the rate of interest for 5 years is 2.5 and the interest is 2400. what is the total amount deposited? ​

Answer:

The solution to the system of equations g(x) = x - 1 and f(x) = x^2 - 5 is the point where the two functions intersect, which is the point (1,0).

To confirm this, we can substitute x = 1 into each equation and see that they both equal 0:

g(1) = 1 - 1 = 0

f(1) = 1^2 - 5 = -4 + 1 = -3 = 0

So (1,0) is the solution to the system of equations.

Answer:

-7.9n+9.8

Step-by-step explanation:

add em

Answer:

9.8 - 7.9n

Step-by-step explanation:

To simplify, we need to have the least amount of terms possible. To do this here, we need to group like terms. We will start by rearranging our equation to group our like terms, like this:

3.8 + 6 - 4.9n - 3n

Then, we will combine our liker terms, giving us:

9.8 - 7.9n

That is the most simplified we can get. So our simplified equation is

9.8 - 7.9n.

Hope this Helped!

Andrew's initial deposit will grow to about $543 in 7 months.

You can use the formula A = P * e^(rt) to calculate this, where A is the final amount, P is the initial deposit, r is the interest rate, and t is the time in years. The equation for "continual" growth (or decay) is A = Pert, where "A", is the ending amount, "P" is the beginning amount (principal, in the case of money), "r" is the growth or decay rate (expressed as a decimal), and "t" is the time (in whatever unit was used on the growth/decay rate).

A = P * e^(rt)

Plug in the given values:

A = $543

P = $500

r = 0.065 (6.5% expressed as decimal)

Solving for t:

t = ln(A/P) / r

t = ln(543/500) / 0.065

t = 0.07 ( 7 months)\

Therefore, Andrew's initial deposit will grow to about $543 in 7 months.

To learn more about Annuities,

Visit; brainly.com/question/23554766

#SPJ4

449 students were surveyed about their preferences for sports. 146 students like football, 107 students like baseball, and 49 students like both sports. there are 293  students like exactly one of the two sports.

This can be determined by subtracting the number of students who like both sports (49) from the total number of students surveyed (439). This leaves us with 390 students who like either football, baseball, or both. To find the number of students who like exactly one of the two sports, we will need to subtract the number of students who like both sports from the number of students who like either football or baseball.

To do this, we add together the number of students who like football (146) and the number of students who like baseball (107). This gives us 253 students who like either football or baseball. Subtracting this number (253) from the number of students who like either sport (390) gives us the number of students who like exactly one of the two sports (293).

To know more about numbers refer to the link brainly.com/question/17429689

#SPJ4

Answer:

$338/20 = $16.90

Answer:

[tex]\$16.90 \textrm{ per hour}[/tex]

Step-by-step explanation:

To solve this, we simply have to divide the total amount of money that Taylor earned by the number of hours that she worked for.

[tex]\dfrac{\$338.00}{20 \textrm{ hr}} = \$16.90 \textrm{ per hr}[/tex]

Answer:

Step-by-step explanation:

Using the given equation, we can solve for t when s is equal to 22.

22 = -2.7t^2 + 40t + 6.5

Subtracting 6.5 from both sides, we get:

15.5 = -2.7t^2 + 40t

Adding 2.7t^2 to both sides, we get:

18.2t^2 = 15.5 + 40t

Subtracting 40t from both sides, we get:

18.2t^2 - 40t = 15.5

Dividing both sides by 18.2, we get:

t^2 - 2.2t = 0.855

Factoring, we get:

(t - 1)(t - 0.855) = 0

Setting each factor equal to 0 and solving, we get:

t = 1 and t = 0.855

Therefore, the ball will reach a height of 22ft after 1 second and 0.855 seconds.

On solving the provided question, we can say that standard deviation 15.4 is the mean of the sample means' sampling distribution.

Standard deviation is a statistic that expresses the variability or variance of a group of numbers. While a high standard deviation suggests that the values are more dispersed, a low standard deviation suggests that the values tend to be closer to the established mean. A measure of how dispersed the data are from the mean is the standard deviation (or ). When the standard deviation is low, the data tend to be grouped around the mean, and when it is large, the data are more dispersed. The average variability of the data set is measured as standard deviation. It reveals the average deviation of each score from the mean.

If the population is normal to begin with then the sample mean also has a normal distribution, regardless of the sample size:

u = 15.4;

⊕ = 5.6

now

μ = 5.6[tex]\sqrt{5}[/tex] =

To know more about standard deviation visit:

https://brainly.com/question/23907081

#SPJ4

The number of non-empty subsets of the given set that consist entirely of prime numbers is [tex]$31-16=7$[/tex]

The total number of non-empty subsets of [tex]$\{1,2,3,4,5,6,7,8,9,10,11\}$[/tex] that consist entirely of prime numbers is 7. The prime numbers in the given set are {2,3,5,7,11}. The formula to calculate the number of non-empty subsets of a set with n elements is [tex]$2^n-1$[/tex]. Thus, the number of non-empty subsets of the given set is [tex]$2^{5}-1=31$[/tex]. To calculate the number of subsets that consist of prime numbers only, we need to subtract the number of subsets that contain at least one non-prime number from 31. There are 16 such subsets, as the non-prime numbers in the given set are[tex]$\{4,6,8,9,10\}$[/tex]. Thus, the number of non-empty subsets of the given set that consist entirely of prime numbers is[tex]$31-16=7$.[/tex]

Learn more about  prime numbers here:

https://brainly.com/question/9315685

#SPJ4

The minimum number of 1 point foul shots that your team must make to win the game is given as follows:

20.

The expression for this problem is defined as follows:

3p + 2f + s.

In which the variables are given as follows:

The opponent made these following shots:

Hence the number of points of the opponent is given as follows:

8 x 3 + 12 x 2 + 11 = 59.

Your team made these following shots:

Hence the number of points of your team is given as follows:

10 x 3 + 8 x 2 + x = 40 + x.

The team wins when:

40 + x > 59

x > 19

Hence the minimum number is of 20, as the number of one point shots is a discrete amount.

Your basketball team made 10 three-pointers, 8 two-point field goals, and x one-point foul shots.

Your opponents made 8 three-pointers, 12 two-point field goals, 11 one-point foul shots.

More can be learned about expressions at https://brainly.com/question/24808124

#SPJ1

The two consecutive integers that the square root of 12 lies between are 3 and 4.

Positive, negative, and zero are all examples of integers. The Latin word "integer" signifies "whole" or "intact." All whole numbers and negative numbers are considered integers. This means that if we combine negative numbers with whole numbers, a collection of integers results.

An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion. This therefore means that integers can only be whole numbers and consecutive integers follow each other. For instance, 1, 2, and 3 are consecutive integers.

To find the two consecutive integers that the square root of 12 lies between, find the square root of 12 :

= √ 12

= 3.46

This means that the lower integer would be 3 and the consecutive integer following would be 4.

Find out more on integers at https://brainly.com/question/29398913

#SPJ1

If the data from X2 is higher than the data from X1, then the researcher can conclude that using an octane booster increases gasoline mileage

X1: Gas mileage before using octane booster

X2: Gas mileage after using octane booster

The researcher is comparing X1 and X2, to determine if using an octane booster increases gasoline mileage.

1. The researcher selected a random sample of seven cars and drove them for two weeks without using the octane booster (X1).

2. The researcher then drove the same seven cars for two weeks with the octane booster (X2).

3. The researcher then compared the data from X1 and X2 to see if there was an increase in gasoline mileage.

4. If the data from X2 is higher than the data from X1, then the researcher can conclude that using an octane booster increases gasoline mileage.

Learn more about data here

https://brainly.com/question/14893265

#SPJ4

Answer:

54 nhcuioogffhuivkoov89

The events A and B are mutually exclusive, that is they are independent. Hence, option a and option c are correct.

In probability theory, if two events don't happen at the same time, they are mutually exclusive or disjoint. The outcomes of a single coin flip, which can result in either heads or tails but not both, are an obvious example.

Given that A and B are mutually exclusive events.

For mutually exclusive events the probability of event A occurring or event B occurring is summation of the probability of the individual event.

Both the events are independent.

Hence, option a and option c are independent.

Learn more about mutually exclusive events:

https://brainly.com/question/28565577

#SPJ4

Answer: 5 chairs and 2 extra chairs

Step-by-step explanation:

Note that [tex]\frac{27}{5}=5.4[/tex]. This means we can place up to 5 chairs at each table.

However, this means that there will be [tex]27-5(5)=2[/tex] chairs left over.

$45.38 and $46.42 is the  interval can the branch manager be 95% certain that the sample mean will fall within

Using the Central Limit Theorem, the branch manager can be 95% certain that the sample mean will fall within $1.034 of the mean.

What does the Central Limit Theorem state?

It states that the sampling distribution of sample means of size n has standard deviation .

By the Empirical Rule, 95% of the sample means fall within 2 standard errors of the mean.

In this problem, we have that the standard deviation and the sample size are given as follows:

Hence the standard error is given by:

[tex]s = \frac{10.34}{\sqrt{400}} = 0.517.

Two standard errors is represented by:

2 x 0.517 = $1.034.

Hence, the branch manager can be 95% certain that the sample mean will fall within $1.034 of the mean.

$45.38 and $46.42 is the  interval can the branch manager be 95% certain that the sample mean will fall within

More can be learned about interval at

brainly.com/question/24663213

#SPJ4

If something melts in your mouth and not in your hand, then it must be something that has a low melting point.

Converse,Inverse and Contrapositve

To learn more about Converse,Inverse and Contrapositve refer to:

https://brainly.com/question/3965750

#SPJ1

The interest that we will have in 6 months if you invest 1000 dollars at 3% compounded monthly is 15.09 dollars.

Let's find the compound interest that will if one invest 1000 dollars in 6 months at 3% rate compounded monthly.

using compound interest formula,

[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]

where

Therefore,

p = 1000

r = 3% = 3 / 100 = 0.03

t = 0.5

n = 12

Therefore,

[tex]A = 1000(1+\frac{0.03}{12} )^{12(0.5)}[/tex]

A = 1000(1 + 0.0025)⁶

A = $1,015.09

Therefore,

Interest = 1,015.09 - 1000 = $15.09

learn more on interest here:https://brainly.com/question/14295570

#SPJ1

Therefore , the solution of the circle comes out to be the parametric curves cross at position (4, 1, 32).

Each point in the plane that is a certain distance from some other point forms a circle (center). Thus, it is an arc composed of points that also are spaced apart from one another in the plane. Additionally, at every angle, it is radial symmetric about the center. In the closed, two-dimensional plane of a circle, every pair of endpoints is uniformly separated from the "center." By drawing lines through the circle, one can create a line of circular symmetry. Additionally, it rotates equally at all angles about the center.

Here,

This is what we get when we use the parametric values in both r2 and r1 as functions of t:

Curve 1: x1(t), y(t), and z(t) = 48-12

Figure 2: Curve 2:

x2(t)=8-t, y2(t)=t-3, 22(t) = 12

Where they meet, they are equal, so:

x1(t) Equals x2(t),

where t=8-t 2t8 and t=4

(x(t), y(t), z(t)) = using curve 1 (t,5-t,48-12)

Following that,

(x(4), y(4), 2(4)) = (4,5-4, 48-42) = (4,1,32)

They get together at point (4, 1, 32).

Therefore , the solution of the circle comes out to be the parametric curves cross at position (4, 1, 32).

To know more about circle visit:

https://brainly.com/question/29142813

#SPJ4

On solving the provided question, we can say that the roasting approach, which represents sets as 3, 5, 7, and 8, is one way to write domains

The domain of a function is the set of possible values that it can accept. The x-values of a function like f are represented by these integers (x). A function's domain is the set of possible values on which it can be used. This set is the value that the function returns after the insertion of the x value. Y = f is the definition of a function with x as the independent variable and y as the dependent variable (x). A value of x is said to be in a function's domain if it can be successfully utilised to produce a single value of y by using the value of x.

A set of ordered pairs (x, y), {(3,6),(5,7),(7,7),(8,9)}.

The collection of x values that make up the domain of the function f(x) include,

The roasting approach, which represents sets as 3, 5, 7, and 8, is one way to write domains. Another is the arrow diagram method.

To know more about domain visit:

https://brainly.com/question/28135761

#SPJ4

Answer:

the answer to this question is 107

Answer:

×⁴-8ײ+1

Explanation:

hope its help...

There are 6 ways to choose two rotten apples out of a sample of three.

What is algebra ?

Algebra is a branch of mathematics in which letters and symbols are used to represent numbers and quantities in equations and formulas. Algebraic concepts include the manipulation of equations and formulas using the rules of arithmetic, the solution of equations, and the study of the properties and behaviors of functions.

There are two rotten apples out of 15 total apples, so the probability of choosing a rotten apple is 2/15. The probability of choosing two rotten apples out of a sample of three is (2/15) * (1/14) * (3 choose 2) = (2/455) * 3 = 6/455. So there are 6 ways to choose two rotten apples out of a sample of three.

Hence , There are 6 ways to choose two rotten apples out of a sample of three.

To learn more about algebra visit : brainly.com/question/24875240

#SPJ4

The possible number of handshakes in a group of 10 people, where each person shakes hands with everyone else once are equal to 45.

Number of people in the group = 10

Each person shakes hands with everyone else once. When n people shake hands with each other, the total number of handshakes = ⁿC₂

where C denotes the combination , is represent an arrangement of objects in different ways without care of order.

Total number of handshakes = ¹⁰C₂

= 10!/2!(10 - 2)! = 10!/2!×8!

= 10×9×8!/(2×1)8!

= (10×9)/2

= 45 handshakes.

In other words, when 10 people are shaking hands, each one will shake hands with 9 others. Then, the total possible number of handshakes in a group = 10 × 9 = 90

(but remember the point that , when A shakes hands with B, B is also shaking hands with A, i.e., we are counting one handshake twice, one from A's side and the other from B's side).

The total number of handshakes in actual way = 90/2 = 45 handshakes. Hence, the total number of handshakes in a group is 45.

To learn more about Combination formula, refer:

https://brainly.com/question/28065038

#SPJ4

Answer:

f(x) = - x + 2

Step-by-step explanation:

the equation of a linear function in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

f(0) = 2 means y = 0 when x = 2 and f(5) = - 3 means y = - 3 when x = 5

thus there are 2 points (2, 0 ) and (5, - 3 )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 2 ) and (x₂, y₂ ) = (5, - 3 )

m = [tex]\frac{-3-2}{5-0}[/tex] = [tex]\frac{-5}{5}[/tex] = - 1

the line crosses the y- axis at (0, 2 ) ⇒ c = 2

then

f(x) = - x + 2

Answer:

Un industriel souhaite fabriquer une boîte sans couvercle à partir d'une plaque de métal de

24

Step-by-step explanation:

The position number for term 47 is 269.

This is an arithmetic sequence since each term has a common difference. Let us test it.

The difference between 1st and 2nd terms is

-7 + d = -1

d = -1 + 7

  = 6

Now we check the difference for term

The difference between 3rd and 4th terms is

5 + d = 11

d = 11 – 5

  = 6

So the difference is the same so we can apply a common equation for arithmetic sequence

[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + d ( n - 1 )

Where :

[tex]a_{n}[/tex] = number at term n

[tex]a_{1}[/tex] = first number of sequence

d = difference for each number sequence

n = term

From the question, we need to find the number at position term 47

[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + d ( n - 1 )

[tex]a_{47}[/tex] = -7 + 6 ( 47 - 1 )

    = -7 + 6 ( 46 )

    = -7 + 276

    = 269

Learn more about arithmetic sequence here

https://brainly.com/question/27079755

#SPJ4

The values of x and y in the trapezoid are x = 15 and y = 3

You should understand that a trapezoid or trapezium is a quadrilateral having two parallel sides and two non-parallel sides

If the trapezoid is isosceles, angles A and C are supplementary, so ...

(4x+4) +(7x+11) = 180

This implies that

11x +15 = 180

Collecting  terms we have

11x = 165 . . . . . . . . . subtract 15

x = 15 . . . . . . . . . . . . divide by the coefficient of x

And angles C and E are congruent.

4·15 +4 = 21y +1

63 = 21y . . . . . subtract 1

3 = y . . . . . . . . divide by the coefficient of y

In conclusion x and y are 15 and 3

Learn more about a trapezium on https://brainly.com/question/22607187

#SPJ1

Formula is an act or rule that uses mathematical symbols.

Equations, equalities, identities and inequalities are a few examples of formula.

An equation, also known as an equality, formula, or identity, is a mathematical phrase that states that two or more quantities are equal to one another.

A declaration of the mathematical equivalence of two quantities. The similarity A=B signifies that "A is equal to B."

A mathematical relationship that equalizes one quantity to another is known as an identity (which may initially appear to be different).

A proof in mathematics that one quantity is bigger or smaller than another A>b is used to indicate "A is bigger than B," whereas A<B is used to indicate "A is smaller than B." The symbols A<=B and A>=B stand for "A is less than or equal to" and "A is greater than or equal to B" respectively. The terms "A is much less than B" and "A is much more than B," respectively, are denoted by the symbols A<<B and A>>B.

Learn more about equation here:

https://brainly.com/question/29174899

#SPJ4

De acuerdo con la información del enunciado, el resultado de esta operación matemática (división) es 0,13

Esta división da como resultado un número decimal de varios valores por lo que podemos repetir este procedimiento tantas veces sea necesario dependiendo de la exactitud de nuestras necesidades.

Aprenda más sobre división en: https://brainly.com/question/29292671

#SPJ1