Gavin invested $11,000 in a savings account. If the interest rate is 7%, how much will be in the account in 10 years with monthly compounding?
Round your answer to the nearest cent.
Do NOT round until you calculate the final answer

a.

A gardener can afford to buy 125 vinca plants and 60 phlox plants. $1.20/plant Vinca $2.50/plant Phlox.

The equation in standard form that models the possible combinations of x vinca plants and y phlox plants the gardener can afford to buy is

⇒ $1.20*x + $2.50*y

b.

An equation that models the possible combinations is

⇒ $1.20*125 + $2.50*60 = 300

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The magnitude of the boats resultant vector is 314.1 mi

A vector is a physical quantity that has both magnitude and direction.

A resultant vector is the sum of two or more vectors.

Since the boat sails 285 miles south and then 132 miles west, we have that its first direction vector is r = (285 mi)j. Also, its direction vector west is r' = -(132 mi)i

So, the resultant vector R = r + r'

=  (285 mi)j + (132 mi)i

=  (132 mi)i + (285 mi)j

So, the magnitude of the resultant vector is R = √(r² + r'²)

So, substituting thevalues of the variables into the equation, we have

R = √(r² + r'²)

R = √((285 mi)² + (132 mi)²)

R = √(81225 mi² + 17424 mi²)

R = √(98649 mi²)

R = 314.08 mi

R ≅ 314.1 mi

So, the resultant vector is 314.1 mi

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The image of the corresponding to each slope is attached

A line's steepness can be determined by looking at its slope.

Slope is determined mathematically as "rise over run" (change in y divided change in x).

assuming slope is m

m = (y₂ - y₁) / (x₂ - x₁) = change in y / change in x

considering the formula

slope is between 0 and 1 when rise (change in y) is so smaller than run (change in x) hence the line is closer to horizontal

slope is greater than 1 then the rise is more than run, in this case the line is approaching vertical line

numbers less than zero are negative hence slope has a negative value

A horizontal line is a line that has a slope of of zero while vertical lines has its slope as infinity

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According to the solving Probability the value are as follows.

a) P(Blue)= 0/10

b) P(Red)= 5/10

c) P(Red or Yellow)= 9/10

The definition of probability is "How likely something is to happen."

Probability is indeed a number ranging from 0 to 1 that expresses the likelihood that an event will take place as specified.

First, 0 P(E) 1 (where P(E) specifies the probability of an event E) and second, the sum of the probabilities of any collection of mutually and exclusive exhaustive occurrences equals 1 are the two characteristics that define a probability.

We have a Bag of marbles has 4 yellow, 5 red, and 1 purple.

Total balls in a bag= 4+5+1=10 balls.

Something that is IMPOSSIBLE to happen.

P(Blue)= 0/10

Something that is EQUALLY LIKELY to happen.

P(Red)= 5/10

Something that is LIKELY to happen.

P(Red or Yellow)= 9/10

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Answer: x= 0.5

Step-by-step explanation:

8x-4=2(4x-4)

You would want to take away the smaller x which is (4x)

4x-4=2-4

+4         +4

4x-4=2

+4  +4

4x=2

daddy ;)

The standard form of linear equation is 4x - y = 1.

What is the standard form of a linear equation?

Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y).

The slope intercepts form a linear equation is y = mx + c, where m is the slope and c is y-intercept of the line.

Given linear equation is:

4y=16x-4

Subtract 16x from both sides:

4y - 16x = -4

Divide both sides by -4

-y + 4x = 1

4x - y = 1

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Answer:

y=-2x-5

Step-by-step explanation:

m =-2 and b=-5 so when substituted it will get you y=-2x-5

Answer:

$ 52.63

Step-by-step explanation:

The brand C detergent has the best value.

The mathematical branch known as arithmetic deals with the study and application of numbers, their relationships, and mathematical observations.

As per the given data in the question:

The information regarding the quantity and cost of 3 detergents is given in the question.

We have to find out which detergent is the most economical.

The detergent with the lowest cost/quantity will be the most economical.

For Brand A

Cost = $14.99

Quantity = 40 ounces

cost/quantity = 14.99/40 = 0.374 dollar/ounce

For Brand B

Cost = $19.99

Quantity = 50 ounces

cost/quantity = 19.99/50 = 0.399 dollar/ounce

For Brand C

Cost = $21.99

Quantity = 1/2 gallon = 64 ounces

cost/quantity = 21.99/64 = 0.343 dollar/ounce

The brand C detergent has the best value.

Hence, The brand C detergent has the best value.

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Answer:

Step-by-step explanation:

Louie can choose the vessel for exhibition using combination in 3003 ways

information from the question include

Louie is studying ceramics and he is to submit 5 vessels

He has 15 vessels

The problem will be solved using combination

combination is method of choosing or making selection when order does not matter

Louie can choose any 5 of his vessel with no particular order

The formula is ₁₅C₅

₁₅C₅ = 15! / {5!(15 - 5)! )

= 15! / {5! * 10!}

= 3003 ways

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Answer:

1:commutative

2:distribution

3:3+0=3

4:distributive

5:

The probability that the sample proportion of the number of people using the courier will differ from the population proportion by greater than 0.03 is 0.0504

The probability is calculated using z score, this is used to determine the amount of standard deviations a sample, X is from the mean

The z score is given by the formula

z = (X - μ) / σ

Definition of variables

mean, μ  = p = 0.05

sample size, n = 202

standard deviation, σ

= √{(p(1 - p)) / n}

= √{(0.05(1 - 0.05)) / 202}

= √{(0.05 * 0.95) / 202}

= 0.01533

The probability

differ from the population proportion by less than 3%

|X - 0.05| > 0.03

X < 0.02 OR X > 0.08

P(z < 0.02) + P(z > 0.08 )

z score for z < 0.02

z = (0.02 - 0.05) / 0.01533

= -1.9569

p value for z < -1.9569 = 0.02518

z score for z > 0.08

z = (0.08 - 0.05) / 0.02196

= 1.9569

p value for z > 1.9569 = 1 - 0.9748 = 0.02518

The probability required = 0.02518 + 0.02518 = 0.0504 = 5.04%

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Answer:

0.97m : 1.08m

Step-by-step explanation:

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The probability of rolling a number that is less than 3 is P = 1/2.

A standard six-sided die has the following outcomes:

{1, 2, 3, 4, 5, 6}

The outcomes that are less than or equal to 3 are:

{1, 2, 3}

Assuming all the outcomes have the same probability, the probability of rolling a number less than or equal to 3 on a standard six-sided die will be equal to the quotient between the number of outcomes that meet the condition and the total number of outcomes.

It will give:

P = 3/6 = 1/2 = 0.5

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The sum of the fraction 74/10 + 42/5 is 15 4/5.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, the fraction will be illustrated as:

= 74/10 + 42/5

Change to mixed numbers

= 7 4/10 + 8 2/5

= 7 4/10 + 8 4/10

= 15 8/10

= 15 4/5

The value is 15 4/5.

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Differentiation of f(x) is [tex]-8x^{3} sinx^{4}[/tex].

Given,

f(x) = [tex]cos2x^{4}[/tex]

Now, we will differentiate f(x) with respect to x,

[tex]\frac{d}{dx}cos2x^{4} = (\frac{d}{dx}cos2x^{4})(\frac{d}{dx}2x^{4} )[/tex]

              [tex]= (-sin2x^{4})(2*4x^{3})[/tex]

              [tex]= -8x^{3}sin2x^{4}[/tex]

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Step-by-step explanation:

Square has perimeter 4a because every side is equal,

so :

if a=√8 , then 4a = 4*√8 or 11.313708499

and the number is rational

The major criteria to be considered when going for a bank to have a new savings account registered with them are as follows:

As an entrepreneur, finding a good bank to open a savings account with might be much tedious to do. However, I have live to understand that banks with low interest rate are a better catch if I am considering a good saving lifestyles. I cannot stand a banking system that charges me unnecessarily all the time all in the name of fee or the other, which results to reducing my money in their system.

That being said, discovering a bank which has welcoming and helping customer service is also an important factor to be considered when choosing to right banking system.

In conclusion, it can be deduced that a bank with which does not deduct one's money anyhow all in the name of interest is worth having a savings account with.

Complete question:

What are the conditions to be considered in choosing the best bank for a new savings account?

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Answer:

Box A: -2x

Box B: 2/9

Step-by-step explanation:

Multiply 1/3 by each of the expressions above the rectangle.

Box A: 1/3 × (-6x) = -2x

Box B: 1/3 × 2/3 = 2/9

Answer:

Step-by-step explanation:

I think the slope and the y is not 1/x because 2 is not part of the slope, im not sure

[tex]\textit{area of a rectangle}\\\\ A=Lw ~~ \begin{cases} L=length\\ w=width\\[-0.5em] \hrulefill\\ A=224\\ w=\stackrel{\textit{half-length plus 6}}{\frac{L}{2}+6~\hfill } \end{cases}\implies 224=L\left( \cfrac{L}{2}+6 \right)\implies 224=\cfrac{L^2}{2}+6L[/tex]

[tex]\stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2}}{2(224)=2\left( \cfrac{L^2}{2}+6L \right)}\implies 448=L^2+12L \\\\\\ 0=L^2+12L-448\implies 0=(L-16)(L+28)\implies \boxed{L= \begin{cases} -28\\\\ 16 ~~ \textit{\LARGE \checkmark} \end{cases}} \\\\\\ \stackrel{\textit{since we know that}}{w=\cfrac{L}{2}+6}\implies w=\cfrac{16}{2}+6\implies \boxed{w=14}[/tex]

now, let's notice, "L" has two valid values but for this case "L" cannot be negative.

Answer:

$370.62

Step-by-step explanation:

Ken spends $344.76 before tax at a hardware store. If the sales tax rate in his city is 7.5%, what is the total cost of his purchase? Round to the nearest cent if necessary.

7.5% = 0.075

0.075 * $344.76  = $25.857 in tax so:

cost + tax

$344.76 + $25.857 = $370.617

rounded:  $370.62

Using the simplification, the equivalent expression of 2.1+(–3.7h)+1.9h–1.4 is 0.7–1.8h.

In the given question we have to find the equivalent expression of the given expression.

The given expression is 2.1+(–3.7h)+1.9h–1.4

Now solving the given expression to find the equivalent expression.

Now solving the expression

=2.1 + (–3.7h) + 1.9h – 1.4

Firstly simplifying the bracket

=2.1–3.7h+ 1.9h – 1.4

=(–3.7h+ 1.9h)+(– 1.4+2.1)

= –1.8h + 0.7

We can write it as

=0.7–1.8h

Hence, the equivalent expression of 2.1+(–3.7h)+1.9h–1.4 is 0.7–1.8h.

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When it rains at the same rate for 15 more minutes, the fraction of the rain gauge that will be filled is 2/15.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split.

From the information, after raining for 3/4 of an hour, a rain gauge 2/5 of the way full. It's important to note that 3/4 is (3 × 1/4).

Therefore, we will divide 2/5 by 3 and this will be:

= 2/5 ÷ 3

= 2/5 × 1/3

= 2/15

This is the value of the rain gauge.

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Answer: f (x)= -2x + 4

From the proportional relationship graphed, it is found that:

A proportional relationship is a special case of a linear function, with slope represented by the constant of proportionality of k and intercept of 0, meaning that the relationship passes through the origin.

When the two variables x and y are direct proportional, the output variable y is obtained multiplying the input variable x by the constant of proportionality k, according to the rule presented follows:

y = kx.

From point (2,16) in this problem, the constant is given as follows:

k = 16/2 = 8.

Hence the equation is:

y = 8x.

Meaning that her rate is of:

8 miles per hour.

If she ran faster, the slope = constant would increase, as it represents the velocity.

The problem is given by the image at the end of the answer.

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Mr. Dunston spend is $35.

Given:

Mr. Dunston and Mr. Dolland spent $45 all together.

Mr. Dunston and Ms. Campbell spent $65 all together.

If Ms. Campbell spent 3 times as much as Mr. Dolland.

Let x , y , z be spend of dunston ,dolland and campbell.

x + y = 45

x + z = 65

z = 3*y

x + 3y = 65

on substracting x + y = 45 and x + 3y = 65 we get,

x + y - x - 3y = 45 - 65

-2y = -20

2y = 20

y = $10.

substitute y value,

x + 10 = 45

x = 45 - 10

x = $35

Therefore Mr.Dunston spend $35.

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Answer:

130-60m

Step-by-step explanation: