synthetic division?
Synthetic division is usually used to find factors of polynomials of degree 3 that cannot be factored by grouping the polynomial.
Synthetic division is also used to find factor polynomials of degree 4 or higher.
We use synthetic division if and only if no other methods will work since there is a trial and error aspect to using it.
Taking an example:
We have to find the roots of the polynomial, [tex]f(x)= x^3+3x^2-4[/tex]
Substituting x=1 in the above equation, we get,
f(1)= [tex]1^3+3-4[/tex]=0
Thus, (x-1) is a root of the above polynomial.
Dividing the given function by (x-1)
[tex]x^3+3x^2-4/x-1\\=x^2+4x+4\\=(x+2)^2[/tex]
Thus, the roots of the given polynomial are given as, (x-1) and [tex](x+2)^2[/tex].
Hence, this is the synthetic division to find out the roots of the polynomial.
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Mekala has an mp3 player called the jumble. The jumble randomly selects a song for the user to listen to. Mekala's jumble has 444 techno songs, 222 country songs, and 333 jazz songs on it. Mekala plans to listen to 270270270 songs. Complete the following statement with the best prediction. Mekala will listen to.
The statement that "close to 60 country songs" but probably not exactly 60 country songs is, best prediction to complete the given statement .
So, the correct option is option (B).
Mekala has MP3 player Jumble has 4 techno songs, 2 country songs, and 3 jazz songs on it.
firstly, we represent this songs in ratio format :
Now, the ratio of techno songs to country songs to jazz songs = 4 : 2 : 3
Let the total number of songs which is unknowns be" x". So,
Total number of techno songs = 4x
Total number of country songs = 2x
Total number of jazz songs = 3x
Total number of songs that Mekala plans to Listen = 270
Then, 4 x + 2 x + 3 x = 270
=> 9 x = 270
Dividing both sides by 9, we get
=> x = 30
So, Number of techno songs = 4 × 30
= 120
Number of country songs = 2×30 = 60
Number of jazz songs = 3 × 30 = 90
but all this is based on prediction only.
Hence, the total country songs are close to 60 but not exactly 60.
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Complete question:
Mekala has an MP3 player called the Jumble. The Jumble randomly selects a song for the user to listen to. Mekala's Jumble has 4 techno songs, 2 country songs, and3 jazz songs on it. Mekala plans to listen to 270 songs.
Complete the following statement with the best prediction.
Mekala will listen to...
Please choose from one of the following options.
a) Exactly 60 country songs
b) Close to 60 country songs but probably not exactly 60country songs
c)Exactly 210 country songs
d)Close to 210 country songs but probably not exactly 210 country songs
What is 11C9?
O A. 66
OB. 55
OC. 45
OD. 36
A 14 seater matatu charges sh 20 per passenger during normal hours and sh 30 per passenger during rush hours. if it made 10 trips and earned sh 3540.how many rush hours trip did it make
Answer:
2
Step-by-step explanation:
A 14 seater matatu makes 1420 = <<1420=280>>280 shillings per trip during normal hours.
It makes 1430 = <<1430=420>>420 shillings per trip during rush hours.
Since the matatu made 10 trips and earned 3540 shillings, then it made 10-3540/280 = <<10-3540/280=12>>12 trips during normal hours.
This means it made 10-12 = <<10-12=2>>2 trips during rush hours. Answer: {2}.
You are working on an air conditioning system. A roll of cylindrical copper tubing has an outside diameter of 78 inch and an inside diameter of 34 inch. How much refrigerant can 12 feet of the tubing hold?.
557,568 inch³ of refrigerant can be held by the tubing.
Here we have to find how much a refrigerant can hold.
Data given:
outer diameter (d) = 78inch
outer radius(r) = 39 inch
inner diameter (d') = 34 inch
inner radius (r') = 17inch
Height (h) = 12 feet
= 12 × 12
= 144 inch
the formula to find the volume of the cylinder:
volume= пr²h
So here we get
Refrigerant hold = Volume of the outer cylinder - the volume of the inner cylinder
= πr²h - πr'²h
= πh(r² - r'²)
= π ×144 ( 39² - 17²)
= π × 144 ×56 × 22
= 22/7 × 144 × 56 × 22
= 557,568 inch³
Therefore the refrigerant can hold 557,568 inch³.
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Consider the following two points:
A (1,3)
B (6,13)
What is the initial value of the linear function through A and B?
Initial value of the linear function through A and B is 3.
Define initial value.The starting output value, or the y-value when x = 0, is the initial value. The rate of change is the rate at which the input or, in the case of a graph, the rate at which y changes in relation to x. A function's starting value in mathematics denotes the function's y-intercept. The constant in an equation can also be used to determine initial values. In graph functions, understanding the y-intercept is beneficial. By substituting 0 0 for x x and finding y y, you may verify the starting value.
Given,
Points
A (1,3)
B (6,13)
Linear function,
f(x) = ax + b
Equating,
f(x) = x + 3
Let x = 0
f(x) = 3
As we know,
The graph of a linear function is a straight line. The following is the form of a linear function. a + bx = y = f(x). One independent variable and one dependent variable make up a linear function. X and Y are the independent and dependent variables, respectively.
Initial value of the linear function through A and B is 3.
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I have a couple of questions but whoever gives me the equation for all 3 and answers 1st will get the brainiest and a ton of points LOL( 50 POINTSSS)
1-what is the equation of the line that passes through (-5,4) and has a slope of 0
2-what is the equation of the line that passes through (-2,0) and has a slope of 2
3-what is the equation of the line that passes through the points (5,3)and has and unidentified slope
Thanksssssss :)
1) The line's equation is y = 4 because it passes through the coordinates (-5,4).
2) The equation of the line is y= 2x + 4
What is slope ?
A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).
1) A line with a slope of 0 is considered to be horizontal.
The equation is y=4 because along a horizontal line, the y-values remain constant.
The line's equation is y=4 because it passes through the coordinates (-5,4).
2) (x1,y1) = (-2,0) , m=2
y-y1=m(x-x1)
y-0 = 2 (x-(-2))
y=2(x+2)
y= 2x + 4
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What is the value of x? Responses 12√2 4√3 12 4
Answer:
x = 4[tex]\sqrt{3}[/tex]
Step-by-step explanation:
using the sine ratio in the right triangle and the exact value
sin60° = [tex]\frac{\sqrt{3} }{2}[/tex]
sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{8}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
2x = 8[tex]\sqrt{3}[/tex] ( divide both sides by 2 )
x = 4[tex]\sqrt{3}[/tex]
A store is having a sale. They are offering $15 off the
purchase of 4 video games and 10% off if you are a
first time customer.
The discounts could be applied in two different orders.
Which do you PREDICT would save you the most
money?
Use intuition, don't calculate.
You will save more by getting $15 off, then 10% off
You will save more by getting 10% off, then $15 off
You will save the same amount either way
Answer:
You would be saving the same amount of money either way.
Step-by-step explanation:
It's the commutative property.
What is the type of scale in which the representative factor is 1 is to 1?
A full size scale is a type of scale in which the representative factor is 1 is to 1
A scale factor is defined as the ratio of the scale of a given original object to the scale of a new object that is its representation but of a different size.
To determine the scale factor, first identify the corresponding sides on the two figures.
Then, divide the new figure's measurement by the original figure's measurement. The resulting value is your scale factor, or how many times your new figure is larger or smaller than the original.
A full size scale is a scale in which the length of the drawing is proportional to the actual length of the object.
As a result, its representative fraction is 1:1 by definition. The drawing is drawn in full size scale with the actual measurement
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The interpretation of the slope is different in a multiple linear regression model as compared to a simple linear regression model.a. True
b. False
It is true that a multiple linear regression model interprets the slope differently than a simple linear regression model.
The link between two variables is determined through simple linear regression. The slope of a straight line used to represent linear regression indicates how changing one variable impacts another variable.
For the complex relationships between data, multiple linear regression is used. More than one variable may contribute to the explanation of this relationship.
One y-intercept and numerous slopes (one for each variable) make up a multiple regression formula. The formula is understood in the same way as a simple linear regression formula, however more than one variable influences the relationship's slope.
Therefore, the statement is true.
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A line has a slope of
7/10 and includes the points (c, -3) and (10, 4). What is the value of c?
Answer:
0
Step-by-step explanation:
Slope=(y2-y1)/(x2-x1)
=(4-(-3))/(10-c)=7/10
=7/(10-c)=7/10
c=0
7) Mrs. Bell's favorite coffee place used to charge $2 for a small coffee,
now they charge $5. Find the percent of change in the price.
Answer:
150%
Step-by-step explanation:
2 x 2 = 4
Remainder=1
50% OR 0.5 x 2 = 1
Whats is 3/2 x 2/3 mas a mixed number
Answer:
3/2*2/3=1
Step-by-step explanation:
3/2*2/3. Everything cancels out, and you are left with 1.
3/2*2/3=6/6=1
Answer:
=1
Using the given fractions,
3/2×2/3
Applying the fractions formula for multiplication,
=3×2/2×3
=6/6
Simplifying 6/6, the answer is
=1
the incubation period of ebola virus is known to have a normal distribution with a mean of 10 days and a standard deviation of 7 days suppose a group of researchers claimed that the true mean is shorter than 10 days. a test is conducted using a random sample of 23 patients. consider a rejection region suppose the test failed to reject . if the true mean incubation period is 6 days, what is the type ii error probability of the test using (round off to third decimal place)?
The required type ii error probability of the test using is 0.085.
What is probability of the test?It is determined by duplicating the pretest chances by the probability of a positive or negative test (as we will show). Post-test probability is characterized, as the likelihood of the objective problem after a symptomatic experimental outcome is known.
According to question:We have,
standard deviation = 7, mean = 6, size of the sample = 23.
P(type II error) = P(Xbar >=8 given mean =6)
=P(Z>(8-6)×√(23)/7) =P(Z>1.37)=1-P(Z<1.37)
=1-0.9147=0.0853 =0.085
Thus, required probability is 0.085
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A rectangular board has an area of 648 square centimeters. The triangular part of the board has an area of 162 square centimeters. A dart is randomly thrown at the board. Assuming the dart lands in the rectangle, what is the probability that it lands inside the triangle? round to the nearest whole percent. 18% 25% 35% 50%.
Answer: 25% i believe
Step-by-step explanation:
The probability that it lands inside the triangle is,
P = 25%
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Since, the probability is equal to,
P = size of the event space/size of the sample space
Here, In this problem
size of the sample size = area of the rectangular dartboard = 648 square centimeters
And, size of the event space = area of the triangular part = 162 square centimeters.
Hence, the probability that it lands inside the triangle is,
P = 162 / 648
P = 0.25
P = 25%
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On Saturday, 3 child tickets were sold for every 2 adult tickets sold. The ratio of child tickets sold to adult tickets sold is?
Answer: 3:2
Step-by-step explanation:
We know that every 3 child tickets were sold for every 2 adults tickets sold
So the ratio is 3:2
Please help mee im desperate
By using the concept of unitary method, ratio and percentage, it can be calculated that-
7) Option D is correct
6) Option C is correct
8) Option D is correct
What is Unitary method, ratio and percentage?
Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity
Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.
Ratio is used to determine how much one quantity is bigger as compared to another. The first part of the ratio is called antecedant and the second part of the ratio is called consequent.
Suppose there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.
Here, unitary method, ratio and percentage will be used.
7) The scale on a map reads [tex]\frac{1}{2} \ inch = 30 \ miles\\[/tex]
1 inch = [tex]30 \div \frac{1}{2} \ miles[/tex] = 60 miles
[tex]\frac{23}{4} \ inches[/tex] = [tex]\frac{23}{4} \times 60 \ miles[/tex] = 345 miles
Option D is correct
6) Let the number of empty seats be 3x and the number of full seats be 7x
Total number of seats = 3x + 7x = 10x
By the problem,
7x = 203
x = [tex]\frac{203}{7}[/tex]
x = 29
Total number of seats = [tex]29 \times 10[/tex] = 290
Option C is correct
8) Let the number of students be x
Percentage of students in the band = [tex]\frac{37.5}{100} \times x[/tex]
By the problem,
[tex]\frac{37.5}{100} \times x =42\\x = \frac{42 \times 100}{37.5}\\x = 112[/tex]
Option D is correct
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what is the probability of getting at least 1 gram more cereal than advertised? there is a 0.1234 probability of getting at least 1 gram more cereal than advertised. there is a 0.0905 probability of getting at least 1 gram more cereal than advertised. there is a 0.5726 probability of getting at least 1 gram more cereal than advertised. there is a 0.7705 probability of getting at least 1 gram more cereal than advertised. there is a 0.8766 probability of getting at least 1 gram more cereal than advertised.
P(Z3)=0.1170 is the likelihood of earning at least 1 gram of extra cereal.A probability seems to be a number that expresses the possibility or probability that a specific event will take place.
How is probability determined?The probability is computed by dividing the total possible outcomes by the number of possible ways the event could occur. Probabilistic and odds are two distinct ideas. Odds are the likelihood that something will occur and the variety of outcomes that can result in success. the overall number of outcomes that could occur. For instance, there is only one way to receive a head and there are a total of two possible outcomes, hence the probability of flipping the coin and getting heads is 1 in 2.
Y=1.8945 grams.
Y = 0.8405 grams.
The z-score is the result of dividing the standard deviation by the value that has been decreased by the mean:
z= σx−μ = 0.85053−1.9845≈1.19
Table A can be used to determine the relevant value:
P(Z≥3)=P(Z>1.19)=1−P(Z<1.19)=1−0.8830=0.1170
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A group of hikers started at an elevation of 1,803 feet. A squid is swimming 300 feet below sea level. What is the distance between the hikers and the squid
Answer:
1503
Step-by-step explanation:
1803 - 300
A line segment with a length of 16 units is reflected across the y-axis, then translated 5 units down on a coordinate plane, resulting in a new segment.
What is the length of this new line segment? ________________ units
The solution is 16 units
The length of the line segment is 16 units
How does the transformation of a function happen?
The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
Right shift by c units: y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given data ,
Let the length of the line segment be = A
Now , the initial length of the line segment = 16 units
The line is reflected across the y-axis
So , when you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y)
And , the resulting line is translated 5 units down
But , the line segment does not change in dimension at all
So , the reflection and a translation does not affect the length of the line segment
Hence , the length of the line segment is 16 units
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What is (-9,8) reflected across the y-axis?
Answer: ( -9, -8)
Step-by-step explanation:
When reflected across the y-axis, the y-coordinate will be the opposite!
So the answer is (-9, -8)
5) Find the perimeter of JKL. j 5x-8 8r-35 I ㅏ N 7y-9 2y + 11 -32- K
=======================================================
Explanation:
Segments JK, KL, and JL are tangent to the circle.
We can break those segments into smaller pieces and notice we have these 3 pairs of congruent tangents:
MJ = NJKN = KOLM = LOLet's use the first equation to solve for x.
MJ = NJ
5x-8 = 8x-35
5x-8x = -35+8
-3x = -27
x = -27/(-3)
x = 9
Use the same idea to find y.
KN = KO
7y-9 = 2y+11
7y-2y = 11+9
5y = 20
y = 20/5
y = 4
Now compute the length of segment KO.
KO = 2y+11 = 2*4+11 = 19 units
Subtract this from LK to find LO
LO = LK - KO
LO = 32 - 19
LO = 13
This makes segment LM to be also 13 units long.
Now use the value of x to find sides MJ and NJ
MJ = 5x-8 = 5*9-13 = 32
NJ = 32 as well
--------------------------------------------------------------
We have these pieces:
MJ = NJ = 32KN = KO = 19LM = LO = 13which give us
JK = NJ+KN = 32+19 = 51KL = KO+LO = 19+13 = 32JL = MJ+LM = 32+13 = 45Therefore, the perimeter of triangle JLK is:
JK+KL+JL = 51+32+45 = 128 units
Two positive numbers have a sum of 8 and a product of 13. Algebraically determine the value of the larger of the two numbers to the nearest hundredth
The value of the larger of the two numbers is 5.73.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Two numbers = M and N
M + N = 8 _____(1)
M = 8 - N _____(2)
MN = 13 _____(3)
Putting (2) in (3) we get,
(8 - N)N = 13
8N - N² = 13
N² - 8N + 13 = 0
This is in the form of ax² + bx + c = 0
a = 1, b = -8 and c = 13
Using the determinant we have,
N = -b ± √(b² - 4ac) / 2a
N = 8 ± √(64 - 52) / 2
N = 8 ± √12 / 2
N = 8 ± 2√3 / 2
N = 4 ± √3
N = 4 + √3 and N = 4 - √3
[√3 = 1.73]
N = 5.73
N = 2.27
Now,
When N = 5.73, M = 8 - 5.73 = 2.27
When N = 2.27, M = 8 - 2.27 = 5.73
Now,
The two numbers are 5.73 and 2.27
Thus,
The larger of the two numbers is 5.73.
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What is the average rate of change of the function on the interval from x = 0 to x = 5? f(x)=12(3)x.
the average rate of change of the function on the interval from x = 0 to x = 5 is 580.8
Average rate of change of a function f(x) between x-values x1 and x2 = (f(x2) -f(x1)/ (x2 -x1)
For this given function f(x)=12(3)x then it will mean that
f(x) = 12.3^x and x-values 0 and 5, the average rate of change is
the average rate of change = (f(5) -f(0))/(5 -0) = (2916 -12)/5 = 580.8
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HELP ASAP !!!
-PHOTO ATTACTHED :D
Find the area of the figure.
Answer: Area=35km^2
Step-by-step explanation:
You need to find the areas of the rectangle and then the triangle.
First, you start with splitting up the figure to a rectangle and a triangle.
Secondly 6*5= 30 so the area of the rectangle is 30 km.
Thirdly, you add that to the area of the triangle, which you figure out because the opposite side of the figure is 6 km so the remaining length is going to be 2km. The area of a triangle is (1/2)(Base)(Height), so (1/2)(5)(2)= 5.
Add the 30 with the 5 and you get a total of 35 km for the area.
Answer:
i think the answer is 240km cuz you multiply 8x5x6. hope this helps, boo!
Step-by-step explanation:
The Sugar Sweet Company is going to transport its sugar to market. It will cost $5000 to rent trucks, and it will cost an additional $200 for each ton of sugar transported. Let C represent the total cost (in dollars), and let S represent the amount of sugar (in tons) transported. Write an equation relating C to S, and then graph your equation using the axes below.
The equation relating C and S is given as follows:
C(S) = 5000 + 200S.
The graph of the equation is then given by the image shown at the end of the answer.
How to define the function?The first step in defining the function is verifying the input and the output variables, as follows:
Output: Cost.Input: Tons of Sugar.Then from these variables, we identify the type of function, which is linear, as for each additional ton of sugar, the cost increases by a fixed amount.
This fixed amount is of $200, hence it represents the slope of the function. The fixed fee of $5,000 to rent trucks is the intercept, hence the equation is defined as follows:
C(S) = 5000 + 200S.
And then the graph starting at (0,5000) and connecting point (10, 7000) is given at the end of the answer.
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The sample mean is 12.8, and the sample standard deviation is two. The sample size is 20. What distribution should you use to perform a hypothesis test? Assume the underlying population is normal.
A. Student's t-distribution
B. geometric distribution
C. exponential distribution
D. normal distribution
E. binomial distribution
If the sample mean is 12.8, sample standard deviation is 2 and sample size is 20, then the student's t-distribution should be use to perform the hypothesis test
The population mean = 13
The sample mean = 12.8
The standard deviation = 2
The sample size of the population = 20
The given condition is the underlying population is normal.
Here population standard deviation is missing in the given data. So to perform a hypothesis test when the population standard deviation is missing then we have to use the student t-distribution
Therefore, the student's t-distribution should be use to perform the hypothesis test
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What's the slope of 7x Y =- 4?
To find the slope of a line given an equation in the form of ax + by = c .The slope of 7x + y = -4 is 7.
To find the slope of a line given an equation in the form of ax + by = c, you first need to put the equation into slope-intercept form, which is y = mx + b. To do this, start by subtracting ax from both sides of the equation, leaving you with by = c - ax. Then divide both sides by b, giving you y = (c - ax) / b. This is the equation in slope-intercept form, with m being the slope, which in this case is 7.
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