Answer: a = -3.25, b = -4, c = 0.5 and d = -4
Step-by-step explanation:
To find the coefficient of a cubic function, we can use the values in the given table to set up a system of equations and then solve for the unknowns.
Here is the system of equations we can set up using the values in the table:
y = ax^3 + bx^2 + c*x + d
0 = 0a + 0b + 0c + d
-4 = 1a - 4b + 1c + d
-26 = 8a - 4b + 2c + d
-48 = 27a - 4b + 3c + d
We can then solve this system of equations using matrix operations or Cramer's rule.
a = -26/8 = -3.25
b = -4
c = -26-8a = -26+26.5 = 0.5
d = -48-27a-4b-3c = -48+91.75-44-30.5 = -4
Therefore, the coefficient a = -3.25, b = -4, c = 0.5 and d = -4 for the cubic function y = ax³ + bx² + cx+d
It's important to note that this method of solving a system of equations is the most common way but not the only way to get the coefficients in this case.
843 tudent in a high chool were aked weather they had governmental cholarhip or private cholarhip. 112 had private and 17 had both government and private. 209 had only one of the two cholarhip. How many had a private cholarhip?
129 students had a private scholarship.
Out of the 843 students,
112 had a private scholarship17 had both government and private scholarships209 had only one of the two scholarships.To calculate the total number of students with a private scholarship, we need to add the number of students who had a private scholarship (112) and the number of students who had both scholarships (17). This gives us a total of 129 students with a private scholarship. The rest of the students, who had either a government scholarship (80) or no scholarship (651), do not have a private scholarship.
209 students had only one of the two scholarships, so 209 - 129 = 80 students had a government scholarship.
So in total, 112 + 80 = 192 students had either a private or a government scholarship.
Therefore, 843 - 192 = 651 students did not have either a private or a government scholarship.
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maggie green just borrowed $5,000. she is planning to pay it back in 5 equal installments of $1,200. what is the irr?
As per the borrowed amount, the value of IRR is 6.40%
The term IRR is the internal rate of return is a metric used in financial analysis to estimate the profitability of potential investments.
Here we have know that Maggie green just borrowed $5,000. she is planning to pay it back in 5 equal installments of $1,200.
Now, we have to calculate the value of IRR,
The general form of the IRR formula is written as,
=> NPV = [tex]\sum\limits^T_{t=1} {\frac{C_t}{(1+r)^t} }\ -C_0[/tex]
where r is the discount rate / interest rate and T is the number of cash flow periods with t denoting a specific period, C0 is the initial investment while Ct is the return during period t.
Here we apply the values on it, then we get,
=> [tex]NPV = \sum\limits^5_{t=1} {\frac{1200_t}{(1+r)^t} }\ -5000[/tex]
When we simplify this one then we get,
=> Internal Rate of Return = 6.402%
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TRIGONOMETRY QUESTION-
alright my friend and i have been stuck on this FOREVER!
use properties of similar triangles to find the value of "x" and the length of the sides involving "x".
in this situation we are given two triangles, triangle ABC to triangle FEG (in that order, its weird, i know).
A = 5 F = 2x
B = x+4 E = 18
C = ? G = ?
I know usually you would set up the proportions, however when i do that i get 90=2x^2+8x, and i dont think i should be using the quadratic equation to find the side of a triangle. What is my best method of approach? if you leave the answer, please let me know how you did it!
You were on the right track, I totally understand why you'd get stuck where you are currently in the process. To start with, you technically found the wrong ratio between the two triangles. Your ratio is just 2x, while it should be 2x/5.
To start, let's find the ratio between triangle FEG and ABC by dividing angle F by and A:
[tex]R=\frac{2x}{5}[/tex]
Now, multiply angle B by this ratio:
[tex](x+4)(\frac{2x}{5} )=\frac{2x^2}{5}+\frac{8x}{5}=\frac{2x^2+8x}{5}[/tex]
We can now set this expression equal to angle E, as we have multiplied by the common ratio:
[tex]\frac{2x^2+8x}{5} =18[/tex]
This looks rather daunting, but let's keep calm... you can do this!!
Start by subtracting 18 from both sides:
[tex]\frac{2x^2+8x}{5}-18=0[/tex]
Now, let's get the whole expression under the denominator 5:
[tex]\frac{2x^2+8x-90}{5}=0[/tex]
Notice that the denominator can now be removed:
[tex]2x^2+8x-90=0[/tex]
Now, factor the equation (you could also use the quadratic eq if you want)
[tex]2(x-5)(x+9)=0[/tex]
Notice that we have two potential values for x (5 and -9).
Think about this logically... If we use -9 and plug it in for x, we will end up with values of -5 degrees for an angle, which is impossible! Therefore 5 is the only valid answer!
I encourage you to also approach the problem from a different angle and use the common factor (5/2x) and multiply it by 18 :)
Nora spent 3 hours calling actors, 2 hours finding props,
2 hours at rehearsal, and 4 hours in meetings.
How many hours did she work?
Answer: Nora spent 11 ours working.
Step-by-step explanation: 3 + 2 + 2 + 4 = 11
Answer:
7
Step-by-step explanation:
meetings don't count
The graph shows the absolute value parent function.
which statement is true?
(image attached)
Answer:
Letter D
Step-by-step explanation:
not always zero
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Help quick I need help
Answer: there’s no attachment so I’m not sure what you need help with
Step-by-step explanation:
Given the definitions of f(x) and g(x) below, find the value of (gof)(0).
f(x) = -3x+1
g(x) = 3x² + 3x – 10
PLEASE HURRYYYYY!!! The graph shows how many centimeters a bamboo plant can grow (g ) and the number of hours (t ) that the plant has been growing.
Part A: Does the growth of the bamboo plant vary directly with the time? How do you know?
Answer:
Yes it does!
Step-by-step explanation:
Given, the growth of the bamboo changes over time. Therefore, the growth is directly proportional as it grows more with increase in time.
Jada's credit card has an 18% APR. During the last 30-day month, she had the following transactions on her credit card.
Her balance on the first day of the month was $324.16.
On the 11th day of the month, she made a purchase of $75.88 .
the 21 day of the month, she made a purchase of $106.09.
What is the finance charge on Jada's card for this month? Please help me it’s due by 2:25pm
The current month's finance charge on Jada's credit card is found as : 7.48.
Explain the term finance charge?The entire sum of money you spend to use a certain credit is known as a finance fee. As a result, we can define the finance fee as the sum paid over and above the borrowed amount. It takes into consideration all expenses associated with your credit as well as the interest that has accumulated on your account. Finance fee, then, is what you pay for borrowing money.The provided data:
APR ; 18% = 0.18Carried unpaid balance: $324.16 + $75.88 + $106.09 = $506.13.Number of Days in Billing Cycle = 30Calculation for the finance charge:
Daily interest rate = APR / 100 / 365
Daily interest rate = 0.18 / 365 = 0.00049315.
Daily finance charge = Carried unpaid balance × Daily interest rate
= $506.13 x 0.00049315
= 0.249
Finance charge = Daily finance charge × Number of Days in Billing Cycle
= 0.249 x 30
= 7.48
Thus, the current month's finance charge on Jada's credit card is found as : 7.48.
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The table how the height (in feet) of a high jump bar and the number of people who uccefully complete each jump. Identify the correlation of coefficient. Round your anwer to three decimal place
The correlation of coefficient is -0.988 and it is in negative form.
A correlation coefficient is a statistical measure that indicates the strength and direction of the relationship between two variables.
The correlation coefficient is a value between -1 and 1 that indicates the strength and direction of the relationship between the two variables. A positive correlation means that as x increases, y also increases.
A negative correlation means that as x increases, y decreases. And a correlation of zero means that there is no relationship between x and y.
Here by using the correlation coefficient as −0.988.
Therefore the correlation coefficient is negative, implying that the relationship between heights of a high jump bar and number of people successfully completing each jump is negative.
Complete Question:
The table shows the heights (in feet) of a high jump bar and the number of people who successfully complete each jump. Identify and interpret the correlation coefficient.
Height (ft), x Completions, y
4 27
4.2 22
4.4 18
4.5 16
4.6 11
4.7 8
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john has several coins with total value of $3.50. he has twice as many nickels as quarters, two more dimes than nickels and no other coin type. how many coins of each type does he have?
John has 6 quarters, 12 nickels, and 6 dimes, for a total of 24 coins. This is because he has twice as many nickels as quarters (12 nickels, 6 quarters), and two more dimes than nickels (12 nickels, 6 dimes). With this combination, the total value of all the coins would be $3.50.
To calculate the number of coins John has, we can use the following steps:
Calculate the total value of the coins: 3.50Divide the total value of the coins by the value of each coin type: a. Quarters: 3.50 / 0.25 = 14 b. Nickels: 3.50 / 0.05 = 70 c. Dimes: 3.50 / 0.10 = 35Since John has twice as many nickels as quarters and two more dimes than nickels, we can set up the following equation: 2x + x + 2 = 70Solve the equation: x = 6Calculate the number of coins of each type: a. Quarters: 6 b. Nickels: 12 c. Dimes: 6Add all the coins together to get the total number of coins: 6 + 12 + 6 = 24 coinsLearn more about equations:
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the top speed of a segway scooter is 21km/h .if moses rode 7km at maximum speed ,how many minutes did it take him
Use the formula: time = distance / speed
time = 7 km / 21 km/h = 1/3 hours
To convert hours into minutes, you can multiply the number of hours by the conversion factor 60.
1/3 x 60 = 20
It takes Moses 20 minutes to ride 7 km on a segway scooter at a top speed of 21 km/h.
Blue Tide Swim Shop is having its annual summer sale, when every item in the store gets marked down. During the sale, rashguards sell for $5 less than full price. Miguel purchases 3 rashguards and pays a total of $60.
Which equation can you use to find how much money, f, each rashguard costs at full price?
A rashguard costs $25 at full price, which is calculated as 3x - 15 = 60.
What are linear equations?When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."
There are both one-variable and two-variable linear equations.
Given Blue Tide Swim Shop is having its annual summer sale,
rashguards sell for $5 less than the full price,
let the actual price of rashguards be x
price to be payed = x - 5
Miguel purchases 3 rashguards,
at cost = $60
cost of 3 rashguards is 3(x - 5) = 3x - 15
3x - 15 = $60
3x = 60 + 15
3x = 75
x = 75/3
x = 25
cost of rashguards is $25.
Hence the actual cost is $25, and the equation is 3x - 15 = 60.
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a sample of 500 shoppers was selected in a large metropolitan area to determine various information concerning consumer behavior. among the questions asked was, "do you enjoy shopping for clothing?" of 240 males, 136 answered yes. of 260 females, 224 answered yes. what are the critical values for the decision rule when the level of significance is 0.10? round your answer to two decimal places.
The critical values for a two-sample z-test with a level of significance of 0.10 are -1.28 and 1.28.
This test is used to compare the proportions of two groups (males and females) who answered "yes" to the question "do you enjoy shopping for clothing?" The null hypothesis is that the proportion of males who enjoy shopping for clothing is equal to the proportion of females who enjoy shopping for clothing. The alternative hypothesis is that they are not equal.
To find the critical values, we use a standard normal table and find the z-scores that correspond to a cumulative probability of 0.05 (0.10/2) in both tails of the distribution. These values are -1.28 and 1.28.
In other words, if the calculated z-statistic is less than -1.28 or greater than 1.28, we reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis that the proportions of males and females who enjoy shopping for clothing are not equal.
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convert =12sin() to an equation in rectangular coordinates. (use symbolic notation and fractions where needed.)
The rectangular coordinates form of r = 12 sinθ is x² + y² - 12y = 0
Given r = 12 sinθ and we are asked to convert this equation into rectangular coordinates.
The relation between polar coordinates (r,θ) and rectangular coordinates (x, y) is given by
x = r cosθ and y = r sinθ
Also, r² = (x² + y²)
r = 12 sinθ
Multiplying r both sides
r x r = 12 sinθ x r
r² = 12r sinθ
We know r sinθ = y and r² = (x² + y²)
So, x² + y² = 12y
x² + y² - 12y = 0
Hence, the rectangular coordinates form is x² + y² - 12y = 0
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calculate r-squared,--the coefficient of determination--given that the linear correlation coefficient, r, is 0.817. what does this tell you about the explained variation and the unexplained variation of the data about the regression line?
R-squared is calculated as the square of the linear correlation coefficient (r). In this case, the linear correlation coefficient is 0.817, so the R-squared can be calculated as follows:
R-squared = r^2 = 0.817^2 = 0.67
R-squared measures the proportion of variation in the dependent variable that is explained by the independent variable in a regression analysis. A value of R-squared close to 1 indicates that a large proportion of the variation in the dependent variable is explained by the independent variable, while a value close to 0 indicates the opposite.
In this case, a value of 0.67 for R-squared indicates that 67% of the variation in the dependent variable is explained by the independent variable, while the remaining 33% is unexplained.
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The two polygons are similar. Find the values of x and y.
Based on the definition of similar polygons, the values of x and y are:
x = 10.7
y = 120°.
What are Similar Polygons?Similar polygon is a term used in geometry to describe two polygon shapes that have the same shape but not necessarily the same size.
Two polygon are said to be similar if and only if:
Corresponding angles are congruent.Corresponding sides are in proportion.The ratios of corresponding side lengths are equal, meaning that they are scaled versions of each other.Therefore:
x + 4 / 22 = 12/18
18(x + 4) = (22)(12)
18x + 72 = 264
18x = 264 - 72
18x = 192
18x/18 = 192/18
x = 10.7
y = 180 - 60
y = 120°
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Kapitan tiago bought a car. He obtained a 60% loan from a bank. He paid the balance of 560,000 by cah. How much did be barrow from the bank?
Kapitan Tiago borrowed 560,000 × 60 % = 336,000 from the bank.
To find the amount borrowed, we multiply the balance Kapitan Tiago paid in cash by the loan percentage he obtained. The loan percentage is expressed as a decimal, so we multiply 560,000 by 0.6 to get 336,000.
This means Kapitan Tiago borrowed 336,000 from the bank and paid
560,000 - 336,000 = 224,000 in cash.
The total amount he spent on the car is
336,000 + 224,000 = 560,000.
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Sharon Wilson is single and has health insurance benefits as shown in the table her recent network health care cost include co-payments for 9 physician visits and 10 specialist visits. following hospital surgery, she made co payments for 15 physical therapy visits at $95 each and she had 5 co-payments at her local pharmacy 2 generic and 3 name drugs. Her hospital admission charge was $240 and she had a hospital bill for $54,860 find the amount she paid
Hi, could you help me with this?
3.5 capfuls of vitamin is required for the 350 liter fish tank, to keep the fish healthy.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
To keep the fish healthy, 2 drops of vitamin is required per 5 liter of water. Hence, for 350 liter:
5 liter = 2 drops
350 liter = 350 liter * 2 drops per 5 liter = 140 drops
40 drops = 1 capful
Hence:
140 drops = 140 drops * 1 capful per 40 drops = 3.5 capfuls
3.5 capful is required for the 350 liter
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Explain this paradox: a simple harmonic oscillator mẍ = -kx is a system that oscillates in one dimension (along the x-axis). But the text says one-dimensional systems can't oscillate.
This dilemma arises because oscillation requires two degrees of freedom while a equation one-dimensional system can never have more than one. An example of a constrained system is a basic harmonic oscillator.
This paradox results from the fact that oscillation needs two degrees of freedom whereas a one-dimensional system only has one. Position is the only variable in a one-dimensional system, hence oscillation is not feasible. But one example of a restricted system, where a constraint provides an additional degree of freedom, is a straightforward harmonic oscillator. The constraint in this scenario is a spring's force, which acts as a restoring force whenever the system deviates from its equilibrium state. The system can oscillate and move back and forth along the x-axis thanks to this restoring force. Thus, although having only one degree of freedom, the basic harmonic oscillator is an example of a one-dimensional system that can oscillate.
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(5,1.5) And (20,6). What’s the constant of proportionality
Answer: 0.3
Step-by-step explanation:
To find the constant of proportionality, you divide the y-value by the x-value.
[tex]\displaystyle \frac{y}{x} =\frac{1.5}{5}= \frac{6}{20} \;\;=0.3[/tex]
A company's revenue increased by 15% and then decreased by 10%. What is the overall percentage change in revenue.
1a. Emily ran 731.6 meters in 12.4 minutes. How many meters/minute did she run?
1b. Hailey's plane climbed 1,004.7 feet in 59.1 seconds. How fast did her plane climb every second?
Emily ran 731.6/12.4 = 59 meters per minute.
Hailey's plane climbed 1004.7/59.1 = 17 feet every second.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
1a.
Emily ran 731.6 meters in 12.4 minutes.
She ran 731.6/12.4 = 59 meters per minute.
1b.
Hailey's plane climbed 1,004.7 feet in 59.1 seconds.
Her plane climbed 1004.7/59.1 = 17 feet every second.
Therefore, all the required values are given above.
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you are introducing a data visualization during your presentation and are concerned that it may overwhelm your audience. how can you help your audience when you first introduce it? 1 point thoroughly explain the context describe each graph quickly wait five seconds define each parameter
When introducing a data visualization to your audience, it is important to explain the context and the purpose of the visualization.
This will help your audience understand the visualization and its implications better. Additionally, you should quickly describe each graph and define each parameter to make sure that your audience is familiar with the data they are seeing. Finally, you should give your audience a few moments to process the information before you move on. This will help ensure that they can fully understand and appreciate the visualization.
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what is the unsigned base 9 equivalent of the following unsigned decimal integer value? 6239124
The unsigned base 9 equivalent of the unsigned decimal integer value is 2233322
Decimal is a base 10 number system that we use in our daily lives to represent numbers.
In this case, the decimal number 6239124 is being converted to an unsigned base 9 equivalent.
To do this, we first divide the decimal number by 9 to get the first digit of the base 9 equivalent.
In this case, 6239124 divided by 9 is 693234 with a remainder of 2. So, the first digit of the base 9 equivalent is 2.
Next, we take the result of the division
=> (693234) / 9 = 76803 with a remainder of 3.
So, the second digit of the base 9 equivalent is 3.
We repeat this process until the result of the division is 0.
The final result is the base 9 equivalent of the decimal number 6239124. In this case, the base 9 equivalent is 2233322.
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What is the transformation
"none of these" is the transformation rule applied to this figure that is option B.
What is transformation?A transformation in geometry is an operation that moves, flips, or modifies a shape (called the preimage) to generate a new shape (called the image). A translation is a sort of transformation in which every point in a figure moves the same distance in the same direction. a logic principle that establishes the circumstances under which one assertion can be derived or legitimately inferred from one or more other statements, particularly in a codified language. Transformations are classified into four types: translation, reflection, rotation, and dilation. A transformation equation is an equation that transforms from one equation to another and whose provided roots are inverse to the roots in the given equation.
Here,
The transformation rule applied to this figure is "none of these" that is option B.
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which of the following graphs is increasing only when x <0?
The only correct option from the given graph is Graph X.
Role of function's derivative to detect whether a function is rising or decreasing on any interval in its domain.A function's derivative can be used to detect whether a function is rising or decreasing on any interval in its domain. If f′(x) > 0 at every point in an interval I, the function is said to increase on I. If f′(x) 0 at every point in an interval I, the function is said to be declining on I.
When we draw tangents to the curve, we can see that if the gradient of the tangent is positive, the function is rising, and if the gradient is negative, the function is dropping.
The given figure Y is the graphs only increase when x = 0.
Let's look at each graph individually.
When x0, graph W really decreases, therefore it is erroneous.
Because graph X grows when x0 but not when x0, it is a plausible explanation.
Because graph Y drops at x0, it is erroneous.
Graph Z grows when x0, but it also increases when x0, indicating that Graph Z is erroneous.
The only right answer is Graph X.
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The average life expectancy y of a person bom x years after 1960 can be approximated by the linear equation y = 1/6 x + 70. a. What interpretation can be given to the y-intercept of the graph? b. In what year did people born that year have an average life expectancy of 75 years? c. What is the average life expectancy of people born in 1999?
(a) the value of y-intercepts is 70 (b) In what year did people born that year have an average life expectancy of 75 years= 1990 (c) the average life expectancy =76.5 years.
The average life expectancy y of a person born x years after 1960 can be approximated by the linear equation y = 1/6 x + 70.
(a) What interpretation can be given to the y-intercept of the graph?
we know that the standard form of a straight line is = y=mx+c
where c is y-intercepts,
So, we have y=0.1666x+70
here the value of C=70
hence, it is y intercepts=70
b)
In what year did people born that year have an average life expectancy of 75 years,
we have y=75
x=30
So year = 1960+30=1990.
c) What is the average life expectancy of people born in 1999?
1999-1960=39=x
y=76.5 year.
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4p+-7(-5+-9p)
we need to simplify this equation but like it's too hard for me can anyone help please youll get 20 points
Answer:
67p + 35
Step-by-step explanation:
Reduce all the unnecessary plus and minus signs. A plus and negative sign equates to just a minus sign.
4p + -7(-5 + -9p) = 4p - 7(-5 - 9p)
Expand the variables in the brackets. These take priority over regular evaluation of the other signs. Two negative values multiplied together produces a positive product.
4p - 7(-5 - 9p) = 4p + 35 + 63p
Add all like products together.
4p + 35 + 63p = 67p + 35
Check that the final simplification can no longer be simplified.
