The equation of the degree 6 polynomial with a root at 3, a double root at 2, and a triple root at -1, and y-intercept at y = 5 is given as follows:
y = -5/12(x - 3)(x - 2)²(x + 1)³.
How to define the polynomial?The equation of the function is obtained considering the Factor Theorem, as a product of the linear factors of the function.
The zeros of the function, along with their multiplicities, are given as follows:
Zero at x = 3 with a multiplicity of 1.Zero at x = 2 with a multiplicity of 2.Zero at x = -1 with a multiplicity of 3.Then the linear factors of the function are given as follows:
(x - 3).(x - 2)².(x + 1)³.The function is then defined as:
y = a(x - 3)(x - 2)²(x + 1)³.
In which a is the leading coefficient.
When x = 0, y = 5, due to the y-intercept, hence the leading coefficient a is obtained as follows:
5 = -12a
a = -5/12
Hence the polynomial is:
y = -5/12(x - 3)(x - 2)²(x + 1)³.
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How do you find Z score with mean and standard deviation in R?.
A z-score can be calculated using the formula z = (x-)/, where x is the raw score, the mean of the population, and the standard deviation of the population.
The z-score is simply the raw score minus the mean of the population divided by the standard deviation of the population, as the formula demonstrates.
How can I use R to convert data to z-scores?Typically, z-scores, or standardized scores, are calculated by dividing the mean of all data points by the standard deviation of all data points, then subtracting the mean from each individual data point. Again, using scale(), this can be done in one call.
On a TI 84, how can the mean and standard deviation be used to calculate the z-score?Press EDIT after pressing Stat. Press Enter after highlighting L2 and entering the formula (L1-10) / 5.558. In column L2, the z-score for each individual value will be displayed automatically: Note: Press 2 and then 1 to enter "L1" into the formula.
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A farmhouse shelters 11 animals. Some are goats and some are ducks. Altogether there are 34 legs. How many of each animal are there?(with work)
Answer: 6 Goats and 5 Ducks
Hope this helps :)
Step-by-step explanation:
6 goats (4 legs) = 24 legs
5 ducks (2 legs) = 10 legs
6 * 4 = 24
5 * 2 = 10
24 + 10 = 34
6 + 5 = 11
Answer:
6 goats and 5 ducks
Step-by-step explanation:
Given: g+d=11
Goats have 4 legs. Ducks have 2 legs. For total of 34 legs.
Use the word problem to create equation: 4g+2d=34
We can solve for either, we'll solve for g(goat) first:
4g+2d=34
2d=34-4g
d=17-2g
Plug what we found for d into other equation:
g+d=11
g+(17-2g)=11
-g+17=11
-g=-6
g=6
Plug what we found for g into equation to solve for d(duck):
g+d=11
6+d=11
d=5
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Scale factor = 2/5
15inches high; 35 inches length
What is the dimensions?
The new dimensions are height is 6 inches and length is 14 inches.
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
The basic formula to find the scale factor of a figure is expressed as,
Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.
Given that, scale factor = 2/5, 15 inches high and 35 inches length.
Here, height is
2/5 = New height/15
New dimension =30/5
= 6 inches
Length of a shape is
2/5 =New length/35
= 70/5
= 14 inches
Therefore, the new dimensions are height is 6 inches and length is 14 inches.
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Yall could help a scholar out real quick? xx
Answer: 1 apple = 3 bananas
Step-by-step explanation:
10 bananas = 2 pineapples
which means
5 bananas = 1 pineapple eq_i
1 pineapple = 2 bananas + 1 apple eq_ii
Using eq_i and eq_ii, we conclude
1 apple = 3 bananas ... answer
hope that helps...
Is the function 2x 3 Surjective?.
The function f(x)=2x-3 is not surjective.
The surjective function is defined with reference to the elements of the range set, such that every element of the range is a co-domain.
A surjective function is a function whose image is equal to its co-domain, and every element y can be mapped from element x so that f(x) = y.
it suffices to give an example of y∈Z such that f(x)=y has no solutions. Just pick y=−2 and derive that
f(x)=−2⟺2x−3=−2⟺2x=1
and it should be quite clear that this has the unique solution x=0.5 over Q so no solutions for Z.
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3/5 divied by what is 3/4
[tex]\it \dfrac{3}{5}:x=\dfrac{3}{4} \Rightarrow x=\dfrac{3}{5}:\dfrac{3}{4}=\dfrac{\not3}{5}\cdot\dfrac{4}{\not3}=\dfrac{4}{5}[/tex]
[tex]\it So,\ \ \dfrac{3}{5}\ divided\ by\ \dfrac{4}{5}\ is\ \dfrac{3}{4}[/tex]
80x
/
A company sells shirts for $10 each. Its revenue function is r(x) = 10x.
Its costs are $3 per shirt plus $9,000 of fixed costs. Its cost function is
c(x) = 3x + 9000. Use this information for Problems 13-15. The first
one is done for you.
13. Find the company's revenue and costs if it sells 2000 shirts.
Revenue = $20,000; costs = $15,000
14. Profit equals the difference between revenue and cost. Write the
function, p(x), for this company.
15. In 2012, the company sold 5000 shirts. Find its profit.
in Hercourt Additions and changes to the original content are the respon
a) To find the company's revenue and costs if it sells 2000 shirts, we can substitute 2000 for x in the given revenue and cost functions:
What does a math equation mean?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Revenue: r(x) = 10x, so r(2000) = 10(2000) = $20,000
Costs: c(x) = 3x + 9000, so c(2000) = 3(2000) + 9000 = $15,000
b) The profit function, p(x), is the difference between the revenue function and the cost function. So, the profit function for this company is:
p(x) = r(x) - c(x) = 10x - (3x + 9000) = 7x - 9000
c) To find the company's profit in 2012, when it sold 5000 shirts, we substitute 5000 for x in the profit function:
p(5000) = 7(5000) - 9000 = $20,000
So, the company had a profit of $20,000 in 2012 when it sold 5000 shirts.
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Contruct a quadrilateral ABCD given that AB=2. 4cm,BC=4. 3cm,CD=3. 1cm,AD=2cm and diagonal BD=3. 9cm
We can draw a quadrilateral ABCD with sides AB, BC, CD, and AD having lengths of 2.4 cm, 4.3 cm, 3.1 cm and 2 cm respectively. The diagonal BD has a length of 3.9 cm.
Step 1: Draw a line segment AB with length 2.4 cm.
Step 2: Draw a line segment BC with length 4.3 cm.
Step 3: Draw a line segment CD with length 3.1 cm.
Step 4: Draw a line segment AD with length 2 cm.
Step 5: Draw the diagonal BD with length 3.9 cm.
Step 6: Connect the endpoints of the line segments AB, BC, CD, and AD to form a quadrilateral ABCD.
We can construct a quadrilateral ABCD given the given dimensions. To begin, we will draw a line segment AB with a length of 2.4 cm. This will be the first side of our quadrilateral. Next, we will draw a line segment BC with a length of 4.3 cm. This will be the second side of our quadrilateral. After that, we will draw a line segment CD with a length of 3.1 cm. This will be the third side of our quadrilateral. Then, we will draw a line segment AD with a length of 2 cm. This will be the fourth side of our quadrilateral. Finally, we will draw the diagonal BD with a length of 3.9 cm. To complete the quadrilateral, we will connect the endpoints of the line segments AB, BC, CD, and AD. This will form a quadrilateral with the given dimensions. The quadrilateral ABCD will have side lengths of 2.4 cm, 4.3 cm, 3.1 cm, and 2 cm respectively. The diagonal BD will have a length of 3.9 cm. Our quadrilateral ABCD is now constructed and ready to use.
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If Jon runs 35 miles a week, and Jacky runs 57 miles a week, how much more does Jacky run than Jon?
Answer:
22 miles
Step-by-step explanation:
trust
Answer in simplest radical form if necessary (NO DECIMALS!). Copy and paste this symbol if needed: √
The value of x from the given figure is 12 units.
What are similar triangles?Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.
From the given figure,
Consider ΔDEF and ΔEGF,
∠F=∠F (Reflex property)
EF=EF (Reflex property)
∠DEF=∠EGF=90°
By AA similarity, ΔDEF ~ ΔEGF
So, DF/EF = EF/GF
12/x = x/2
x²=12×2
x=2√6 units
Therefore, the value of x from the given figure is 2√6 units.
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Find the area of a rectangle whose length is 6.4 and breadth is 5cm
Answer:
Answer in attached photo.
Step-by-step explanation:
SolutionSolution is in the attached photo, do note this question tests on finding the area of shapes.
Alex went to Seattle for the weekend d with his parents. He went into the Hard Rock Cafe and bought a sweatshirt for 59.99. Sales tax is 7.5% how much did Alex pay the cashier?
Alex paid 64.48
price of sweatshirt which alex bought : 59.99
sales tax : 4.499
total price alex paid is 64.48
calculation of salex tax
price of sweatshirt :59.99.
sales tax :4.499
{59.99 x 7.5% } = 4.49
Alex paid 64.48
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Which angle has sides DB and DC? Select all that apply.
No, rectangle DABC is not the result of a dilation of rectangle HEFG with a center of dilation at the origin.
What is dilation?Dilation is a geometrical transformation that changes the size of a shape or figure. It is one of the four basic transformations of geometry alongside translation, rotation, and reflection. Dilation involves resizing a shape by a scale factor and keeping its overall shape intact. The scale factor is the ratio of the size of the image to the size of the original figure.
Dilation involves a scaling of a shape, where each point on the shape is moved away from or closer to the center of dilation, proportional to its distance from the center. In this case, the angles of rectangle DABC are different from the angles of rectangle HEFG, so it is not the result of a dilation. The angles of rectangle HEFG are ∠2, ∠33, ∠EDC, whereas the angles of rectangle DABC are ∠ADB, ∠BDC, and ∠CDB.
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1. The simple interest owed on a loan of $4000 after 3 years is $240. What percent
represents the annual interest rate on the loan? Please, Please show your work and
write your answer here
The annual interest rate on the loan is 0.02 or 2%.
What is the annual interest rate?To find the annual interest rate on the loan, we need to use the formula for simple interest:
I = Prt
where:
I is the interest,
P is the principal (the amount of the loan),
r is the annual interest rate (expressed as a decimal),
t is the time in years
We know the following information:
I = $240
P = $4000
t = 3
We can use this information to set up the equation and solve for r:
240 = 4000 * r * 3
240 = 12000r
r = 240/12000
r = 0.02
Therefore, the annual interest rate on the loan is 0.02 or 2%.
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Which expression is equivalent to 24+56
Answer:
24+56 is equivalent to 80.
PLEASE HELP I WILL MARK BRAINIEST
Answer:
y = 8
Step-by-step explanation:
The angle represented by (8x - 31)° = angle represented by (6x + 3)° since they are alternate interior angles
8x - 31 = 6x + 3
=> 8x-6x = 3 + 31
2x = 34
x = 17
Angles (8x - 31) and (5y + 35) are adjacent linear angles - they lie on the same straight line. their sum must equal 180
8x - 31 + 5y + 35 = 180
Plugging x = 17
8(17) -31 + 5y + 35 = 180
5y + 140 = 180
5y = 180 - 10 = 40
y = 40/5 = 8
if the sum of three consecutive natural number is increased by 2, the result is 50. find the number?
Answer:
Answer in attached photo.
Step-by-step explanation:
SolutionThe solution is in the attached photo, do take note we will use x,y and z to be the 3 consecutive natural numbers. Do also note in this case, since the three numbers are consecutive, they have a difference of 1 between each other.
20pts for whoever can help me with this
It is been proved that (a² + b²)(c² + d²) = (ac + bd)² + (bc - ad)².
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
(a)
(a² + b²)(c² + d²) = (ac + bd)² + (bc - ad)²
LHS,
= a²(c² + d²) + b² (c² + d²)
= a²c² + a²d² + b²c² + b²d²
= a²c² + b²d² + 2abcd + b²c² + a²d² - 2abcd
= (ac + bd)² + (bc - ad)²
= RHS
Thus, it is been proved that (a² + b²)(c² + d²) = (ac + bd)² + (bc - ad)².
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A car sales associate receives a monthly salary of $1,700 a month plus $140 for every car he sells. How many cars must he sell to earn at least $4,500?
Answer:
20 cars
Step-by-step explanation:
He wants 4500
He makes 1700 salary
4500-1700=2800
Now you need to divide the remaining 2800 needed by the 140 he gets per car he sells
2800÷140=20
So he needs to sell 20 cars
Given the Square JKLM, if the area of JKLM i 64 q in. , what i the length of the diagonal KM?
The length of the diagonal KM is 8√(2) inches.
The area of a square is given by the formula: area = side^2.
So, if the area of square JKLM is 64 square inches, then we know that:
64 = side^2
To find the diagonal KM, we can use the Pythagorean Theorem. The diagonal KM is the hypotenuse of a right triangle where the legs are the side of the square.
So the formula is KM = √(side^2 + side^2)
Substituting in the known area of the square, we have:
KM = √(64 + 64)
KM = √(128)
KM = 8√(2)
Therefore, the length of the diagonal KM is 8√(2) inches.
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KM = √(side^2 + side^2)
Substituting in the known area of the square, we have:
KM = √(64 + 64)
KM = √(128)
KM = 8√(2)
Why do we use log log?.
Data is displayed in two dimensions using log-log graphs, where both axes have logarithmic scales.
A straight line is depicted on a log-log graph when one variable varies as a constant power of the other. We can determine that X and Y do not have a power law connection if the data points do not form a straight line.
The linear function is equivalently written as log Y = log k + n log X. The statement by John Tukey that "the best thing about being a statistician is that you get to play in everyone's backyard" is amply illustrated by this example.
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(1 point) A data set consists of the data given below plus one more data point. When the additional point is included in the data set the sample mean of the resulting data set is 27.917. What is the value of the additional data point?
Note: the additional data point is an integer. If the mean contains decimals, it may be a rounded value.
21, 24, 19, 36, 52, 15, 40, 47, 19, 20, 30
The value of the additional data point is equal to 12.0
What is a sample mean?In Mathematics, a sample mean is sometimes referred to as an arithmetic average and it can be defined as a ratio of the sum of the total number in a data set (population) to the frequency of the data set.
How to calculate the sample mean for the set of data points?Mathematically, the sample mean for this set of data points can be calculated by using the following formula:
Mean = [F(x)]/n
Note: Let the variable x represent the additional data point.
For the total data points, we have;
F(x) = 21 + 24 + 19 + 36 + 52 + 15 + 40 + 47 + 19 + 20 + 30 + x
F(x) = 323 + x.
Now, we can determine the additional data point as follows;
27.917 = 323 + x/12
323 + x = 335.004
x = 335.004 - 323
x = 12.004 ≈ 12.0
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Find the surface area of the soild.
Q.7 ...
[tex]tsa \: of \: cuboid \: = 2(lb + bh + lh) \\ = 2(4 \times 3 + 3 \times 5 + 5 \times 4) \\ = 2(12 + 15 + 20) \\ = 2(47) \\ = 94 \: square \: units \: ...[/tex]
MARK ME AS BRAINLIEST ...
Answer: I CANR
Step-by-step explanation:
Evaluate the expression when a = -5, b = 7, c = -2, and d = 3.2. a-2-b+ (4.7 -d) - c
The value of the expression is -10.5 .
What is expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.
Here the given expression is ,
a-2-b+(4.7-d)-c
Now put a=-5, b=7 , c=-2 and d=3.2 then
=> -5-2-7+(4.7-3.2)-(-2)
=> -14+(1.5)+2
=> -14+3.5
=> -10.5
Hence the value of the expression is -10.5 .
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Hello, can someone help me with this?
Answer:
use the graph
Step-by-step explanation:
How many ¾ cup
servings are in 1 2/3 cup container of trail mix?
Answer: 5/3
Step-by-step explanation:
1 2/3 ÷ 3/4
= 5/4 ÷ 3/4
= 5/4 * 4/3
= 5/3 3/4 cups
The moon is approximately 240,000 miles from earth. What is the distance between the earth and the moon in km?
Answer:
390,000
Step-by-step explanation:
Point MM is located at (-5,1)(−5,1) on the coordinate plane. Point MM is reflected over the yy-axis to create point M'M
′
. Point M'M
′
is then reflected over the xx-axis to create point M''M
′′
. What ordered pair describes the location of M''?M
′′
?
The ordered pair that describes the location of M'' will be (5, -1).
What is a transformation of a point?A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.
The reflection does not change the shape and size of the geometry. But flipped the image.
Point M is located at (−5, 1) on the coordinate plane. The coordinate after the reflection over the y-axis is given as,
M' = (-x, y)
M' = (- (-5), 1)
M' = (5, 1)
The coordinate after the reflection over the x-axis is given as,
M" = (x, -y)
M" = (5, -1)
The ordered pair that describes the location of M'' will be (5, -1).
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what’s x. please find x for me
Answer:
x = 77°
Step-by-step explanation:
When an angle has its vertex on a circle, the arc that gets cut by sides is double the angle.
So arcDF is double angleEFD.
angleEFD = 74°
arcDF = 148°
arcFH is double angleD.
angleD = 29°
arcFH = 58°
All the arcs of the circle all add up to 360°
arcDF + arcFH + arcDH = 360°
148° + 58° + arcDH = 360°
206 + arcDH = 360°
subtract 206
arcDH = 154°
Again, the arc is double the angle, or the angle is half the arc.
arcDH = 154°
angleDFH = 77°
x = 77°
see image.
Find the Average Rate of Change from Equations
According to the given information in the question the average rate of change is 3.
What is average rate of change of a function?Examples of average rates of change include: 80 kilometres per hour is the average speed of a bus. At a pace of 100 each week, a lake's fish population grows. For every 1 volt drop in voltage, the current in an electrical circuit reduces by 0.2 amps.
The average rate at which one item is changing in relation to another is known as the average rate of change. An average rate of change function, put simply, is a calculation that divides the amount of change in one thing by the corresponding amount of change in another.
The formula R = D/T, or rate of change equals the distance travelled, can be used to address rate of change problems in general.
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