Caitlin currently owes $13,000 to a friend who is charging him interest of 2.90% p.m. He is required to settle the loan with two equal payments, one today and the other in six months. Calculate the size of the payments using six months as the focal date.

The value of the expression 3x + 4y² when x = -3 and y = 5 is 91.

Given the expression in the question;

3x + 4y²

To determine the value of the expression when x = -3 and y = 5, plug in x = -3 and y = 5 for every x and values in the expression and simplify.

3x + 4y²

3( -3 ) + 4( 5 )²

Simplify

Take the square of 5

3( -3 ) + 4( 25 )

Multiply 3 and -3

-9 + 4( 25 )

Multiply 4 and 25

-9 + 100

Add -9 and 100

91

Therefore, the value of the expression is 91.

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Answer: Midpoints (-3/2)

Step-by-step explanation:

Midpoint formula is (x1+x2)/2 , (y1+y2)/2

Plugin x values and solve
(-1 +-5)/2 = -3

Plugin y values and solve
(-5+9)/2 = 2

The midpoint is -3/2

I hope this helped you :D

In 50! will have 12 leading zeroes so the power of 10 will be 12 And for 1000! will have 249 Zeroes so here the power of 10 will be 249.

We calculate the leading zeroes by knowing the numbers 2 And 5 So

This number must end with 249 zeroes since there are 249 fives (and more than 249 twos) in its prime factorization. Thus 10 249 is the highest power of 10 that divides 1000!

To see why we have 249 powers of five:

200 + 48 + 8 + 1 = 249

And also we can do this with a formula n−σp(n)/(p−1) where σp(n)  is the sum of the digits of n written in base-p

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.

Answer:

Step-by-step explanation:

0.462

Answer:

0.462 :) hope this helps and please put me as brainiest thankyou !!

Step-by-step explanation:

Step-by-step explanation:

Money she makes=$140

since she saves 4/5 of the money she earns that means that: 4/5×140 = $32

This means that she saves $32 out of $140 she makes or earn

The Rate of plane in still air and rate of wind is 738 , 100 respectively .

What is Linear equation ?

Linear equation can be defined as the equation in which the highest degree is one

Given ,

An airplane travels 4466 kilometers against the wind in 7 hours and 5866 kilometers with the wind in the same amount of time.

Let speed of plane be Vp and Va

Now,

Vp - Va  = 4466 / 7

Vp+Va = 5866 / 7

So, Evaluating the equations,

we get,

2Vp = (4466+5866) / 7

Vp = 1476 / 2

Vp = 738

So substitute Vp =738 in Vp-Va = 4466/7

738 - Va = 638

Va = 738 - 638

Va = 100.

Hence, The Rate of plane in still air and rate of wind is 738 , 100 respectively .

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The solution to an equation is 10.Solving an equation refers to the process of determining its solution.

Make the available

14to obtain the desired amount:

x – 6 + x = 14

Put similar phrases together to get:

2x – 6 = 14

Adding 6 to both sides yields:

2x = 20

x = 10.

The complete question is,

1 4 (4x 24) + x = 14 must be solved.

By dividing the 1 by 4, you can obtain:

Put similar phrases together to get:

Adding 6 to both sides yields:

x =

Consequently, is the necessary response.

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a. The shape of the sampling distribution is normal by the Central Limit Theorem.

b. The mean is 0.23.

c. The standard error is 0.125, which means that the sample proportions differ by around 0.125 from the mean of 0.23.

d. The probability is 0.2877 = 28.77%.

By the Central Limit Theorem, each sample has at least 10 successes and at least 10 failures, and the shape of the distribution is normal.

For each sample, the mean and the standard error are specified as follows:

Hence, the distribution of differences, the mean, and the standard error are specified as follows:

Using the z-score formula, the probability that the difference is greater than 30 is 1 subtracted by the p-value of Z when X = 0.3, Therefore:

Z = (0.3 - 0.23)/0.125

Z = 0.56

Z = 0.56

1 - 0.7123 = 0.2877 = 28.77%.

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The complete question is:

At Westville High School there are 315 seniors and 389 juniors. 65% of the seniors have parking passes and 42% of the juniors have parking passes. The statistics teacher selects an SRS of 30 seniors and a separate SRS of 30 juniors. Let ^ps-^pj be the difference in the sample proportion of seniors and juniors that have parking passes.

a. What is the shape of the sampling distribution of ^ps-^pj? Why?

b. Find the mean of the sampling distribution.

c. Calculate and interpret the standard deviation of the sampling distribution.

d. What is the probability that the difference in sample proportions (senior-junior) of students with parking passes is greater than 30%?

The domain for 'n' will be all integers where n ≥ 1. Then the correct option is A.

A series of non-zero integers where every term after the first is obtained by increasing the one before it by a constant, non-zero value known as the scale factor.

Let a₁ be the first term and r be the common ratio. Then the nth term of the geometric sequence is given as,

aₙ = a₁ · (r)ⁿ⁻¹

The geometric sequence where a₁ = 7 and the common ratio is 3. Then the formula is given as,

aₙ = 7 · (3)ⁿ⁻¹

In the geometric sequence, the value of the exponent should be greater than or equal to zero. Then we have

n - 1 ≥ 0

n ≥ 1

The domain for 'n' will be all integers where n ≥ 1. Then the correct option is A.

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Answer:

B 6

Step-by-step explanation:

Answer:

B. 6

Step-by-step explanation:

6 x -14 = 3x + 4

3x = 18

X = [tex]\frac{18}{3}[/tex] Which equals =

6

Answer:

49. a)  A - C - 1

49. b)  1 - 2R

49. c)  2Q - P

50.  x = 103

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5cm}\underline{Log laws}\\\\$\log_axy=\log_ax + \log_ay$\\\\$\log_a \left(\dfrac{x}{y}\right)=\log_ax - \log_ay$\\\\$\log_ax^n=n\log_ax$\\\\$\log_ab=c \iff b=a^c$\\\\&\log_aa=1$\\ \end{minipage}}[/tex]

Part a

Given:

[tex]\log_5 9=A[/tex]

[tex]\log_5 6=B[/tex]

[tex]\log_5 11=C[/tex]

[tex]\begin{aligned}\log_5 \dfrac{9}{55}&=\log_5 9 - \log_5 55\\&=\log_5 9 - \log_5 (11 \cdot 5)\\&=\log_5 9 - (\log_5 11 + \log_5 5)\\&=\log_5 9 - \log_5 11 - \log_5 5\\&=A-C-1\\\end{aligned}[/tex]

Part b

Given:

[tex]\log_3 10=R[/tex]

[tex]\log_3 4=S[/tex]

[tex]\log_3 11=T[/tex]

[tex]\begin{aligned}\log_3 \dfrac{3}{100}&=\log_3 3 - \log_3 100\\&=\log_3 3 - \log_3 (10 \cdot 10)\\&=\log_3 3 - \log_3 10^2\\&=\log_3 3 - 2\log_3 10\\&=1-2R\\\end{aligned}[/tex]

Part c

Given:

[tex]\log_3 4=P[/tex]

[tex]\log_3 10=Q[/tex]

[tex]\log_3 7=R[/tex]

[tex]\begin{aligned}\log_3 25&=\log_3 \dfrac{100}{4}\\&=\log_3 100 - \log_3 4\\&=\log_3 (10 \cdot 10) - \log_3 4\\&=\log_3 10^2 - \log_3 4\\&=2 \log_3 10 - \log_3 4\\&=2Q-P\end{aligned}[/tex]

The error was in line 4 of the calculation.  The log law

was not applied correctly.

The correct solution is:

[tex]\begin{aligned}3 \log (x-3) + 1 & = 7\\3 \log (x-3) & = 6\\\log (x-3) & = 2\\x-3&=10^2\\x&=3+10^2\\x&=103\end{aligned}[/tex]

a. The total interest paid on the 25-year mortgage is $110411.

b. The total interest paid on the 30-year mortgage is $135644.

What is the meaning of APR?

Annual percentage rate (APR) is the term used to describe the annual interest produced by a sum that is levied against borrowers or distributed to investors. APR is a percentage that expresses the actual yearly cost of borrowing money over the course of a loan or the income from an investment. This does not account for compounding and includes any fees or additional costs related to the transaction. Consumers can compare lenders, credit cards, or investment products using the APR as a benchmark figure.

Given that, the amount that is borrowed is $220,000.

If you borrow it for 25 years, you will pay $1,101.37 monthly.

The amount that you need to pay is (1,101.37×12×25) = 330411.

The total interest is =  (330411 - 220,000) = $110411.

If you borrow it for 30 years, you will pay $987.90 monthly.

The amount that you need to pay is (987.90×12×30) = 355644.

The total interest is =  (355644 - 220,000) = $135644

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The complete function tables are written above.

A function describes a relationship between a dependent and independent variable. Example -

y = f(x) = 5x + 9

A quadratic function is of the form -

f(x) = ax² + bx + c

Given are the function tables as shown in the image attached.

{ 4 } -

Rule : h = 8c

{c}    2    3    4     5    6    7

{h}   16   24  32  45  48  56

{5} -

Rule : k = 2r

{r}    6     7    8    9    12    11    14

{k}   12   14   16   18   24   22  28

{6} -

Rule : k = 2r

{r}    6     7    8    9    12    11    14

{k}   12   14   16   18   24   22  28

Therefore, the complete function tables are written above.

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The significantly low values are:

Lower than 871.6 cm³.

The significantly high values are:

Higher than 1369.6 cm³.

Hence a volume of 1389.6 cm³ is significantly high, as it is more than 2 standard deviations from the mean.

The range rule of thumb states that measures that are more than two standard deviations from the mean in a data-set are considered unusual.

Considering the mean and the standard deviation for this problem, the bounds are given as follows:

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70 + 2x > 100 is an inequality to represent this situation.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

Given, At a local pizza shop, the delivery person earns $2 for every pizza delivered, plus $70 per day.

Let "x" be the number of pizzas he delivers

Thus, the Total money he earns by delivering pizza = 70 + 2x

To earn more than 100$ inequality represents

70 + 2x > 100

So,

2x > 30

x > 15

Therefore, to earn more than 100$ every day he needs to deliver at least 15 pizzas.

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Since the mid-points of opposite sides of a square are equal, the quadrilateral formed will also be a square.

A four-sided polygon whose all sides are equal is a square. This means that the opposite sides of a square are equal in length and the opposite angles are also equal. Furthermore, the diagonals of a square bisect each other at their mid-points. Therefore, if the mid-points of opposite sides of a square are joined, a quadrilateral is formed. Since the opposite sides and angles are equal, the quadrilateral formed is also a square. To prove this, we can draw a line from the mid-point of one side of the square to the mid-point of the opposite side. We can then draw a line from the mid-point of the other side of the square to the mid-point of the opposite side. This will form a quadrilateral, and due to the equal sides and equal angles, it will be a square.

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All u have to do is use the Traingle Inequality theorem, which states that the sum of two sides lenghts of a triangle is always greater than the third side. if this is true for all three combinations of added side lengths then you will have a triangle

Hope this helps :>

Answer:

3, 5, 7

Step-by-step explanation:

given 3 sides, for a triangle to be formed, then the sum of any 2 sides must be greater than the third side.

4 , 4 , 8

4 + 4 = 8 , not greater than 8, so does not form a triangle

1 , 2 , 3

1 + 2 = 3 , not greater than 3, so does not form a triangle

3 , 9 , 14

3 + 9 = 12 < 14 , so does not form a triangle

3 , 5 , 7

3 + 5 = 8 > 7

3 + 7 = 10 > 5

5 + 7 = 12 > 3

condition is satisfied , so will form a triangle

The recursive formula that represents the number of sequences in this sequence is n(n-1)(n-2)/6, where n is the number of terms in the sequence.

This recursive formula is based on the pattern of the sequence. The sequence has three terms, a, b and c, and then three combinations of two terms, ab, ac and bc, and then one combination of all three terms, abc. This pattern of three terms, then three combinations of two terms, then one combination of all three terms continues as the sequence increases.

The recursive formula represents this pattern in a mathematical equation. The formula is n(n-1)(n-2)/6, where n is the number of terms in the sequence. This formula is derived from the fact that for each term there are two other terms that can combine with it to form a two-term combination, and one combination of all three terms. Therefore, for n terms, there are n(n-1)/2 two-term combinations and one combination of all three terms, for a total of n(n-1)(n-2)/6 sequences.

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The complete question is

if the pattern below contiunues which equation(s) is a recursive formula that reprsents the number of sequences in this sequence 5, 10, 20, 40.

The volume of his large vase is 2,373.84cm^3 (option A)

The is 4 times the volume of the small verse. (option A)

A cylinder is a three-dimensional object. It is a prism with a circular base.

volume of a cylinder = nr^2h

Where:

Radius of the small verse = 6/2 = 3 cm

Volume of the small verse = 3.14 x 3² x 21 = 593.46 cm³

Radius of the large verse = (2 x 6) / 2 = 6cm

Volume of the large verse = 3.14 x 6² x 21 = 2,373.84 cm³

Difference in volumes =  2,373.84 cm³/  593.46 cm³ = 4

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Part A: The teacher's method is partially fair.

Part B: She can set up a fair way to make the decision that includes everyone by making it an open tournament for all such that all can participate.

Part A: The teacher's method is fair in terms of giving all students an equal opportunity to win the tickets by playing chess matches and having their names put into the hat.

However, it does not take into account the skill level of the students, which could result in a less skilled student winning the tickets over a more skilled student. To make the method more fair, the teacher could use a combination of wins and chess ratings to determine which students have the best chance to win the tickets.

Part B: To include the new students in the chance to win the tickets, the teacher could have them play chess matches against the current club members and use a combination of wins and chess ratings to determine the two students who will win the tickets.

This method is fair because it gives all students, including the new ones, the opportunity to compete and be recognized for their chess skills, rather than simply giving the tickets to the two students who have been in the club the longest. Additionally, using a combination of wins and ratings ensures that the most skilled players have a better chance of winning the tickets.

Therefore, the correct answer is as given above

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Answer:x=4, y=5

Step-by-step explanation:

The increase in the y-coordinatesis then calculated by dividing it by the change in the x-coordinates.

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If the ratio of dolphins to penguins is 2:5, then for every 2 dolphins, there are 5 penguins. If there are 30 penguins, you can use this ratio to find out how many dolphins there are. To find out how many dolphins there are, you can set up a proportion:

(number of dolphins) / (number of penguins) = (2) / (5)

You know that the number of penguins is 30, so you can substitute that in and solve for the number of dolphins:

(number of dolphins) / 30 = 2 / 5

Multiply both sides by 30 to solve for the number of dolphins:

number of dolphins = (2/5) * 30 = 6

So, if there are 30 penguins, there would be 6 dolphins.

A). The first term represents the total cost of the waffle irons and the second term represents the expenses.

B). The algebraic expression represents if the company sells 350 waffle irons per day will be 350x - 1500

C). The company's profit for a 5-day week is $250.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the algebraic expression 25x - 1,500 can be used to describe the daily profit of a company that makes waffle irons.

A). The first term represents the total cost of the waffle irons and the second term represents the expenses. Here 25 is the number of the waffle iron and the x is the number of days.

B). The algebraic expression represents if the company sells 350 waffle irons per day will be written as:-

350x - 1500

C). The company's profit for a 5-day week will be;-

Profit = 350x - 1500

Profit = ( 350 x 5 ) + 1500

Profit = 1750 - 1500

Profit = 250

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When the domain of x is restricted, the function x2 becomes one-to-one, and the inverse function is x.

It is true that limiting a function's domain might cause it to become invertible. Because it is not one-to-one in the example, the function x2 is not invertible across its complete domain of real numbers (i.e., it assigns multiple outputs to some inputs). However, x2 becomes one-to-one and invertible when the domain of x is constrained to or any subset of that interval. The range of x2, which is, is used to define the inverse function in this situation, which is

The function x2 becomes one-to-one when the domain of x is constrained, and the inverse function is

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Because x is 6, points A, B, and C are collinear.

The intersection of two lines in Euclidean geometry can be the empty set, a point, or another line. Distinguishing these cases and locating the intersection have applications in computer graphics, motion planning, and collision detection, among others. The intersecting lines are two lines that share exactly one common point. The intersecting lines have a point in common. The point of intersection is the common point that exists on all intersecting lines. When two or more lines intersect in a plane, they are referred to as intersecting lines. The intersecting lines share a common point, which exists on all of them and is known as the point of intersection.

Here,

Since the opposite angle are equal in intersecting lines,

42=7x

x=6

The value of x is 6 so that points A, B, and C are collinear.

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The required probability for the given delta airlines is given by :

a. Probability of flight late no more than 5 minutes is 0.25.

b. Probability of flight late more than 10 minutes is 0.5

c. Expected flight time is equal to 130 minutes.

Flight time from Cincinnati to Tampa = 2 hours 5 minutes

Actual time distributed between 2 hours and 2 hours 20 minutes

2 hours = 120 minutes

2 hours 20 minutes = 140 minutes

f(x) =  [tex]\left \{ {{\frac{1}{( 140 - 120)} , 120 \leq x\leq 140\atop {0 , x = 0 }} \right.[/tex]

a. Probability of flight no more than 5 minutes late

[tex]\int_{130}^{125} \frac{1}{20} dx[/tex]

= 1 / 4

= 0.25

b. Probability of flight  more than 10 minutes late

[tex]\int_{135}^{125} \frac{1}{20} dx[/tex]

= 1/2

= 0.5

c. Expected flight time in minutes

= [tex]\int_{140}^{120} \frac{x}{20} dx[/tex]

= 130 minutes

Therefore, the required probability are given by :

a. Probability of flight late no more than 5 minutes is 0.25.

b. Probability of flight late more than 10 minutes is 0.5

c. Expected flight time is equal to 130 minutes.

The above question is incomplete , the complete question is :

Delta Airlines quotes a flight time of 2 hours, 5 minutes for its flights from Cincinnati to Tampa. Suppose we believe that actual flight times are uniformly distributed between 2 hours and 2 hours, 20 minutes.  What is the probability that the flight will be no more than 5 minutes late (to 2 decimals)? What is the probability that the flight will be more than 10 minutes late (to 2 decimals)? What is the expected flight time, in minutes?

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Answer:

[tex]\underline{x\quad \:\:\:\:\:\:-8\quad\quad\;\;-6\quad\quad0\quad\quad\quad\;\; \;\;2}\\y\quad\quad\;\;\;\boxed{\dfrac{1}{3}}\quad\quad\quad \boxed{0} \quad\;\boxed{-1} \quad\quad \boxed{\dfrac{4}{3}}[/tex]

Step-by-step explanation:

The strategy is to substitute the value of each of the given x values into the equation
[tex]y = -\dfrac{x}{6} - 1[/tex]
and find the corresponding value for [tex]y[/tex]

[tex]x\quad\quad\quad\quad\quad\quad\quad\quad\quad y = -\dfrac{x}{6} - 1\\\line(1,0){180}\\\\[/tex]

[tex]-8\quad\quad\quad\quad\quad\quad\quad\quad\quad y = -\dfrac{-8}{6} - 1 = \bf{{\dfrac{1}{3}[/tex]
[tex]-6\quad\quad\quad\quad\quad\quad\quad\quad\quad y = -\dfrac{-6}{6}-1 = \bf{0}[/tex]
[tex]0\quad\quad\quad\quad\quad\quad\quad\quad\quad y = -\dfrac{0}{6}-1 = \bf{-1}[/tex]
[tex]2\quad\quad\quad\quad\quad\quad\quad\quad\quad y = -\dfrac{2}{6} -1 =\bf{-}\dfrac{4}{3}[/tex]

[tex]\line(1,0){180}\\\\[/tex][tex]\line(1,0){180}\\\\[/tex]

The limit in question is

[tex]$$\lim_{n\to \infty} \frac{1^3 + 2^3 + 3^3 + \dots + n^3}{n^4}$$[/tex]

This limit can be interpreted as the Riemann sum of a function defined on the interval [0, 16]. To calculate the sum, we need to first find the function that is being approximated. To do this, we can use the fact that the numerator of the limit can be rewritten as a single summation:

[tex]$$\sum_{k=1}^n k^3 = \frac{n^2 (n+1)^2}{4}$$[/tex]

This means that the function we are approximating is [tex]$f(x) = \frac{x^2 (x+1)^2}{4}$[/tex]

Now, to calculate the Riemann sum, we need to divide the interval [0, 16] into $n$ equal subintervals. The width of each subinterval is given by [tex]$\Delta x = \frac{16}{n}$\\The Riemann sum is given by $$\sum_{i=1}^n f\left(x_i\right) \Delta x = \sum_{i=1}^n \frac{\left(x_i\right)^2 \left(x_i+1\right)^2}{4} \cdot \frac{16}{n}$$[/tex]

where [tex]$x_i = \frac{16i}{n}$[/tex]

Plugging this into the limit, we get

[tex]$$\lim_{n\to \infty} \frac{1^3 + 2^3 + 3^3 + \dots + n^3}{n^4}\\ = \lim_{n\to \infty} \frac{\sum_{i=1}^n \frac{\left(x_i\right)^2 \left(x_i+1\right)^2}{4} \cdot \frac{16}{n}}{n^4} = \\frac{16}{4} \lim_{n\to \infty} \frac{\sum_{i=1}^n \frac{\left(x_i\right)^2 \left(x_i+1\right)^2}{n}}{n^3}$$[/tex]

Finally, we can take the limit of the above expression to get

[tex]$$\lim_{n\to \infty} \frac{1^3 + 2^3 + 3^3 + \dots + n^3}{n^4} = \frac{16}{4} \cdot \frac{f(16)}{16^3} = \frac{1}{4}$$[/tex]

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