Tone's new monthly payment is 16.16% higher than his old monthly payment To solve the problem, we need to use the formula for the monthly payment of a mortgage loan:
monthly payment = (loan amount x monthly interest rate) / (1 - (1 + monthly interest rate)^(-n))
where:
loan amount = the amount of the loan
monthly interest rate = the annual interest rate divided by 12
n = the total number of payments (in months)
Let's first find the loan amount at the beginning of the mortgage. We know that Tone paid $9.99 per thousand, so we can set up a proportion:
$9.99 / 1000 = monthly payment / loan amount
Solving for the loan amount, we get:
loan amount = monthly payment / ($9.99 / 1000) = $1000 * (monthly payment / $9.99)
Substituting the given values, we get:
loan amount = $1000 * (monthly payment / $9.99) = $55,000
This means that Tone borrowed $55,000 at the beginning of the mortgage.
Now, let's find the old monthly payment. We know that Tone had a 10.5% adjustable rate mortgage for 30 years, which means he made 12 x 30 = 360 monthly payments. We can use the formula above to solve for the monthly payment:
monthly interest rate = 10.5% / 12 = 0.00875
n = 360
monthly payment = ($[tex]55,000 x 0.00875) / (1 - (1 + 0.00875)^(-360)[/tex]) = $512.47
Therefore, Tone's old monthly payment was $512.47.
Next, let's find the new monthly payment. We know that Tone will renew his mortgage at 12.5% interest rate, which means the new monthly interest rate is:
monthly interest rate = 12.5% / 12 = 0.01042
We also know that Tone will pay $10.68 per thousand, so we can set up a new proportion:
$10.68 / 1000 = new monthly payment / loan amount
Solving for the new monthly payment, we get:
new monthly payment = $10.68 / ($1000 / $55,000) = $595.40
Therefore, Tone's new monthly payment is $595.40.
Finally, let's find the percent increase in the new monthly payment compared to the old monthly payment. We can use the percent change formula:
percent increase = ((new value - old value) / old value) x 100%
Substituting the given values, we get:
percent increase = (($595.40 - $512.47) / $512.47) x 100% = 16.16%
Therefore, Tone's new monthly payment is 16.16% higher than his old monthly payment
To know more about interest rate click here:
brainly.com/question/14445709
#SPJ1
I need help, I wasn't in school for 2 weeks because of vacation and nobody is helping me in class!
(a) Since M is the midpoint of DE, we have ME = (1/2)b.
Also, CXE is a straight line, so C, X, and E are collinear.
Therefore, we have CX + XE = CE, or a - b + FE = b + (2a - b), which simplifies to FE = a.
(b) n = a/b - 1.
How do we calculate?X is the point on FM such that
FX:XM =n:1,
we have FX = nX and XM = X.
Since M is the midpoint of DE, we have ME = (1/2)b,
so that DX = DE - EX = b - (n + 1)X.
Using the fact that CXE is a straight line,
we have CX + XE = CE, or a - b + FE = b + (2a - b),
which simplifies to FE = a.
Therefore, we have FX + FE = AX, or nX + a = a + b + (n + 1)X.
Simplifying, we get b = (n + 1)X - nX = X.
We know that DX = b - (n + 1)X = 0, so X = b/(n + 1).
Therefore, we have n/(n + 1) = FX/X = (a-b)/b.
Calculating for n, we have n = a/b - 1.
Learn more about straight lines at: https://brainly.com/question/29223887
#SPJ1
Rachel has a large pond on her property. The pond contains many different kinds of fish including bass. She knows that the population of the bass is increasing exponentially each year at a rate of 4.8%. She also knows that there are currently between 250 and 275 bass in the pond.
If P represents the actual population of the bass in the pond and t represents the elapsed time in years, then which of the following systems of inequalities can be used to determine the possible number of bass in the pond over time?
The inequalities that can be used to determine the possible number of bass in the pond over time are:
[tex]P > =250e^{0.048t} , P < =275e^{0.048t}.[/tex]
Rachel has a large pond on her property. The pond contains many different kinds of fish including bass. She knows that the population of bass is increasing exponentially each year at a rate of 4.8%. She also knows that there are currently between 250 and 275 basses in the pond.
Inequalities
Given:
r=4.8/100=0.048
Initial amount:
Lower end=250
Upper end=275
Using this equation to determine the inequalities
A=p×e^rt
Where:
A=Amount
P=Population
r=Growth rate
t=Time
Let's plug in the formula
Inequalities:
[tex]P > =250e^{0.048t}P < =275e^{0.048t}[/tex]
Therefore the inequalities are : [tex]P > =250e^{0.048t} , P < =275e^{0.048t}.[/tex]
Learn more about inequalities here
:brainly.com/question/24372553
#SPJ1
the test scores for the students in two classes are summarized in these box plots. the 17 students in class 1 each earned a different score.the 13 students in class 2 each earned a different score.what is the difference between the number of students who earned a score of 90 or less in class 2 and the number of students who earned less than 75 in class 1?the test scores for the students in two classes are summarized in these box plots. the 17 students in class 1 each earned a different score.the 13 students in class 2 each earned a different score.what is the difference between the number of students who earned a score of 90 or less in class 2 and the number of students who earned less than 75 in class 1?
The number of students who earned a score of 90 or less in class 2 is 7, and the number of students who earned less than 75 in class 1 is 3. The difference between the two is 4.
The given problem presents two box plots representing the test scores for two different classes. Class 1 has 17 students, while class 2 has 13 students. It is required to find the difference between the number of students who earned a score of 90 or less in class 2 and the number of students who earned less than 75 in class 1.
By analyzing the box plots, we can see that 7 students in class 2 earned a score of 90 or less, while only 3 students in class 1 earned less than 75. Therefore, the difference between the two is 4. It is important to understand box plots and their interpretation to solve such problems.
To know more about box plot, here
brainly.com/question/15600223
#SPJ4
Given circle E with diameter CD and radius EA. AB is tangent to E at A. If AC = 9 and AD = 4, solve for CD. Round your answer to the nearest tenth if necessary. If the answer cannot be determined, click "Cannot be determined."
Since AB is tangent to circle E at A, we know that angle CAB is a right angle (tangent is perpendicular to the radius at the point of tangency). Therefore, triangle ADC is a right triangle.
Let's use the Pythagorean theorem to find the length of CE:
CE^2 = AC^2 + AE^2 (using Pythagorean theorem in triangle ACE)
CE^2 = 9^2 + EA^2 (since AE = EA, by definition of radius)
CE^2 = 81 + EA^2
We still need to find EA. Let's use the fact that EA is half the length of CD:
EA = CD/2
Now we can substitute this expression into the previous equation:
CE^2 = 81 + (CD/2)^2
CE^2 = 81 + CD^2/4
Next, let's use the Pythagorean theorem in triangle ADC:
AD^2 + DC^2 = AC^2
4^2 + DC^2 = 9^2
DC^2 = 9^2 - 4^2
DC^2 = 65
Now we can substitute this expression into the previous equation:
CE^2 = 81 + 65/4
CE^2 = 99.25
Taking the square root of both sides, we get:
CE ≈ 9.96
Therefore, CD = 2CE ≈ 19.9.
Answer: CD ≈ 19.9
The preimage shown below is dilated by a scale factor of 1/4 about the point (2,2). If the distance from the center of dilation to point A is 5.7 units, what is the distance from the center of dilation to point A'.
Round your answer to the nearest tenth please :)))
For given dilation of the figure, the distance from the center of dilation to point A' is approximately 1.414 units.
What exactly is dilation in mathematics?
In mathematics, dilation is a transformation that changes the size of a figure but not its shape. It is also known as scaling, enlargement, or reduction.
To perform a dilation, a figure is multiplied or divided by a scale factor, which is a positive number greater than zero. If the scale factor is greater than 1, the figure is enlarged, while if it is less than 1, the figure is reduced. If the scale factor is equal to 1, the figure remains the same size.
Now,
To find the distance from the center of dilation to point A', we need to use the fact that the distance between the center of dilation and any point on the preimage is multiplied by the scale factor to get the corresponding distance on the image.
First, let's find the distance from the center of dilation to point A:
distance from center to A = √((6-2)² + (-2-2)²) = √(4² + (-4)²) = √32 ≈ 5.657 units (rounded to three decimal places)
Next, we can use the fact that the scale factor is 1/4 to find the distance from the center of dilation to point A':
distance from center to A' = (scale factor) x (distance from center to A)
= (1/4) x 5.657
= 1.414 units (rounded to three decimal places)
Therefore, the distance from the center of dilation to point A' is approximately 1.414 units.
To know more about dilation visit the link
brainly.com/question/13176891
#SPJ1
HELP have no idea how to do this
Answer:
use SSS
Step-by-step explanation:
Given two congruent chords AB and BC in circle O, you want to prove ∆AOB is congruent to ∆COB.
Statement . . . . Reason1. circle O, AB≅BC . . . . given
2. OB ≅ OB . . . . reflexive property of congruence
3. OA ≅ OC . . . . definition of a circle
4. ∆AOB ≅ ∆COB . . . . SSS postulate
__
Additional comment
Your erased statement 2 shows you know exactly how to do this.
All the radii of a circle are the same length, so it is easy to show congruence by SSS, given that AB≅BC.
Mary invests $200 in a high-interest savings account. In the first year, the value of her savings increases by 8%. In the second year, there is a further increase of 8%. What is the total value of her investment after two years? Round your answer to the nearest dollar.
The total value of Mary's investment after two years is $233.
If a stone is thrown upward with a speed of 110 feet per second from a height of 500 feet above the surface of a planet, the equation h = 500 + 110t - 5.5t² approximates the height of the stone, in feet, at t seconds. When will the stone be 698 feet above the planet's surface?
We can solve for the time when the stone will be 698 feet above the planet's surface by setting h = 698 and solving for t in the equation h = 500 + 110t - 5.5t²:
698 = 500 + 110t - 5.5t²
Rearranging, we get:
5.5t² - 110t + 198 = 0
Dividing both sides by 5.5, we get:
t² - 20t + 36 = 0
This is a quadratic equation that we can solve using the quadratic formula:
t = (-(-20) ± sqrt((-20)² - 4(1)(36))) / (2(1))
Simplifying, we get:
t = (20 ± sqrt(64)) / 2
t = 10 ± 4
So the possible values of t are t = 14 or t = 6. We can check which value is correct by plugging each value into the original equation and seeing if it gives a height of 698:
When t = 14:
h = 500 + 110(14) - 5.5(14)²
h = 500 + 1540 - 1078
h = 962
When t = 6:
h = 500 + 110(6) - 5.5(6)²
h = 500 + 660 - 198
h = 962
So both values of t give a height of 698. Therefore, the stone will be 698 feet above the planet's surface at t = 6 seconds or t = 14 seconds.
Find the measures of each exterior angle of a regular 66-gon, the round to the nearest tenth.
Angles: 5.4,6.4,173.6,9720
The correct angle measure in degrees for each exterior angle is 5.5. The other values provided in the question, 6.4, 173.6, and 9720, are not relevant to the problem.
What is Exterior angles ?
In a polygon, an exterior angle is an angle formed by a side and an extension of an adjacent side. The measure of an exterior angle of a regular polygon with n sides is given by 360/n degrees.
To find the measure of each exterior angle of a regular polygon, we use the formula:
Measure of each exterior angle = 360 degrees / number of sides
In this case, the polygon is a regular 66-gon, so the number of sides is 66. Thus,
Measure of each exterior angle = 360 degrees / 66 = 5.454545...
Rounding to the nearest tenth, we get:
Measure of each exterior angle ≈ 5.5 degrees
Therefore, the correct angle measure in degrees for each exterior angle is 5.5. The other values provided in the question, 6.4, 173.6, and 9720, are not relevant to the problem.
To learn more about Exterior Angles from given link.
https://brainly.com/question/29064061
#SPJ1
(Using trig to find an angle)
Solve for x. Round to the nearest tenth of a degree, if necessary.
Angle B is approximately 53.15 degrees using trigonometry.
EquationsWe can use trigonometry to solve for angle B in the right triangle BCD. We know that angle CBC is 37 degrees, and BD is 64.
First, we can use the Pythagorean theorem to find the length of BC, which is the hypotenuse of the right triangle:
[tex]BC^{2}[/tex] = [tex]BD^{2}+CD^{2}[/tex]
[tex]BC^{2}[/tex] = 64² + [tex]CD^{2}[/tex]
Since CD is opposite angle B, we can use trigonometry to relate CD to angle B. Specifically, we can use the tangent function:
tan(B) = CD/BD
Rearranging, we have:
CD = BDxtan(B)
Taking the square root of both sides, we have:
BC = 64[tex]\sqrt{(1+tan^{2}B)}[/tex]
Now we can use the fact that BC is the hypotenuse of the right triangle to relate it to angle CBC, which is 37 degrees. Specifically, we can use the sine function:
sin(CBC) = BD/BC
Substituting our expression for BC, we have:
sin(37) = 64/64√(1 + tan²(B))
Simplifying, we get:
sin(37) = 1/[tex]\sqrt{(1+tan^{2}B)}[/tex]
Squaring both sides, we have:
sin²(37) = 1/[tex](1+tan^{2}B)}[/tex]
Substituting the identity cos²(θ) + sin²(θ) = 1, we have:
cos²(37) = cos²(B)
Taking the square root of both sides, we have:
cos(37) = ±cos(B)
Since angle B is acute (it is less than 90 degrees because it is in a right triangle), we know that cos(B) is positive. Therefore, we can take the positive square root:
cos(B) = cos(37)
B = 53.15 degrees (rounded to two decimal places)
To know more about trigonometry, click here,
https://brainly.com/question/29002217
#SPJ1
Bonjour pouvez vous m'aider svp c'est urgent !! Calculer la valeur de chaque expression pour a=3 et b=10: a+b= a-b= -7 ab= a/b= a²= 2b
If Triangle CFE is congruent to triangle PTR, Complete each of the following statements.
(37 points)
"Triangle CFE is congruent to triangle PTR" is true.
If Triangle CFE is congruent to triangle PTR, we can make the following statements:
The corresponding sides of the triangles are congruent:
This means that CF = PT, FE = TR, and CE = PR.
The corresponding angles of the triangles are congruent:
This means that angle CFE is congruent to angle PTR, angle FCE is congruent to angle PRT, and angle ECF is congruent to angle TPR.
The triangles are equal in area: Since the triangles are congruent, they have the same shape and size. Therefore, they will have the same area.
The triangles can be superimposed on each other: This means that we can place triangle CFE on top of triangle PTR in such a way that their corresponding sides and angles overlap.
If we know the measurements of the sides and angles of one triangle, we can find the measurements of the sides and angles of the other triangle: Since the triangles are congruent, we know that their corresponding sides and angles are equal.
Therefore, if we know the measurements of the sides and angles of one triangle, we can find the measurements of the sides and angles of the other triangle by using the congruence criteria.
In conclusion, if Triangle CFE is congruent to triangle PTR, we can make several statements about their corresponding sides and angles, their areas, and their ability to be superimposed on each other.
We can also use the congruence criteria to find the measurements of the sides and angles of one triangle if we know the measurements of the sides and angles of the other triangle.
For similar question on triangle:
brainly.com/question/22165226
#SPJ11
Identify the slope and y-intercept of the following equations:
a. y = 4x + 1
b. y = x - 2
c. y = 1/3x
It'd be so helpful if even one of these were answered. Thank you!
Therefore, the slope is 1/3 and the y-intercept is 0.
a. The equation is in slope-intercept form, y = mx + b, where m is the slope and b are the y-intercept. In this case, the slope is 4, and the y-intercept is 1. Therefore, the slope is 4 and the y-intercept is 1.
b. This equation is also in slope-intercept form, y = mx + b, where m is the slope and b are the y-intercept. In this case, the slope is 1, and the y-intercept is -2. Therefore, the slope is 1 and the y-intercept is -2.
c. This equation is already in slope-intercept form, y = mx + b, where m is the slope and b are the y-intercept. In this case, the slope is 1/3, and the y-intercept is 0 (since there is no constant term). Therefore, the slope is 1/3 and the y-intercept is 0.
To learn more about y-intercept, visit
https://brainly.com/question/14180189
#SPJ1
Find the height of the basketball hoop
Answer: 13.51 (not in inches format)
Step-by-step explanation:
tan(x) = 4.384/12
x = tan^-1 (4.384/12)
x = 20.068°
tan(20.068) = y/(12+25)
tan(20.068) = y/37
20.068 = tan^-1 (y/37)
y = 13.51
Answer:
Step-by-step explanation:
To solve this with similar triangles - you need to set up a proportion.
I changed it all to inches.
12 ft = 144 in
4.384 ft = 51. 84 inches
12 + 25 (you need to add the base of the triangle) = 37 ft = 444 inches
set up smaller triangle in proportion to bigger triangle
51.84"/144" = x/444
cross mulitply then divide
51.84 times 444 = 23016.96
23016.96 ÷ 144 = 159.84 inches
Change back to feet by dividing by 12
159.84 ÷ 12 = 13.32 ft
There is a spinner with 15 equal areas, numbered 1 through 15. If the spinner is spun one time, what is the probability that the result is a multiple of 4 or a multiple of 6?
Answer:
To solve this problem, we need to first find the numbers that are multiples of 4 or 6 between 1 and 15, inclusive.
Multiples of 4: 4, 8, 12
Multiples of 6: 6, 12
The number 12 is a multiple of both 4 and 6, so we only count it once.
So, there are a total of 4 possible outcomes that meet the condition of being a multiple of 4 or 6.
Therefore, the probability of getting a multiple of 4 or 6 is:
P(multiple of 4 or 6) = 4/15
Answer: 4/15.
Hope This Helps!
Y=-x+1
Y= 2/3x-4
How many solutions does it have?
Answer:
x = -5
Y = -22/3
Step-by-step explanation:
Y= 2/3x - 4 Y = -x + 1
We put -x + 1 in for y to solve for x
-x + 1 = 2/3x - 4
-5/3x + 1 = -4
-5/3x = -5
x = -5
Now put -5 in for x and solve for y
Y= 2/3(-5) - 4
Y = -10/3 - 4
Y = -22/3
So, there are only one solution x = -5 and y = -22/3
5. Heidi's family is trying to decide on the shorter
of two routes for a trip from Georgetown to
Cypress City. One route begins in Georgetown
and goes 53 miles to Cycle City, then 28 miles
to Aspen and 98 miles to Cypress City. The
second route also begins in Georgetown and
goes 28 miles to Canon City, then 49 miles to
Grover and 85 miles to Cypress City. Which
route is shorter and by how much?
Answer: We can find the total distance of the first route by adding the individual distances:
53 + 28 + 98 = 179 miles
Similarly, we can find the total distance of the second route:
28 + 49 + 85 = 162 miles
Therefore, the second route is shorter by (179 - 162) = 17 miles.
Step-by-step explanation:
Find the area and perimeter 20 12
This graph represents the revenue in dollars that a company expects if they sell their product for p dollars.Based on this model, which price would generate more revenue for the company, $5 or $17? Explain how you know.
The price that would generate more revenue for the company will be $5 because p(5) > p(17) based on the revenue generation on the graph.
How can we determine which price would generate more revenue for the company on a revenue graph?As we change the price of the product, the quantity sold may also change. This means that the revenue curve will not be a straight line, but rather a curve that increases and then decreases as we move from lower to higher prices. The price point that generates the highest revenue will be the one at which the revenue curve reaches its maximum value.
It is important to note that the price point that maximizes revenue may not necessarily be the same as the price point that maximizes profit, as profit is influenced by both revenue and costs. Therefore, companies must carefully consider both revenue and cost factors when determining the optimal price point for their products.
Read more about graph
brainly.com/question/25184007
#SPJ1
. Explain how to convert a measurement of 165 in to a measurement in yards, feet, and inches.
Answer:
Step-by-step explanation:
One of the sides of a parallelogram has the length
of 5 in. Can the lengths of the diagonals be
4 in. and 6 in.?
Answer:
Yes they can.
The only time they would have to be different lengths is if it was a square
Your father uses text messaging to communicate with his employees. If he sends an average of 17 text messages each day, how many more text messages does he send than you? Write an equation that contains the unknown value, x, and solve for the unknown value
HURRY THIS IS A PROJECT QUESTION
17-x
Because he sends more than you we subtract your value,x,from his 17,mostly because we are unaware of the number of texts you send.Which means 17 minus x will give you the amount of texts he sends more.
Is this dilation a reduction or an enlargement
Answer:
Step-by-step explanation:
A dilation maintains the shape of a figure but changes its size.
A reduction would mean the new figure will be a smaller version of the original.
An enlargement would mean the new figure will be a bigger version of the original.
This particular question doesn’t include a photo so depending on these definitions, one can easily identify the correct answer.
Answer:
In geometry, a dilation is a transformation that changes the size of a figure while keeping its shape the same. Imagine taking a picture of a shape and then making it bigger or smaller without changing its proportions or angles.
If a dilation makes the figure smaller than the original, we call it a reduction. This means that the new figure is a scaled-down version of the original. Conversely, if a dilation makes the figure larger, we call it an enlargement. In this case, the new figure is a scaled-up version of the original.
So, to summarize, dilations can change the size of a figure while preserving its shape, and we can describe the resulting figure as either a reduction or an enlargement depending on whether it is smaller or larger than the original.
Step-by-step explanation:
Liz flips a coin 90 times. the coin lands heads up 27 times and tails up 63 times. Complete each statement
Answer:
The probability of the coin landing heads up on any given flip is 1/2, and the probability of it landing tails up is also 1/2. Therefore, we can use the binomial distribution formula to calculate the probability of getting exactly 27 heads out of 90 flips: P(27 heads) = (90 choose 27) * (1/2)^27 * (1/2)^63 = 1.452 x 10^-9 So the probability of getting exactly 27 heads out of 90 flips is approximately 1.452 x 10^-9.
is would be 50 percent! you're welcome
Can you pls do this i can't do it, it's a little hard and due before 4:00 pm ( Will mark brainliest if 2 answers and 95 pts if you can do it pls and thank you!!)
Based on the given information, Mike's grandmother deposited $6,000 into the savings account.
What is simple interest?
Simple interest is a method of calculating interest on a principal amount, where the interest is calculated only on the original amount of the loan or investment, without taking into account any interest that may have been previously earned. The formula for calculating simple interest is I = P * r * t, where I is the interest earned, P is the principal amount, r is the annual interest rate as a decimal, and t is the time period in years.
We are given that the interest rate is 8% and the interest earned after 10 years is $4,800. So we can write:
4,800 = P * 0.08 * 10
Simplifying the equation, we get:
4,800 = 0.8P
Dividing both sides by 0.8, we get:
P = 6,000
Therefore, Mike's grandmother deposited $6,000 into the savings account.
To know more about simple interest visit:
brainly.com/question/20406888
#SPJ1
Each week, Sophia earns $10 per hour for the first 40 hours she works, and $15 for each hour of work after 40 hours. Her weekly earnings are a function of the amount of time she works. Which function models the amount of money that Sophia earns?
The mathematical function model for Bailey's income is: Regular earning +overtime pay=total earnings
What is a function?A relation between a collection of inputs and outputs is known as a function.
A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
So, we've said the:
12$ =1hours
initial forty hours a week
Then after a week, 18 dollars per hour.
We must ascertain the function that represents Bailey's income.
Then, the formula for regular earnings:
regular hour × regular rate=regular eaning
40(12)=480$
overtime hours × overtime rate=overtime pay
Regular earning +overtime pay=total earnings
The overtime hours in this case are unknown.
Because of this, we are unable to determine total earnings.
Therefore, the mathematical function model for Bailey's income is: Regular earning +overtime pay=total earnings
Know more about functions here:
https://brainly.com/question/22340031
#SPJ1
Correct question:
Each week, Bailey earns $12 per hour for the first 40 hours she works, and $18 for each hour of work after 40 hours. Her weekly earnings are a function of the amount of time she works.
Which function models the amount of money that Bailey earns?
write down a polynomial of degree exactly 5 that interpolates the four points (1, 1), (2, 3), (3, 3), (4, 4).
The required polynomial of exact degree 5 which interpolates the four given points is equals to p(x) = x^3/2 -4x^2 + 63x/6 -6.
Polynomial of degree exactly 5 that interpolates the four points (1, 1), (2, 3), (3, 3), (4, 4).
Apply Lagrange interpolation.
Standard form of the Lagrange interpolation polynomial of degree n passing through n+1 distinct points (x0, y0), (x1, y1), ..., (xn, yn) is,
L(x) = Σ [yi × Π (x - xj) / (xi - xj)], for i = 0, 1, ..., n
where Π is the product operator and j takes all values different from i.
For the given four points, we have n = 3, so the polynomial has degree n+1 = 4.
Using the formula, we have,
L(x) = (1× (x - 2)(x - 3)(x - 4) / ((1 - 2)(1 - 3)(1 - 4)))
+ (3× (x - 1)(x - 3)(x - 4) / ((2 - 1)(2 - 3)(2 - 4)))
+ (3× (x - 1)(x - 2)(x - 4) / ((3 - 1)(3 - 2)(3 - 4)))
+ (4× (x - 1)(x - 2)(x - 3) / ((4 - 1)(4 - 2)(4 - 3)))
Simplifying this expression, we get,
⇒L(x) = (-x^3 + 9x^2 - 26x + 24)/6 + (3x^3/2 - 12x^2 + 57x/2 - 18) +(-3x^3/2 + 21x^2 /2- 21x + 12) + (2x^3/3 - 4x^2 + 22x/3 - 4)
⇒L(x) = x^3/2 -4x^2 + 63x/6 -6
Therefore, the polynomial of degree exactly 5 that interpolates the four points (1, 1), (2, 3), (3, 3), (4, 4) is p(x) = x^3/2 -4x^2 + 63x/6 -6.
Learn more about polynomial here
brainly.com/question/30503501
#SPJ4
The Russell family just bought 6 crates of eggs, and each crate had 12 eggs. The family already had 9 eggs in their refrigerator. How many eggs do they have now?
Answer:
81 eggs
Step-by-step explanation:
already had 9 eggs
6 crates x 12 eggs in each crate
= 72 eggs
72+9=81
Find an for each geometric sequence.
a₁= 3r= 1/10 n=8
O a. 3
Ob. 2 4/10
Oc.
3
10,000,000
Od. 2 1/10
The geometric sequence for the value of a₁= 3 r= 1/10 n=8 is [tex]a_{8} = \frac{3}{10000000}[/tex] i.e option c is correct.
What does the term "geometric sequence" mean?
A geometric sequence is a set of integers where the ratio between each pair of succeeding terms is fixed. The geometric sequence's general ratio is the name of this constant.
We can use the following algorithm to determine the nth term (an) of a geometric sequence:
[tex]a_{n} = a_{1} * r^{n-1}[/tex]
where a1 is the first term in the series, r represents the common ratio, and n denotes the term's number.
Since a1 = 3, r = 1/10, and n = 8, we get:
[tex]a_{8} = 3 * (\frac{1}{10})^{8-1} = 3 *( \frac{1}{10})^{7}[/tex]
[tex]= 3 * \frac{1}{10^{7} }[/tex]
Now, we can condense this equation to get the solution:
a₈ = [tex]\frac{3}{10000000}[/tex]
The solution is therefore [tex]\frac{3}{10000000}[/tex] that option c.
Learn more about geometric sequence here:
https://brainly.com/question/13008517
#SPJ1
The cost of a pair of boots was $84 the sales tax rate is 5% of the purchase what is the sales tax 
Answer: $4.20
Step-by-step explanation:
To answer this question, we will find 5% of $84.
First, a percent divided by 100 becomes a decimal.
5% / 100 = 0.05
Next, we are finding 5% of $84. In mathematics, "of" means multiplication.
0.05 * $84 = $4.20