. A friend opens a savings account by depositing $1000. He deposits an
additional $75 into the account each month.
a. What is a rule that represents the amount of money in the account as an
arithmetic sequence?
b. How much money is in the account after 18 months? Show your work.

Step-by-step explanation:

taking that blank as x

5/2 -x = 1/3

the x will go to the right hand side of the equation which then would make it positive ( making x the subject) and 1/3 will come to the left hand side of the equation becoming -1/3

so the equation will become 5/2-1/3=x

solving the fraction then gives 13/6 or 2.17 as the value of x

The value of the equation is x = 13 / 6

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the unknown number be represented as x

Substituting the values in the equation , we get

( 5/2 ) - x = 1/3   be equation (1)

Adding x on both sides of the equation , we get

( 5/2 ) = ( 1/3 ) + x

Subtracting ( 1/3 ) on both sides of the equation , we get

x = ( 5/2 ) - ( 1/3 )

On simplifying the equation , we get

x = ( 15 - 2 ) / 6

x = 13 / 6

Therefore , the value of x is 13/6

Hence , the equation is x = 13/6

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Answer: $22,241.32 APEX

Final answer:

By calculating the present value of an annuity using the monthly payment, interest rate, and number of payments, we find that Bryce can afford a car with a value of approximately $22,241.32.

Explanation:

To calculate the value of the most expensive car Bryce can afford based on a $350-per-month car payment with a 6-year loan at an APR of 4.2%, compounded monthly, we use the formula for the present value of an annuity:

PV = PMT × ¶ [(1 - (1 + r)^-nt) / r]

Where:

PV = Present Value (what we're solving for, the cost of the car)

PMT = Monthly Payment ($350)

r = monthly interest rate (APR divided by 12)

n = number of times the payment is made per year (12)

t = number of years (6)

Given:

APR = 4.2% per year or 0.042

Monthly interest rate, r = 0.042 / 12 = 0.0035

nt = 12 × 6 = 72 payments in total

Now we substitute the given values into the formula:

PV = $350 × [(1 - (1 + 0.0035)^-72) / 0.0035]

PV = $350 × [(1 - (1 + 0.0035)^-72) / 0.0035]

PV ≈ $350 × [(1 - (1.0035)^-72) / 0.0035]

Using a calculator to find (1.0035)^-72 and then the whole expression, we get:

PV ≈ $350 × 60.4774

PV ≈ $21,167.09

The value that's closest to our calculation and offered in the options is $22,241.32, so the most expensive car Bryce can afford is approximately $22,241.32.

Answer:

Step-by-step explanation:

5x+9y+90

This is just an algebraic expression.

Answer:

0.15

Step-by-step explanation:

3/4÷5

-6r+48

Step-by-step explanation:

Answer:

10.8

Step-by-step explanation:

we move the 3.6 to tge other side so the sighn of it will be negative the we subtract them so m=10.8

Answer:

m=4

Step-by-step explanation:

Answer:

multiply the whole number by the denominator, then add the number you get to the numerator.  :) hope this was helpful!!!

Step-by-step explanation:

Answer: You have to multiply the Main number by the denominator, then add the numerator to that number, and put it above the original denominator.

Step-by-step explanation:

D. The bottom one shows proportional relationships between x and y because it is y = .5x

Answer:

c

Step-by-step explanation:

Answer:

Step-by-step explanation:

The graph of log 2x has the same shape as that of log x, except that it is compressed horizontally by a factor of 2.

Additionally, that +3 indicates that we must translate the above graph upwards by 3 units.

we must replace [tex]x[/tex] by [tex]2\cdot x[/tex] and then translate the function 3 units in the +y direction.

We can transform [tex]y = \log x[/tex] into [tex]y = \log 2\cdot x +3[/tex] by means of the following operations:

That is, we represent the operations defined above mathematically:

1) [tex]y = \log x[/tex]

2) [tex]y = \log 2\cdot x[/tex]

3) [tex]y = \log 2\cdot x + 3[/tex]

In a nutshell, we must replace [tex]x[/tex] by [tex]2\cdot x[/tex] and then translate the function 3 units in the +y direction.

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Answer:

  Min. 1st Qu.  Median    Mean 3rd Qu.    Max.  

 0.580   0.805   1.160   1.085   1.345   1.470

The figure attached represent the boxplot obtained.

Step-by-step explanation:

We can use the following excel code:

data<-c(1.16, 0.72, 1.01, 1.36, 1.28, 1.47, 1.33, 0.68, 1.45, 0.58, 0.89)

> summary(data)

  Min. 1st Qu.  Median    Mean 3rd Qu.    Max.  

 0.580   0.805   1.160   1.085   1.345   1.470

We can order the data on increasing way:

> sort(data)

[1] 0.58 0.68 0.72 0.89 1.01 1.16 1.28 1.33 1.36  1.45 1.47

And for this case we got this:

The minimum on this case is: [tex]Minimum =0.58[/tex]

The maximum would be: [tex]Maximum = 1.47[/tex]

In order to find the median we need to find the value on the 6 position from the data ordered, and we got:

[tex]Median = 1.16[/tex]

And in order to obtain the boxplot we can use R to grapth the boxplot"

> boxplot(data,main="Boxplot")

And the result is on the figurea attached.

The five-number summary of the given data set is 0.58, 0.72, 1.16, 1.36, 1.47, representing the minimum, first quartile, median, third quartile, and maximum values of the data. These can be used to create a box plot to visualize the data.

The five-number summary of a data set includes the minimum, first quartile, median, third quartile, and maximum values of the data set. Here's how we can find those for the given radiation absorption rates:

So, the five-number summary is: 0.58, 0.72, 1.16, 1.36, 1.47.

To make a box plot, draw a number line from the minimum to the maximum and draw a box from the first quartile to the third quartile. Draw a line (the 'median line') inside the box at the median. Finally, draw 'whiskers' from the box to the minimum and maximum.

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Answer:

968 square feet

Step-by-step explanation:

Let x be the new flooring install in 24 hours.

Given:

Ryan can install 121 square feet of flooring in 3 hours.

So, Ryan can install flooring in one hour = [tex]\frac{121}{3} feet^{2}[/tex]

Ryan can install flooring in 24 hours.

[tex]x= 24\times flooring\ in\ one\ hour[/tex]

[tex]x=24\times \frac{121}{3}[/tex]

[tex]x=8\times 121[/tex]

[tex]x=968\ feet^{2}[/tex]

Therefore, Ryan can install 968 square feet of flooring in 24 hours.

Answer:

216

Step-by-step explanation:

Multiply 80x270, which gives you 21,600, then move the decimal at the end of the number two times to the left and you'll get 216

Answer:

[tex]6\frac{1}{12}\ yd[/tex]

Step-by-step explanation:

The correct question is

Marcella bought 12 1/4 yards of ribbon. She uses 2 1/2 yards of ribbon for gift packages and 3 2/3 yards to tie balloons.

How many yards of ribbon does Marcella have left?

we know that

To find out how many yards of ribbon Marcella has left, add up the yards of ribbon used for the gift packages plus the yards of ribbon used to tie the balloons. and subtract this result from the total yards of ribbon bought by Marcella

so

[tex]12\frac{1}{4}-(2\frac{1}{2}+3\frac{2}{3})[/tex]

but first convert mixed number to an improper fractions

[tex]12\frac{1}{4}=\frac{12*4+1}{4}=\frac{49}{4}[/tex]

[tex]2\frac{1}{2}=\frac{2*2+1}{2}=\frac{5}{2}[/tex]

[tex]3\frac{2}{3}=\frac{3*3+2}{3}=\frac{11}{3}[/tex]

substitute in the expression above

[tex]\frac{49}{4}-(\frac{5}{2}+\frac{11}{3})[/tex]

[tex]\frac{49}{4}-(\frac{5*3+2*11}{6})[/tex]

[tex]\frac{49}{4}-(\frac{37}{6})[/tex]

[tex]\frac{3*49-37*2}{12}[/tex]

[tex]\frac{73}{12}\ yd[/tex]

Convert to mixed number

[tex]\frac{73}{12}\ yd=\frac{72}{12}+\frac{1}{12}=6\frac{1}{12}\ yd[/tex]

Final answer:

After calculating the total ribbon used in yards and subtracting it from the amount Marcella bought, we find that she has 5 13/42 yards of ribbon left.

Explanation:

To determine how many yards of ribbon Marcella has left, we need to subtract the total amount of ribbon she used from the initial amount she bought. Marcella originally bought 12/14 yards of ribbon. She used 2 1/2 yards for gift packages and 3 2/3 yards for tying balloons.

To make the subtraction easier, we'll first convert the mixed numbers to improper fractions. The mixed number 2 1/2 becomes 5/2 when we multiply 2 (the whole number) by the denominator (2) and then add the numerator (1), resulting in 4 + 1 = 5 over the original denominator 2. Similarly, 3 2/3 becomes 11/3 when we multiply 3 (the whole number) by the denominator (3) and then add the numerator (2), resulting in 9 + 2 = 11 over the original denominator 3.

Now, let's perform the subtraction:

First, simplify 12/14 to 6/7 by dividing both the numerator and denominator by 2.

Next, find a common denominator for all three fractions. The least common denominator for 2, 3, and 7 is 42.

Convert each fraction to have the denominator of 42.

12/14 yards (or 6/7 yards when simplified) is (6/7) * (42/42) which equals 36/42 yards.

2 1/2 yards as an improper fraction is 5/2, and when converted to have a denominator of 42, it becomes (5/2) * (21/21) which equals 105/42 yards. Similarly, 3 2/3 yards is 11/3, and when converted to have a denominator of 42, it becomes (11/3) * (14/14) which equals 154/42 yards.

Now subtract both of these amounts from 36/42 to find out how much ribbon Marcella has left:

36/42 - 105/42 - 154/42 = (36 - 105 - 154)/42 = -223/42

Because we cannot have a negative amount of ribbon, we realize we made an error. We should add the fractions instead of subtracting:

36/42 - (105/42 + 154/42) = (36/42) - (259/42)

This simplifies to -223/42, which is an improper fraction. To convert this back to a mixed number, we divide 223 by 42.

223 divided by 42 is 5 with a remainder of 13, so Marcella has 5 13/42 yards of ribbon left. However, we need the positive value since ribbon length cannot be negative. Thus, we keep the positive difference:

Marcella has 5 13/42 yards of ribbon remaining.

In conclusion, after Marcella uses ribbon for gift packages and tying balloons, she is left with 5 13/42 yards of ribbon.

Answer:

11

Step-by-step explanation:

2x11 equals 22, and that plus 5 is 27

300 students attend Washington middle school.

Step-by-step explanation:

Given,

Percentage of students who play sport = 64%

Number of students who play sport = 192

Let,

x represent the total number of students at Washington middle school.

64% of x = 192

[tex]\frac{64}{100}x=192\\0.64x=192[/tex]

Dividing both sides by 0.64

[tex]\frac{0.64x}{0.64}=\frac{192}{0.64}\\x=300[/tex]

300 students attend Washington middle school.

Keywords: percentage, division

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Answer:

Step-by-step explanation:

METHOD 1:

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Substitute the coordinates of the given points (-4, 6) and (9, 6):

[tex]d=\sqrt{(9-(-4))^2+(6-6)^2}=\sqrt{(9+4)^2+0^2}=\sqrt{13^2}=13[/tex]

METHOD 2:

We can see that the second coordinates of the points (ordinate) are the same. Therefore, they lie on a horizontal line. The distance between them is the distance between the x coordinates (abscissa).

The formula of a distance between two numbers:

[tex]d=|b-a|[/tex]

We have

[tex]a=-4,\ b=9[/tex]

Substitute:

[tex]d=|9-(-4)|=|9+4|=|13|=13[/tex]

Answer:

B  [tex]x^4-x^3+x^2-x+1[/tex]

Step-by-step explanation:

Given,

Dividend = [tex](x^5+1)[/tex]

Divisor = [tex](x+1)[/tex]

Step 1: First The dividend is [tex](x^5+1)[/tex] and Divisor is [tex](x+1)[/tex] when divided first time the quotient will be [tex]x^4[/tex] and remainder will be [tex]-x^4+1[/tex]

Step: 2 Now the new dividend is [tex]-x^4+1[/tex] and Divisor is [tex](x+1)[/tex]  when divided the quotient will be [tex]x^4-x^3[/tex] and remainder will be [tex]x^3+1[/tex]

Step: 3 Now the new dividend is [tex]x^3+1[/tex] and Divisor is [tex](x+1)[/tex]  when divided the quotient will be [tex]x^4-x^3+x^2[/tex] and remainder will be [tex]-x^2+1[/tex]

Step: 4 Now the new dividend is [tex]-x^2+1[/tex] and Divisor is [tex](x+1)[/tex]  when divided the quotient will be [tex]x^4-x^3+x^2-x[/tex] and remainder will be [tex]x+1[/tex]

Step: 5 Now the new dividend is [tex]x+1[/tex] and Divisor is [tex](x+1)[/tex]  when divided the quotient will be [tex]x^4-x^3+x^2-x+1[/tex] and remainder will be 0.

Hence When the polynomial [tex](x^5+1)[/tex] is divided by  [tex](x+1)[/tex] the answer or quotient will be equal to  [tex]x^4-x^3+x^2-x+1[/tex] and remainder will be 0.

Answer:

Step-by-step explanation:

All of the answer choices are in slope-intercept form.

The slope-intercept form is y=mx+b where m=slope and b=y-intercept.

Answer:

B

Step-by-step explanation:

Question is Incomplete, Complete question is given below.

Prove that a triangle with the sides (a − 1) cm, 2√a cm and (a + 1) cm is a right angled triangle.

Answer:

∆ABC is right angled triangle with right angle at B.

Step-by-step explanation:

Given : Triangle having sides (a - 1) cm, 2√a and (a + 1) cm.  

We need to prove that triangle is the right angled triangle.

Let the triangle be denoted by Δ ABC with side as;

AB = (a - 1) cm

BC = (2√ a) cm

CA = (a + 1) cm  

Hence,

[tex]{AB}^2 = (a -1)^2[/tex] 

Now We know that

[tex](a- b)^2 = a^2+b^2 - 2ab[/tex]

So;

[tex]{AB}^2= a^2 + 1^2 -2\times a \times1[/tex]

[tex]{AB}^2 = a^2 + 1 -2a[/tex]

Now;

[tex]{BC}^2 = (2\sqrt{a})^2= 4a[/tex]

Also;

[tex]{CA}^2 = (a + 1)^2[/tex]

Now We know that

[tex](a+ b)^2 = a^2+b^2 + 2ab[/tex]

[tex]{CA}^2= a^2 + 1^2 +2\times a \times1[/tex]

[tex]{CA}^2 = a^2 + 1 +2a[/tex]

[tex]{CA}^2 = AB^2 + BC^2[/tex]

[By Pythagoras theorem]

[tex]a^2 + 1 +2a = a^2 + 1 - 2a + 4a\\\\a^2 + 1 +2a= a^2 + 1 +2a[/tex]

Hence, [tex]{CA}^2 = AB^2 + BC^2[/tex]

Now In right angled triangle the sum of square of two sides of triangle is equal to square of the third side.

This proves that ∆ABC is right angled triangle with right angle at B.

Answer:

[tex]A=18000 \cdot e^{0.0125 \cdot 2}[/tex]

[tex]A=18455.67[/tex] (Approximated)

Step-by-step explanation:

[tex]A=Pe^{rt}[/tex]

We are given the following along with the equation we are to use:

[tex]P=18000[/tex]

[tex]r=1.25\%=\frac{1.25}{100}=0.0125[/tex]

Be careful it says [tex]t[/tex] is in years and it gives us a time that is in months.

[tex]12 \text{months}=1 \text{ year}[/tex]:

[tex]t=\frac{24}{12}=2[/tex]

Let's plug in our information:

[tex]A=18000 \cdot e^{0.0125 \cdot 2}[/tex]

Plugging in the right hand side into my calculator gives:

[tex]A=18455.67[/tex] (Approximated)

Explanation:

Note: As you haven't clearly specified the answer choices. But, I am assuming one of the answer choices may have included some negative number under a square root, as a real number cannot have a negative number under a square root. So, whatever the choice may have contained the negative number under a square root would represent the complex number. Anyhow, I would try to clear your concept.

So, lets move forward.

A complex number is basically the combination of a real number and imaginary number which can be expressed in the form of [tex]a+ib[/tex]. where a and b are termed as real numbers and i is a solution of the equation x² = -1.

So,

In  [tex]a+ib[/tex],

For example, let us consider

[tex]2 + \sqrt{-1}[/tex]

Therefore, [tex]2 + \sqrt{-1}[/tex] is a complex number.

Keywords: complex number, iota

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500 guitar picks

order 15 boxes with 9 picks each

sell 19 boxes with 10 picks each

-> the store ordered about 150 picks (15 x 9 -> 15 x 10)

-> the store sold about 200 picks (19 x 10 -> 20 x 10)

it is reasonable, since they have 50 fewer picks which is about 450.

(second option)

Answer:

in full, on time, every time

Step-by-step explanation:

in full, on time, every time because even if little is left out it would again a large amount together with the interest. Also as the limit is low it can easily be reimbursed

Answer:

The address of Ainsley is 24 and that of Lane is 25.

Step-by-step explanation:

All the houses on sequence lane have an address whose numerical portions are greater than that of the prior house.

Now, if Ainsley and Lane are next-door neighbors and the sum of the numerical portions of their addresses is 49.

Let the Ainsley has the address with numeric portion x, then Lane has the address with numeric portion x + 1.

Therefore, x + (x + 1) = 49

⇒ 2x = 48

⇒ x = 24

So, the address of Ainsley is 24 and that of Lane is 25. (Answer)

Answer:

32 is 99% of 33 cause 33 is 100% of 33

Step-by-step explanation:

Step-by-step explanation: First we have "what number" which we can represent by the variable x. Next we have is which means "is equal to" so we write an equals sign, then we have 99% which we need to write as a decimal so we move the decimal point 2 places to the left to get 0.99 and "of 33" means times 33.

Now we have the following equation.

X = (.99)(33)

Answer:

Step-by-step explanation:

Money spent on jersey and pant = 65 * 17.50 + 65*11 = 65 * (17.50+11)

                                                       = 65 * 28.50 = $1852.50

Answer:

7.5

Step-by-step explanation:

5(x+2)-4(x+1)

5x+10-4x-4

5x-4x+10-4

x+6

1.5+6=7.5

Answer:

7.5

Step-by-step explanation:

Substitute 1.5 into the equation

5(1.5+2) − 4(1.5+1)

5(3.5) − 4(2.5)

17.5 - 10 = 7.5

Answer:

[tex] - 25 + ( - 18) \\ - 25 - 18 \\ = - 43[/tex]

hope this helps you....

Answer:

15 in2

Step-by-step explanation:

3*5= 15

length*width= area

Hope it helped!!!

PLZ GIVE BRAINLIEST!!!!!

Answer: 16 square inch

Step-by-step explanation: 5+5+3+3=16