A person invests 4000 dollars in a bank. The bank pays 5.75% interest compounded quarterly. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 5900 dollars?
Answer:
t = 6.8 years
Step-by-step explanation:
The formula for compound interest is
\(A(t)=P(1+r/n)^n^t\), where P is the principal/amount invested, r is the interest rate, n is the number of compound periods per year (4 for quarterly), and t in the time in years.
We know that A = $5900, P = $4000, and r = 0.0575 (we must convert the percentage to a decimal). We must solve for t and round to the nearest tenth:
\(5900=4000(1+0.0575/4)^(^4^t^)\\\\59/40=(1623/1600)^4^t\\\\log(59/40)=log(1623/1600^4^t)\\\\log(59/40)=4t*log(1623/1600)\\\\log(59/40)/log(1623/1600)=4t\\\\1/4(log(59/40)/log(1623/1600))=t\\\\6.80773607=t\\\\6.8=t\)
Graph the set of points. Which model is most appropriate for the set?
(-2,3), (-1,-3), (0, -5), (1, -3), (2,3)
Model B is the most appropriate for the set (-2,3), (-1,-3), (0, -5), (1, -3), (2,3).
What is Linear, Quadratic, & Exponential Models?A mathematical model that may be expressed as a series of quadratic equations or as a quadratic equation, such as Y = aX2 + bX + c. When a quadratic equation is graphed, the connection between the variables is represented by a parabola.The y-values in a linear connection differ by an equal amount. The y-values have identical ratios in an exponential relationship.First differences are constant in linear functions. Second differences in quadratic functions are always the same. A constant ratio characterises exponential functions.Based on an equation like: where Y = deterioration, T = time, and A and B = parameters to be calculated by the regression approach based on historical data, the exponential model represents the degradation failure process.Learn more about Linear, Quadratic, & Exponential Models refer to :
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What is the slope of the line that passes through the points (-10, -8) and
(-8, -16)? Write your answer in simplest form.
Answer:
Equation: y = -4x + 32
Slope: -4
Step-by-step explanation:
Given : (-10,-8) and (-8, -16)
Slope Formula: \(\frac{y_1 - y_2}{x_1-x_2}\)
Solve For Slope, Input Given Points:
\(\frac{-8 - (-16)}{-10 - (-8)}\)\(\frac{8}{-2}\)\(-4\)Solve for y-intercept:
Input the slope into the equation y = mx + b. Plugin x and y values for the x and y variables to find b.
y = -4x + b-8 = -10(4) + b-8 = -40 + bb = 32Equation of LIne: y = -4x + 32
-Chetan K
Answer:
(1,-4)
Step-by-step explanation:
Remember this formula:
y2 - y1/x2-x1
Your two cordinates:
(-10,-8) and (-8,-16)
First do -16-(-8)
That should equal -8
Note: This is for the Y
Next do -8-(-10)
That should equal 2
Note: This is for the X
So now our slope is (2,-8)
If you want the simplest form:
Divide by (2,2)
So the answer shall be (1,-4).
Gareth has 15 total quarters and dimes with a total value of $2.10. A photo of a stack of quarters and a stack of dimes is shown. The system of equations can be used to solve for the number of each Gareth has. {Q+D=15 25Q+10D=210 Complete in the table to show the quantities and values of the coins Gareth has.
Answer:
4 Quarters and 11 Dimes
Step-by-step explanation:
In the first equation, we know that \(D=15-Q\) If we plug this into the second equation, we get 25q+10(15-Q)=210. If we simplify this equation, we get 25q+150-10q=210, which can be simplified to 15q+150=210. And since 15q=60, q=4. Then, you subtract 4 from 15, to get 11 dimes. So, there are 4 quarters and 11 dimes. Hopefully, this helps!
20p-8p-6p=12 please make sure it's right
Answer: step by step
Step-by-step explanation:
not totally sure what you're asking but in this equation p=2
What value of x will make the triangle congruent
Answer:
x = 3/5 = 0.6
Step-by-step explanation:
By the ASA Triangle Congruence Theorem, the two given triangles are congruent (vertical angles are congruent). Because we know that corresponding parts of congruent triangles are congruent, we can write the following equation: 7x - 3 = 2x. Now we can solve:
7x - 3 = 2x
-3 = -5x
3/5 = x
i) Consider the linear system
4x1 − 7x2 = −33
−3x1 + 8x2 = 44
−3x1 + 7x2 = 37
Note that there are three equations in only two unknowns. Write the solution values of x1, x2 in the comments, and it not consistent, explain why. Why is the solution not the augmented column of the RREF in this case? (ii) Explain in the comments using precise terminology from the class the answer to the following questions: (1) What are the conditions for the augmented column of the RREF to be the solution to the system. (2) In the case of a unique solution to a system with more equations than variables, how should the solutions be obtained 1 2 from the RREF? (3) In the case of a consistent system where there are more variables than equations, what information is contained in the augmented column of the RREF?
The general solution is a set of infinitely many solutions that satisfy the system. The augmented column of the RREF contains the coefficients of the variables that can be arbitrary, allowing for an infinite number of solutions.
The general solution provides a relationship between the variables that satisfies the system, but it does not give specific values for the variables. To find specific values, additional information, such as boundary conditions or initial conditions, is required
.i) This system of linear equations is inconsistent because the third equation, -3x1 + 7x2 = 37, contradicts the first equation, 4x1 - 7x2 = -33. This means that there is no solution that satisfies all three equations simultaneously.
(ii) (1) The conditions for the augmented column of the RREF to be the solution to the system is that the system must be consistent and the number of variables must equal the number of non-trivial (non-zero) rows in the RREF.
(2) In the case of a unique solution to a system with more equations than variables, the solution should be obtained by solving the system using a method such as Gaussian elimination or Gauss-Jordan elimination to reduce the system to its RREF. The values of the variables are then read off from the non-trivial rows of the RREF.
(3) In the case of a consistent system where there are more variables than equations, the information contained in the augmented column of the RREF is the general solution to the system
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The range of f(x) = [xl is y 2 0. If a < 0 for g(x) = a[x], what is the range of function g?
A ysa
B. y < 0
C. y20
D. ys 0
Answer:5
Step-by-step explanation:
The range of the function g(x) = a[x], where a < 0, is y ≤ 0.
What is the greatest integer function?The function f(x) = [x], where [x] represents the greatest integer less than or equal to x, has a range of y ≤ 0. This means that the output of the function f(x) can be any number less than or equal to zero, including negative integers, zero, and non-negative fractions.
Consider the function g(x) = a[x], where a is a negative constant. When we multiply the input x by a the output of the function is also multiplied by a. Since a is negative, the sign of the output is flipped. Moreover, the output is an integer, as [x] is an integer for all x.
Here, the range of the function g(x) = a[x] is y ≤ 0.
This means that the output of the function g(x) can be any negative integer, zero, or any non-positive fraction, as these are the numbers that are less than or equal to zero.
Thus, the range of the function g(x) = a[x], where a < 0, is y ≤ 0.
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What is the relationship between angle a and angle b A) Vertical Angles B) Complementary Angles C) Supplementary Angles D) None of the above
Answer:
C. Supplementary
Step-by-step explanation:
Angle a and angle b are on the line CZA.
We can assume that line CZA is a straight line, which is equal to 180 degrees.
Since angle a and b are on the straight line together, they must add to 180 degrees. Therefore, they are supplementary angles.
So, choice C. Supplementary angles is correct.
The product of three consecutive integers n - 1, n, and n + 1 is 210. Write and solve an equation to find the numbers.
We can write an equation to represent the relationship between the three integers n - 1, n, and n + 1 by multiplying these three numbers together:
(n - 1) * n * (n + 1) = 210.We can then solve this equation to find the value of n.
To solve the equation, we can first factor the left-hand side to get (n - 1) * (n + 1) * n = 210. This expression can be further simplified to n^2 - 1 = 210. We can then solve this equation by adding 1 to both sides to get n^2 = 211, and then taking the square root of both sides to get n = sqrt(211).
The value of n must be an integer, so the only possible value for n is 14. This means that the three consecutive integers are 13, 14, and 15.
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How is this number read? 14.102
Answer:
fourteen and one-hundred-two
Step-by-step explanation:
we tend to read "." as "point" but the proper reading would be to read the number left to the decimal point (14), add the word "and" and then read the number to the right of the decimal point (102)
Exercise 1 (7 points)
The following data represent the scores of students in an Inferential
Statistics examination 5-12-8-14-11.
1. Determine the mean, variance and standard deviation of this population
2. How many simple random samples of size 2 can be constructed in an
exhaustive manner?
3. The sampling distribution of the sample means is studied, determine
the mean, variance and standard error of this sampling distribution.
4. Determine the variance of this sampling distribution.
5. This is considered to be data from a simple random sample, determine a
point estimate of the population mean and variance.
Answer: 1.To find the mean, we sum up all the scores and divide by the number of scores:
Mean = (5 + 12 + 8 + 14 + 11) / 5 = 50 / 5 = 10
To find the variance, we first find the deviation of each score from the mean:
5 - 10 = -5
12 - 10 = 2
8 - 10 = -2
14 - 10 = 4
11 - 10 = 1
We square each deviation and sum them up:
(-5)^2 + 2^2 + (-2)^2 + 4^2 + 1^2 = 26
Then, we divide by the number of scores to find the variance:
Variance = 26 / 5 = 5.2
Finally, we find the standard deviation by taking the square root of the variance:
Standard deviation = √5.2 = 2.28
2. To construct a simple random sample of size 2, we can choose any two scores from the population. The number of ways to do this is given by the combination formula:
C(5,2) = 5! / (2! * (5 - 2)!) = 10
Therefore, there are 10 simple random samples of size 2 that can be constructed.
3.The mean of the sampling distribution of the sample means is equal to the population mean, which we found to be 10. The variance of the sampling distribution is equal to the population variance divided by the sample size:
Variance of sampling distribution = Variance / Sample size = 5.2 / 2 = 2.6
The standard error of the sampling distribution is the square root of the variance:
Standard error = √2.6 = 1.61
4.The variance of the sampling distribution is 2.6, as we found in part
5. Since this is considered to be data from a simple random sample, we can use the sample mean as a point estimate of the population mean. Therefore, the point estimate of the population mean is 10.
Similarly, we can use the sample variance as a point estimate of the population variance. However, we need to correct for the bias in the sample variance by dividing by (n-1) instead of n:
Point estimate of population variance = Variance * (n / (n-1)) = 5.2 * (5 / 4) = 6.5
Step-by-step explanation:
Which of the following is a statistical question that can result in numerical data?
What is the name of your favorite pizza store?
How many hours this week did you spend on homework?
How many times did you go swimming this year?
How many pink erasers do the students in your class have?
A statistical question that can result in numerical data is How many times did you go swimming this year? So, the correct option is A).
The statistical question that can result in numerical data is "How many hours this week did you spend on homework?" and "How many times did you go swimming this year?".
These questions involve counting or measuring quantities, which can be represented using numerical data. The other two questions do not involve numerical data and therefore cannot be considered statistical questions that result in numerical data. So, the correct answer is B).
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Answer:
How many pink erasers do the students in your class have?
Select the correct answer.
Which expression is equivalent to the given expression?
2x² - 14x +24
A. (2x - 12)(x - 2)
B. 2(x - 3)(x - 4)
C. 2(x - 8)(x + 3)
D. 2(x - 5)(x - 2)
Answer: B. 2(x - 3)(x - 4)
Step-by-step explanation:
Which of the following represents 20 = 5 x 4
A. 5 is 4 times as many as 20
B. 20 is 2 times as many as 10
C. 4 is 5 times as many as 20
D. 20 is 5 times as many as 4
Answer:
D
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
the answer is d because
20 is "=" 5 times "×" as 4
so the formula derived is
20= 5x4
is represents =
times represents ×
hope you get it
A coffee place is selling coffees for $2.50 each and cappuccinos for $3.75 each.
Today the coffee place sold a total of 70 drinks (coffees and cappuccinos) for a total of $222.50.
a) Write an equation that represents the information.
b) Solve the equation in (a) to find how many coffees and how many cappuccinos the coffee place sold today.
Answer:
Step-by-step explanation:
a) Let's denote the number of coffees sold as 'x' and the number of cappuccinos sold as 'y'.
The equation that represents the given information is:
2.50x + 3.75y = 222.50
b) To solve the equation, we need to find the values of 'x' and 'y' that satisfy the equation.
Since we have two variables and only one equation, we cannot determine the exact values of 'x' and 'y' independently. However, we can find possible combinations that satisfy the equation.
Let's proceed by assuming values for one of the variables and solving for the other. For example, let's assume 'x' is 40 (number of coffees):
2.50(40) + 3.75y = 222.50
100 + 3.75y = 222.50
3.75y = 222.50 - 100
3.75y = 122.50
y = 122.50 / 3.75
y ≈ 32.67
In this case, assuming 40 coffees were sold, we get approximately 32.67 cappuccinos.
We can also assume different values for 'x' and solve for 'y' to find other possible combinations. However, keep in mind that the number of drinks sold should be a whole number since it cannot be fractional.
Therefore, one possible combination could be around 40 coffees and 33 cappuccinos sold.
Use the following table to find the probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Students on the Student Government Board
On-Campus Housing Off-Campus Housing
Freshman 2 2
Sophomore 2 4
Junior 0 3
Senior 4 2
Graduate Student 2 0
The probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing is 8/25 or 0.32 (rounded to the nearest millionth).
1. Calculate the total number of students on the Student Government Board by summing up the numbers in the table:
Total Students = 2 + 2 + 2 + 4 + 0 + 3 + 4 + 2 = 19
2. Calculate the total number of graduate students on the Student Government Board:
Total Graduate Students = 2 + 0 = 2
3. Calculate the total number of students living in on-campus housing:
Total On-Campus Housing = 2 + 2 + 0 + 4 + 2 = 10
4. Calculate the probability of selecting a graduate student from the Student Government Board by dividing the total number of graduate students by the total number of students:
Probability of Graduate Student = Total Graduate Students / Total Students = 2 / 19
5. Calculate the probability of selecting a student living in on-campus housing by dividing the total number of students in on-campus housing by the total number of students:
Probability of On-Campus Housing = Total On-Campus Housing / Total Students = 10 / 19
6. Calculate the probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing by summing up the probabilities from steps 4 and 5:
Probability = Probability of Graduate Student + Probability of On-Campus Housing = 2 / 19 + 10 / 19
7. Simplify the fraction if necessary. In this case, the fraction cannot be simplified further, so the final probability is 2 / 19 + 10 / 19 = 12 / 19.
8. Convert the fraction to a decimal by dividing the numerator by the denominator: 12 / 19 ≈ 0.631578947, which rounds to 0.632 (rounded to the nearest thousandth).
9. Finally, express the probability as a fraction in lowest terms: 12 / 19 is already in lowest terms.
Therefore, the probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing is 12/19 or approximately 0.632 (rounded to the nearest thousandth).
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#3 Preimage point B is
located at (5,-4).
B' is located at (20, -16).
Write the algebraic rule for
the transformation.
The algebraic rule for the transformation is B' = (Bx + 15, By - 12)
Given data ,
To determine the algebraic rule for the transformation from point B to point B', we need to find the equations that relate the coordinates of the preimage point B to the image point B'.
Let's denote the translation amounts in the x-direction and y-direction as (dx, dy). The coordinates of B' can be obtained by adding these translation amounts to the coordinates of B:
B' = (Bx + dx, By + dy)
Given that B is located at (5, -4) and B' is located at (20, -16), we can calculate the translation amounts:
dx = 20 - 5 = 15
dy = -16 - (-4) = -12
Hence , the algebraic rule for the transformation is B' = (Bx + 15, By - 12)
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what is Bethany's score on the test if she answered 23 out of 30 right?
part:
whole:
percent:
Answer: 76.67%
Step-by-step explanation:
X intersection of sets x minus y
Answer:
The intersection of sets X and (X - Y) is equal to the set X minus Y.
or
X ∩ (X - Y) = X - Y
Step-by-step explanation:
The intersection of sets X and (X - Y) can be written as:
X ∩ (X - Y)
We know that (X - Y) represents the set of elements that are in X but not in Y. Therefore, the elements in the intersection of X and (X - Y) must be in both sets.
Let's say a particular element x is in both sets. This means that x is in X and x is in (X - Y). But if x is in (X - Y), then it is in X but not in Y. So, x is in X and not in Y. This implies that x is in the set X intersect Y, since it is in X and it is also in the set of elements that are in both X and Y.
Therefore, we can conclude that:
X ∩ (X - Y) = X - Y
Answer:
Step-by-step explanation:
Assuming that "X" refers to a set and "x" and "y" refer to elements of sets, the expression "X intersection of sets x minus y" is not well-formed.
To take the intersection of sets, we need to have two or more sets. So, if we assume that "x" and "y" are themselves sets, we could write the expression as follows:
X ∩ (x \ y)
In this expression, "∩" is the intersection operator, and "" is the set difference operator. So "x \ y" is the set of elements in "x" that are not in "y", and the intersection of that set with "X" gives us the elements that are in both "X" and "x", but not in "y".
For example, if we had:
X = {1, 2, 3, 4}
x = {2, 3, 5, 6}
y = {3, 4, 6, 7}
Then:
x \ y = {2, 5}
X ∩ (x \ y) = {2}
If two angles are complementary then the sum of their measures is _______.
(Answer with a number ONLY)
If the two angles are complementary, then their sum is 90 degrees.
The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
Complementary angle - Two angles are said to be complementary angles if their sum is 90 degrees.
If the two angles are complementary, then their sum is 90 degrees.
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need help with this question!
maybe a but the equation seems wrong
3 QUESTIONS
Company 1 charges $2500 for the first 100 feet of fence, and $25 for each
additional foot. Write an equation and determine the cost of Company 1 to
complete the fencing job.
Company 2 charges $39 per foot of fence. Write an equation and determine
the cost of Company 2 to complete the fencing job.
if both companies charge 7% sales tax, which company would you choose?why?
I would select company 2 because it has lower cost and tax amount for complete fencing job.
What is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Let, f = Total feet of the fence
For company 1 :
Given that 25 $
eq : (f-1)x25 + 2500
= (100 -1)25 + 2500
= 99 x 25 = 2500
= 4975 $
For company 2 :
Given that 39 $
Now if company 1 charges 7 % taxes then,
4975 x 7%
= 4975 + 348.25
= 5323.25$
and for company 2
39 x 7%
= 39 + 2.73
= 41.93 $
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2 1/2 ÷ by 5/8=? Whats the answer
Answer:
4
Step-by-step explanation:
5/8 x 4 =2.5
2.5 is also 2 1/2
please show me how to solve for z
8-12z=92
Answer: z = -7
Step-by-step explanation:
Simplify the equation so the Integer is on the right:
8 - 12z = 92
-12z + 8 = 92
Now subtract 8 from both sides:
-12z + 8 - 8 = 92 - 8
-12z = 84
Now divide both sides by 12 to get z by itself:
-12z/-12 = 84/-12
z = -7
Answer:
-7 (The other person copied me)
Step-by-step explanation:
Simplify both sides of the equation.
8−12z=92
8+−12z=92
−12z+8=92
Subtract 8 from both sides.
−12z+8−8=92−8
−12z=84
Divide both sides by -12.
−12z/−12 = 84/−12
z=−7
each side of a regular septagon has length 5 inches find the area of the region between the sptagon and its circumscribing circle?
The area of the region is equal to the area of the septagon minus the area of the circumscribing circle. The area of the septagon = 7 x (5^2 x (1 + sqrt(3))/4). The area of the circumscribing circle = pi x (5^2/2).
The area of the region between the septagon and its circumscribing circle can be found by subtracting the area of the circumscribing circle from the area of the septagon. The side length of the septagon is 5 inches. The area of the septagon can be calculated using the formula A = 7 x (5^2 x (1 + sqrt(3))/4). This is equal to 58.82 inches squared. The area of the circumscribing circle can be calculated using the formula A = pi x (5^2/2). This is equal to 78.54 inches squared. Therefore, the area of the region between the septagon and its circumscribing circle is 58.82 inches squared minus 78.54 inches squared, which is equal to 19.72 inches squared.
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Give two decimals that round to 5.24 when rounding to the nearest hundredths
Answer:
5.236, 5.235
Step-by-step explanation:
ya just round em up
Mai's class volunteered to clean a park with an area of square mile. Before they took a lunch break, the class had cleaned of the park. How many square miles had they cleaned before lunch?
The class had cleaned x × A square miles before lunch.
Let's assume that the area of the park is A square miles, and the portion of the park cleaned by Mai's class before the lunch break is represented by x (a fraction or decimal between 0 and 1).
If the class had cleaned x portion of the park, then the area they had cleaned is x times the total area of the park:
Area cleaned before lunch = x × A
Since x represents a fraction or decimal, multiplying it by the total area A gives us the corresponding portion of the park that was cleaned.
Let's say the park has an area of A square miles, and the area that Mai's class cleaned up before lunch is denoted by the number x (a fraction or decimal between 0 and 1).
If the class had cleaned a certain percentage of the park, their cleaned area would be x times the park's overall area:
Before lunch, the area was cleaned = x A
We may calculate the proportion of the park that was cleaned by multiplying x by the entire area A because it indicates a fraction or decimal.
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Which is the correct equation for a line that passes through the points (-2,7) and (2,-5)?
y=3x+5
y=1/3x+3
y= -3x-12
y= -3x+1
Answer:
y= -3x+1
Step-by-step explanation:
x1= -2 x2=2 y1=7 y2=-5
using the formula
(y-y1)/(x-x1)=(y2-y1)/(x2-x1)
(y-7)/(x-(-2))=(-5-7)/(2-(-2))
(y-7)/(x+2)=(-5-7)/(2+2)
(y-7)/(x+2)=(-12)/4
(y-7)/(x+2)=-3
cross multiply
y-7=-3(x+2)
y-7=-3x-6
y=-3x-6+7
y=-3x+1
Why Is 3 times 1/10 less than 3 times 10?k
3 times 1/10 is equal to 3/10, whereas 3 times 10 is equal to 30.
3/ 10 is less than 30.
We can write this as 3 * 1/10 compared to 3 * 10
If we divide both sides by 3, we then compare 1/10 and 10.
1/10 is less than 10, so 3 times 1/10 is less than 3 times 10.
We can rewrite 1/10 = 0.1, so 3 * 0.1 is 0.3 whereas 3 * 10 = 30.
Answer:
See Explanation
Step-by-step explanation:
When you multiply 3 * 1/10, 3 goes in the numerator so you get 3/10 which is 0.3
On the other hand 3*10 is 30.
0.3 is less than 30 that's why.
Here's the thing you had one pizza slice (equal to 1/10), and your parents gave you three times more the pizza slice. You will have three slices of pizza (each slice being 1/10) not 30 pizzas.
Hope that makes sense. I can explain again if you need me to!