Answer:57.6^3
thats t
We have graph, 5 points on the graph , and need to answer on question b(ii) b(iii), and c) it is connected .The rest of the questions are answered. So an not go separately . Thank you
The evaluation of the cubic function represented by the graph can be presented as follows;
a. The equation of the function, S = a·t³ + b·t² + c·t + d, indicates that the equation is a cubic equation
b. i. d = -5
ii. The three equations are;
a + b + c = 8...(1)
8·a + 4·b + 2·c = 4...(2)
27·a + 9·b + 3·c = 0...(3)
iii. a = 2, b = -12, and c = 18
c. The student is expected to be in debt for 2 years, 4 months and 3 days
What is a cubic function?A cubic function is a degree three polynomial that can be expressed in the form; f(x) = a·x³ + b·x² + c·x + d.
The specified function can be presented as follows;
S = a·t³ + b·t² + c·t + d
a. A feature of the graph that indicates that a cubic equation is the appropriate model, is the largest power of the input time variable t in the function is 3, which is the same as the power of a cubic function.
b. i. The value of d can be found by plugging in t = 0, in the function; S = a·t³ + b·t² + c·t + d
From the table in the question, we get;
At t = 0, S = -5
Therefore;
S = a×0³ + b×0² + c×0 + d = -5
d = -5
The value of d = -5
b. ii. The simultaneous equations can be obtained by plugging in the values of t from the table into the function for S as follows;
S = a·t³ + b·t² + c·t + d
S = a·t³ + b·t² + c·t - 5
When t = 1, we get;
S = a·1³ + b·1² + c·1 - 5 = 3
a + b + c - 5 = 3
a + b + c = 3 + 5 = 8
a + b + c = 8...(1)When t = 2, we get;
S = a·2³ + b·2² + c·2 - 5 = 3
8·a + 4·b + 2·c - 5 = -1
8·a + 4·b + 2·c = -1 + 5 = 4
8·a + 4·b + 2·c = 4...(2)When t = 3, we get;
S = a·3³ + b·3² + c·3 - 5 = 3
27·a + 9·b + 3·c - 5 = -5
27·a + 9·b + 3·c = -5 + 5 = 0
27·a + 9·b + 3·c = 0...(3)iii. Solving the system of equations using a graphing calculator, indicates that we get;
a = 2, b = -12, and c = 18c. Plugging in the values into the specified equation, we get;
S = 2·t³ - 12·t² + 18·t - 5
The solution of the above equation can be found as follows;
2·t³ - 12·t² + 18·t - 5 = 0
Based on an online tool, the Newton Raphson method indicates that a solution of the equation is; t ≈ 0.35821, which indicates that a factor of the equation, 2·t³ - 12·t² + 18·t - 5 = 0 is; (x - 0.35821)
(2·t³ - 12·t² + 18·t - 5) ÷ (x - 0.35821) ≈ 2·t² - 11.28356·t + 13.95804
The other solutions are therefore;
t ≈ 1.83, and t ≈ 3.81
The student is expected to be in debt at time t = 0, and from the graph, cross the x-axis out of depth first at time, t ≈ 0.35821 of a year
The student will be in dept again between t ≈ 1.83 and t ≈ 3.81
The total time the student is expected to be in debt is therefore;
∑t = 0.35821 + (3.81 - 1.83) ≈ 2.33821 years ≈ 2 years 4 months and 3 daysLearn more on cubic functions here: https://brainly.com/question/2456468
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Select the correct answer. A line t runs downward to the right through two parallel horizontal lines a and b, forming 8 angles numbered from 1 to 8. In the diagram, transversal t cuts parallel lines a and b. Which equation is necessarily true? A. m∠1 = m∠7 B. m∠3 = m∠6 C. m∠5 + m∠8 = 90° D. m∠6 + m∠7 = 180°
Answer:
Step-by-step explanation:
The correct answer is D. m∠6 + m∠7 = 180°.
When a transversal cuts two parallel lines, corresponding angles are equal and alternate interior angles are supplementary. This means that the sum of alternate interior angles is equal to 180°. In this diagram, ∠6 and ∠7 are alternate interior angles, so it is necessarily true that m∠6 + m∠7 = 180°.
The other options are not necessarily true. Option A states that m∠1 = m∠7, but this is only true if the two lines being cut by the transversal are perpendicular. Option B states that m∠3 = m∠6, but this is only true if the two lines being cut by the transversal are parallel. Option C states that m∠5 + m∠8 = 90°, but this is only true if the two lines being cut by the transversal are perpendicular.
PLEASE HELP ME!!!!! CORRECT ANSWER GETS BRAINLIEST
Answer:
So, Darmal needs to work more than 8.96 hours to earn more than $128.
Step-by-step explanation:
The situation represented by the inequality 14.25x > 128 is B. Darmal earns $14.25 per hour at his job. How many hours does he need to work to earn more than $128?
The inequality states that the product of 14.25 and x (representing the number of hours worked) is greater than 128. Solving for x, we can find the number of hours Darmal needs to work to earn more than $128:
14.25x > 128
x > 128 / 14.25
x > 8.96
So, Darmal needs to work more than 8.96 hours to earn more than $128.
How to solve evaluate the limit
Step-by-step explanation:
for z -> 3 (3z - 2) -> (3×3 - 2) = 7
At the local grocery store, A 12 ounce bottle of stay clean shampoo costs 8 and an 8 ounce bottle of shampoo costs 6. Which size bottle has the lesser cost per ounce?
Using their unit rates, the 12-ounce bottle costs lesser per ounce than the 8-ounce bottle of stay clean shampoo.
What is the unit rate?The unit rate is the cost per unit.
The unit rate is computed as the quotient of the total cost and the number of units.
The cost of a 12-ounce bottle of stay clean shampoo = $8
The unit rate per ounce of the 12-ounce bottle = $0.67 ($8/12)
The cost of an 8-ounce bottle of stay clean shampoo = $6
The unit rate per ounce of the 8-ounce bottle = $0.75 ($6/8)
Thus, comparing the unit rate of the 12-ounce bottle with the 8-ounce bottle, we can conclude that it costs more per ounce to buy the 8-ounce bottle than the 12-ounce bottle.
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For a particular 4 leaf clover, the highway had to be compacted on the south side making the circles two different sizes. The two circles on the north of the highway have a radius of 128 feet and the two on the south side have radius of 102 feetCalculate the total area of grass seed needed for these four circles
The total area of the two circles will be 168316.9 square feet.
What is a circle?The circle is defined as a two-dimensional figure having a fixed point and the number of the points is traced around the curved path at an equal distance from the fixed point. The overall figure is called a circle.
The area of the circle is calculated by the formula:-
Area = πr²
Given that the south side of the highway needed to be compacted in order to create two circles of various sizes for a specific four-leaf clover. The two circles on the north side of the road have a 128-foot radius, whereas the two on the south side have a 102-foot radius.
The total area will be calculated as:-
Area = 2 x π x 128² + 2 x π x 102²
Area = 102943.25 + 65370.25
Area = 168316.9 square feet
Hence, the total area will be 168316.9 square feet.
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Cone B is the image of cone A after dilation by a scale factor of 1/4.
If the volume of cone B is 1 m³, find the volume of cone A, the preimage.
The volume of the Cone A will be 4m³.
What is a cone?
A cone is a shape constructed by connecting a common point, known as the apex or vertex, to all the points of a circular base using a collection of line segments (which does not contain the apex). The height of the cone is the distance from the vertex to the base. The radius of the circular base has been measured. The slant height is the length of the cone from the apex to any point on the perimeter of the base. Based on these values, formulae for the cone's surface area and volume have been developed. The cone in the illustration is characterised by its height, radius of base, and slant height.
Volume of cone=πr²h where r=radius of base and h=height of cone
Curved surface area=πrL , where L=slant height
Now,
As given Cone B is the image of cone A after dilation by a scale factor of 1/4. If the volume of cone B is 1 m³
After dilation volume also decreases/increases with respect to scale factor of dilation. Here scale factor is 1/4
and Then volume of A=1*4
=4 m³
hence,
The volume of the Cone A will be 4m³.
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Answer: it is actually 64m^3
Step-by-step explanation:
i did it and this was the right answer
answer all pls get 100 pointa
a).The function1 changes at greater rate of 45.
b). At x = 1; the function1 = 45 and function2 = 50.
c).The functions are equal to 90 at x = 2.
What is a function in the form y = mx + cA function in the equation form "y = mx + c" represents a straight line in a two-dimensional coordinate system. "y" and "x" are variables representing the coordinates of points on the line, "m" is the slope of the line, and "c" is the y-intercept, which is the point at which the line crosses the y-axis.
The slope "m" represents the rate at which the line rises or falls as x increases. The y-intercept "c" determines the location of the line along the y-axis. This equation is known as the slope-intercept form of a linear equation.
For the function1, when y = 0 and x = 0, we can solve for c and m as follows:
0 = 0m + c
c = 0
when y = 90 and x = 2;
90 = 2m + 0
m = 45
Hence, the function1 with y = 45x changes at a greater rate of 45.
At x = 1:
for function1;
y = 45(1) + 0 = 45
for function2;
y = 40(1) + 10 = 50.
At the point when x = 2:
for function1;
y = 45(2) + 0 = 90
for function2;
y = 40(2) + 10 = 90.
Therefore, the function1 changes at greater rate of 45. At x = 1; the function1 = 45 and function2 = 50. The functions are equal to 90at x = 2.
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Let A be an m×n matrix and let u be a vector in R^n that satisfies the equation Ax=0. Show that for any scalar c, the vector cu also satisfies Ax=0.[ That is, show that A(cu)=0.]
Using the distributive property of matrix multiplication A(cu) = 0, which implies that cu also satisfies the equation Ax = 0 for any scalar c.
We have given that Ax = 0, where A is an m × n matrix and x is an n-dimensional vector in Rn.
To show that A(cu) = 0 for any scalar c, we can use the distributive property of matrix multiplication, which states that A(B + C) = AB + AC for any matrices A, B, and C of appropriate dimensions.
Let us substitute cu for x in the equation Ax = 0, then we get:
A(cu) = A(c × u)
Using the distributive property, we can write:
A(c × u) = c × A(u)
Since u satisfies the equation Ax = 0, we have:
A(u) = 0
Substituting this into the above equation, we get:
c × A(u) = c × 0 = 0
Therefore, we have shown that A(cu) = 0, which implies that cu also satisfies the equation Ax = 0 for any scalar c.
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Which of the following tables represents a linear relationship that is also proportional?
x 2 34
y -303
O
x 4 20
y-2 -1 0
X-214
У 0 12
x012
y-404
The table that represents a linear relationship that is also proportional is; Table 2
How to find the proportional relationship?A proportional relationship is defined as one where there is multiplying or dividing between the two numbers. A linear relationship can be a proportional one (for example y = 2x is proportional), but usually a linear equation has a proportional component plus some constant number (for example y = 2x + 3).
Table 1:
The proportions are;
-3/2, 0/3, 3/4
They are not equal and so not proportional
Table 2:
The proportions are;
-2/4 and -1/2
They are equal and so are proportional
Table 3:
The proportions are;
0/-2, 1/1 and 2/4
They are not equal and so not proportional.
Table 4:
The proportions are;
-4/0, 0/1 and 4/2
They are not equal and so not proportional.
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In which quadrant does the point (-21 , 13) lie?
Each night different meteorologists give us the probability that it wil rain the next day.
To judge how well these people predict, we will score each of them as follows:
If a meteorologist says that it will rain with probability p, then he or she will receive a score of:
{1-(1-p)^2 if it does rain
(1 - p^2 if it does not rain
We will then keep track of scores over a certain time span and conclude that the meteorologist with the highest average score is the best predictor of weather.
Suppose now that a given meteorologist is aware of this and so wants to maximize his or her expected score.
If this person truly believes that it will rain tomorrow with probability q, what value of p should he or she assert so as to maximize the expected score?
a)Choice of p= (I know this is p=q). What are the other answers?
b)With this choice, what is the expected payoff in terms of q?
c)
On the other hand, if the payoffs are
{1-(1-p)^2
{1-1.1p^2
Choice of p=
(a) When q = 0 or q = 1, we get p = 0.5, but for other values of q, the optimal value of p is different.
(b) When q = 1, the expected score is 1, which is the maximum possible score.
(c) The optimal value of p also depends on the value of q in this case.
a) The expected score of the meteorologist can be expressed as the weighted average of the two possible scores, where the weights are the probabilities of it raining or not raining:
Expected score = p(1 - (1 - q)^2) + (1 - p)(1 - q^2)
To maximize the expected score, we need to differentiate it with respect to p, set the derivative equal to zero, and solve for p. This gives:
2q(1 - q) = 1 - 2p
Solving for p, we get:
p = (1 - 2q + 2q^2) / 2
So the optimal value of p depends on the value of q. When q = 0 or q = 1, we get p = 0.5, but for other values of q, the optimal value of p is different.
b) If the meteorologist chooses p = q, then the expected score simplifies to:
Expected score = q(1 - (1 - q)^2) + (1 - q)(1 - q^2)
= q^3 + (1 - 2q)q^2 + (1 - q)
To find the maximum expected score, we can take the derivative of this expression with respect to q, set it equal to zero, and solve for q. This gives:
3q^2 - 4q + 1 = 0
This quadratic equation has two roots: q = 1/3 and q = 1. When q = 1, the expected score is 1, which is the maximum possible score. When q = 1/3, the expected score is (8/27), which is the maximum score for any value of q between 0 and 1.
c) If the payoffs are {1 - (1 - p)^2, 1 - 1.1p^2}, then the expected score of the meteorologist is:
Expected score = p(1 - (1 - q)^2) + (1 - p)(1 - 1.1q^2)
To maximize this expected score, we can differentiate it with respect to p, set the derivative equal to zero, and solve for p. This gives:
2.2q^2 - 2q + 1 = 2p
Solving for p, we get:
p = (2.2q^2 - 2q + 1) / 2
So, in this scenario, the value of q also affects the ideal value of p.
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Show the work steps for finding the roots of x^4-13x^2+36 algebraically
The factors of given polynomial are (x+3), (x-3), (x+2) and (x-2).
What are factors of polynomial?The factors are the polynomials which are multiplied to produce the original polynomial.
The given polynomial is x⁴-13x²+36
Here, x⁴-13x²+36 can be written as x⁴-9x²-4x²+36
= x²(x²-9)-4(x²-9)
= (x²-9)(x²-4)
= (x²-3²)(x²-2²)
By using the identity a²-b²=(a+b)(a-b)
So, (x+3)(x-3)(x+2)(x-2)
Therefore, the factors are (x+3), (x-3), (x+2) and (x-2).
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In the diagram, $ABCD$ABCD is a parallelogram. Which congruence theorem(s) can you use to show that $\triangle AED\ \cong\ \triangle CEB$△AED ≅ △CEB ? Select all that apply. Parallelogram A B C D is drawn with diagonals intersecting at point E.
Answer:
you are to use patagorious theory
Correct the one error. Just ten more day's and I'll be in London!
Just ten more days and I'll be in London!
Answer:
Just ten more days and I'll be in London!
help me with this please i need help because i dont get it <33
Answer: B
Step-by-step explanation:
Use the scale to help you solve the equation and find the value of x?
A figure has a perimeter of 12 units. Which describes the perimeter of the figure after a dilation with a scale factor of 4?
The perimeter of the figure after a dilation with a scale factor of 4 is
How to calculate the scale factor?Suppose the initial measurement of a figure was x units.
And let the figure is scaled and new measurement is of y units.
Since the scaling is done by multiplication of some constant, that constant is called scale factor. Let that constant be 's'.
Then we have:
[tex]s \times x = y\\s = \dfrac{y}{x}\\[/tex]
Thus, scale factor is the ratio of the new measurement to the old measurement.
Given;
The perimeter= 12units
Scale factor=4
Now,
Dilation with the given scale factor;
= 12*1/4
=12/4
=3
Therefore, dilation by the given scale factor will be 3.
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(a) Describe the relationship among the lengths of the segments formed by the two secants. You may use words and/or an equation.
(b) Suppose = 3 in., = 2 in. and = 5 in. Is it possible to find the length of ? If so, show how to find the length. If not, explain why not.
Answer:a
Step-by-step explanation:
Name the relationship
1). Adjacent angle
2). Alternate angles
3). Corresponding angles
4). Vertical angles
5). Supplementary angles
It looks like 1) adjacent angles.
The Zoo-venir Stand sells zoo-related souvenirs.
Use the stem-and-leaf plot to answer 14 and 15.
14. Interpret the mean of the Zoo-venir Stand sales.
15. Interpret the range of the Zoo-venir Stand sales.
14. The mean of the Zoo-venir Stand sales is of 23.9, representing the quotient between the sum of all the amounts and the number of observations.
15. The range of the Zoo-venir Stand sales is of 30, representing the difference between the highest number and the lowest number.
How to calculate the mean and range?Considering the key format of the stem-and-leaf plot, the observations are given as follows:
12, 13, 13, 13, 14, 15, 15, 16, 17, 20, 21, 21, 22, 22, 23, 24, 25, 25, 25, 26, 27, 27, 28, 29, 29, 32, 34, 34, 37, 41, 42.
The mean is given by the sum of all observations divided by the number of observations, hence it's value is of: 23.9.
The range is the difference between the highest observation and the lowest observation, hence it is of:
42 - 12 = 30.
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We want to obtain a sample to estimate a population mean. Based on previous evidence, researchers believe the population standard deviation is approximately
. We would like to be 99.5% confident that the estimate is within 0.1 of the true population mean. How large of a sample size is required?
n=
Answer:
5,144,079
Step-by-step explanation:
[tex]\displaystyle CI=\mu\pm z\biggr(\frac{\sigma}{\sqrt{n}}\biggr)\\\\CI_{99.5\%}=\mu\pm2.807\biggr(\frac{80.8}{\sqrt{n}}\biggr)\\\\0.1=2.807\biggr(\frac{80.8}{\sqrt{n}}\biggr)\\\\0.1\sqrt{n}=226.8056\\\\\sqrt{n}=2268.056\\\\n=5144078.01914\\\\n=5144079[/tex]
Thus, you would need a sample size of 5,144,079 to be 99.5% confident that the true population mean is ±0.1 away from it with a population standard deviation of 80.8 (aka. our margin of error).
Use the formula for continuous compounding to compute the balance in the account after 1, 5, and 20 years. Also, find the APY for the account. A $1000 deposit in an account with an APR of 3%. The balance in the account after 1 year is approximately
The balance in the account after 1 year due to continuous compounding is approximately $1030.45 and AYP is 3.04%.
What is meant by continuous compounding?
If compound interest is calculated and reinvested into the balance of an account across an essentially unlimited number of periods, continuous compounding is the mathematical limit that compound interest can reach. Continuous compounding determines interest by assuming constant compounding across an infinite number of periods, as opposed to computing interest on a finite number of periods, such as annually or monthly.
Given,
rate per period = 3%
Principal amount = $1000
Compounding is done after 1,5 and 20 years.
But we are asked to find the amount after continuous compounding after 1 year.
The formula of the amount after continuous compounding is:
[tex]A = Pe^{rt}[/tex]
where A = amount after continuous compounding
r = rate of period
t = time period
P = principal amount
[tex]A = Pe^{rt} = 1000e^{0.03*1}[/tex] = $1030.45
Annual yield formula (AYP) = [tex](1+\frac{r}{n} )^n-1[/tex]
n = times it compounds per year = 365
r = 0.03
AYP = [tex](1+\frac{0.03}{365} )^{365}-1 = 0.0304[/tex]
= 3.04%
Therefore The balance in the account after 1 year due to continuous compounding is approximately $1030.45 and AYP is 3.04%.
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The function, y=-16x^2+32x+48, represents the height, in feet, of a firework x seconds after it is launched.
After how many seconds does the firework hit the ground
x=___seconds
Answer: 3
Step-by-step explanation:
Took the test
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QUESTION 5. 1 POINT
1
A company offers one free book download to anyone that registers. The total number of people that register can be
modeled by the function f(x) = 8x³ +70x² +145x+182, where x is the number of months passed since starting the
company. The number of free books available to choose from can be modeled as 2x + 13. Write an expression that can be
used to determine the average number of people that download each of the free books.
Ous
Provide your answer below:
The expression for the average number of people (8x³ +70x² +145x+182)/(2x + 13)
How to determine the expression to determine the average number of peopleFrom the question, we have the following parameters that can be used in our computation:
The total number of people, f(x) = 8x³ +70x² +145x+182
Number of free books = 2x + 13
To determine the average number of people that download each of the free books,
We need to divide the total number of people that register by the number of free books available.
So, we have
Expression = (8x³ +70x² +145x+182)/(2x + 13)
Hence, the expression is (8x³ +70x² +145x+182)/(2x + 13)
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Find the perimeter of the figure.
Answer:
≈29.93 [units].
Step-by-step explanation:
according to the attachment the required perimeter is:
P=2*6+4.25*2+3.1415*3=12+8.5+9.4245=29.9245 [units].
Is 7. 787887888. A rational number?
A. Yes; it has a pattern which is repeating.
B. Yes; it has a pattern which is terminating
C. No; it has a pattern which is predictable, but no repeating
D. No; it has a pattern which is non repeating and non termination
The number 7.787887888 is option (C) not a rational number, it has a pattern which is predictable, but not repeating
The given number is 7.787887888
The rational numbers is a number that can be expressed as the p/q format, where p and q are integers and p will not be equal to zero. So the rational number is the ratio of the two integers.
Here the given number is 7.787887888.
So this is an non terminating number
But here we can see that there is a pattern which is predictable but its not repeating
Therefore, it is not a rational number ,but it has a pattern which is predictable, but not repeating
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hand consists of 3 cards from a well-shuffled deck of 52 cards.
a. Find the total number of possible 3-card poker hands.
b. A black flush is a 3-card hand consisting of all black cards. Find the number of possible black flushes.
c. Find the probability of being dealt a black flush.
a)
The total number of possible 3-card poker hands is 22100
b)
The number of possible black flushes is 2600
c)
The probability of being dealt a black flush is 0.1176
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
Number of cards = 52
Number of cards in hand = 3
Combination formula.
[tex]^nC_r[/tex] = n! / r! (n -r)!
a)
The total number of possible 3-card poker hands.
= [tex]^{52}C_3[/tex]
= (52 x 51 x 50) / (3 x 2)
= 22100
b.
Number of black cards (spades and clubs) = 13 + 13 = 26
The number of possible black flushes.
= [tex]^{26}C_3[/tex]
= (26 x 25 x 24) / (3 x 2)
= 2600
c.
The probability of being dealt a black flush.
From (a) and (b)
= 2600/22100
= 0.1176
Thus,
The total number of possible 3-card poker hands = 22100
The number of possible black flushes = 2600
The probability of being dealt a black flush = 0.1176
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A cable installer charges $40.00 per hour
plus a $50.00 service charge. Your father's firm hires him to hook up his
company's Internet service.
Here is the cost function used to
represent this situation in terms of then number of hours worked:
c(h) = 40h +50
Find the total charges if it takes the cable installer 6.5 hours to complete the task.
__________
Enter the correct answer.
Answer:
Set up the equation ... 60 + 40X = total charges... where X is the number of hours (6.5)
60 + 40(6.5) = ?
60 + 260 = ?
320 = total charges
2. Чему равна разность? Сравните результаты.
Answer:
[tex] \frac {3}{8} + \frac{2}{8} = \frac{5}{8} = 1 \frac{3}{8} [/tex]
[tex] = \frac{5}{ \\ 8} = 1 \frac{3}{8} [/tex]
