a tree is 8ft tall and grows 8 inches each year. In how many years will the tree reach a height of 30 feet?

A.27
B.33
C.45
D.52​

Answer:

Part a) The constant of variation is [tex]r=0.0567[/tex] or [tex]r=5.67\%[/tex]

Part b) [tex]I=\$662.03[/tex]

Step-by-step explanation:

Part a) Find the constant of variation.

we know that

The simple interest formula is equal to

[tex]I=P(rt)[/tex]

In this linear direct variation the constant r represent the constant of proportionality

where

I is the Interest Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

[tex]t=5/12\ years\\ P=\$3,892\\ I=\$92\\r=?[/tex]

substitute the values and solve for r

[tex]92=3,892(r(5/12))[/tex]

[tex]r=(92*12)/(3,892*5)[/tex]

[tex]r=0.0567[/tex]

Part b) what will the interest be after 3 years

in this part we have

[tex]t=3\ years\\ P=\$3,892\\ I=?\\r=0.0567[/tex]

substitute the values

[tex]I=3,892(0.0567*3)=\$662.03[/tex]

The LEFT side is the correct answer

Debits are entered on the left side of a T-account.

Debits and credits are fundamental concepts in accounting used to record financial transactions. In a T-account format, which visually splits an account into two sides, debits are always entered on the left side of the T-account. Conversely, credits are recorded on the right side.

For example, when a company purchases office supplies for cash, the office supplies account will have a debit entry (left side), while the cash account will have a credit entry (right side). This ensures that the accounting equation balances.

Answer:

b1= -1/2, b2= 2/7

Step-by-step explanation:

14b^2-2+3b=0

14b^2+7b-4b

7b(2b+1)-2(2b+1)=0

(2b+1)(7b-2)=0

2b+1=0 , 7b-2=0

b= -1/2 , b= 2/7

This is using the Factor Method

Answer: Interquartile: 8.25

Mean: 14.5

Median: 15.5

Step-by-step explanation:

The total number of flights delayed at several airport based on the histogram is 25.

An histogram is a graphical display of numerical data in the form of upright bars, with the area of each bar representing frequency.

Flight delayed 0 - 1 hour = 9

Flight delayed 1 - 2 hour = 3

Flight delayed 3 - 4 hour = 7

Flight delayed 4 - 5 hour = 5

Flight delayed 6 - 7 hour = 1

Total flights delayed = 9 + 3 + 7 + 5 + 1

= 25

Therefore, 25 flights were delayed.

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The closest integers to -0.001 are 0 and -1. -0.001 lies just to the left of 0 on the number line, making 0 the nearest positive integer and -1 the nearest negative integer.

The two integers that are closest to -0.001 are 0 and -1. Since -0.001 is a negative number that is very close to zero, it lies between these two integers on the number line. The integer 0 is the closest on the positive side, and -1 is the closest on the negative side.

The answer is 5 slices because a pie is 360 degrees and 360/72=5 making each slice 72 degrees and 5 slices in all.

Answer:

1/7

Step-by-step explanation:

The list of numbers generated is; 0, 1, 2, 3, 4, 5, 6,

There are 7 possible outcomes and each outcome is equally likely. The probability or chance that each number will occur is given by;

number of times the number occurs / 7

In our case, each number occurs only once, so the chance will be;

1/7

Answer:

of it say 0 out of 3 its on the one with 3 numbers

Answer: x = 6.25

5 ÷ 0.8

= 6.25

Answer:

the answer is 84

Step-by-step explanation:

a dozen is 12 so you take 12 times 7 and get 84

Heyaaa

The answer is 84 Candles .

There are 12 in a dozen , and there are 7 dozen.

12 x 7 = 84

Good luck :)

[tex]\huge\text{Slope: $\boxed{-\frac{3}{5}}$}\\\huge\text{$y$-intercept: $\boxed{9}$}[/tex]

We need to convert this line to slope-intercept form, or [tex]y=mx+b[/tex], where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.

[tex]\begin{aligned}3x+5y&=45&&\smash{\Big|}&&\text{Start with the original equation.}\\5y&=-3x+45&&\smash{\Big|}&&\text{Subtract $3x$ from both sides.}\\y&=\boxed{-\frac{3}{5}}x+\boxed{9}&&\smash{\Big|}&&\text{Divide everything by $5$.}\end{aligned}[/tex]

Answer:

A   942

Step-by-step explanation:

3/5ths is .6

125.6 / 2 = 62.8

62.8 * 15 = 942

Answer: Its A 942 hope this helped

Answer:

The correct answer is four

Step-by-step explanation:

From the figure we can see that, it is a triangular pyramid.

The base is a triangle.

In the lateral surface there are 3 faces.  All the three faces are triangle shape.

Therefore the given figure consists of four faces.

All the the four faces are in triangular faces.

The correct answer is four

The given polyhedron have four faces where all four faces are in triangular faces.

In a polyhedron, faces refer to the flat surfaces or sides of the three-dimensional object.

These faces are typically polygonal regions and are connected by edges and vertices.

In the figure, the base is a triangle.

and, in the lateral surface there are 3 faces.  

Therefore. the given figure consists of four faces.

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The answer is 1.

To find the answer you would take y/ x for the first thing in the table ( -2/1 ) then the second row of the table ( -1/2 ) then you would find out how much the points increased or decreased.

In this case y went up 1 and so did x so the slope would be 1/1 or just 1. Then check with the other points to make sure it is linear throughout then bam done. :)

Answer: [tex]x^4+4x^3+6x^2+7x+2[/tex]

Step-by-step explanation:

To solve the exercise you must apply the following proccedure:

- Apply the distributive property.

- Keep on mind that when you multiply two powers with equal base, you must add the exponents.

- Add like terms.

Therefore, you obtain the following product:

[tex]=x^{(2+2)}+x^{(2+1)}+2x^2+3x^{(1+2)}+3x^{(1+1)}}+6x+x^{2}+x+2\\=x^4+x^3+2x^2+3x^3+3x^2+6x+x^2+x+2\\=x^4+4x^3+6x^2+7x+2[/tex]

The answer is: [tex]x^{4}+4x^{3}+6x^{2}+7x+2[/tex]

To find the product of the given expression, we need to apply the distributive property and then, group each like term.

The distributive property states that:

(a+b+c)(d+e+f)=a*d+a*e+a*f+b*d+b*e+b*f+c*d+c*e+c*f

Then, we have to group each like term. Like terms are the terms that have the same variable and exponent , for example:

[tex]x+x+x^{2}=2x+x^{2}[/tex]

For this case, the variable "x" has two Like terms, since both have the same exponent (1), then, we add each other in order to group term.

Also, we must remember the following power property:

Product of powers property,

[tex]a^{n}*a^{m}=a^{n+m}[/tex]

So, solving the product we have:

[tex](x^{2}+3x+1)(x^{2}+x+2)=x^{2}*x^{2}+x*x^{2}+2x^{2}+3x*x^{2}+3x*x+6x+x^{2}+x+2\\(x^{2}+3x+1)(x^{2}+x+2)=x^{2+2}+x^{1+2}+2x^{2}+3x^{2+1}+3x^{1+1}+6x+x^{2}+x+2\\(x^{2}+3x+1)(x^{2}+x+2)=x^{4}+4x^{3}+6x^{2}+7x+2[/tex]

Have a nice day!

Answer: [tex]m=-\frac{4}{5}[/tex]

Step-by-step explanation:

To calculate  the slope of the line that has the coordinates given in the problem you must use the formula shown below:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Given the points  (-2, 7) (3 , 3), when you substitute them into the eequation shown above, you obtain that the slope is the following:

[tex]m=\frac{3-7}{3-(-2)}\\m=-\frac{4}{5}[/tex]

Answer:

[tex] - \frac { 4 } { 5 } [/tex]

Step-by-step explanation:

We are given the following two points on a line and we are to find the slope of this line:

(-2, 7) and (3,3)

We know the formula of the slope is given by:

[tex] \frac { y_2 - y_1 } { x_2 - x_1 } [/tex]

Substituting the given coordinates in the above formula to get:

Slope = [tex] \frac { 7 - 3 } { -2 - 3 } = - \frac { 4 } { 5 } [/tex]

Answer: d

Step-by-step explanation:

so 16+16=32

and to make things easier 32+32=64

64-8=56

The age of Julia is,

⇒ 6 years

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Dave is 8 years younger than 4 times Julia‘s age.

Let Julia age = x

Hence, Age of Dave is,

⇒ 4x - 8

Here, Age of Dave is, 16

Hence,

⇒ 4x - 8 = 16

⇒ 4x = 16 + 8

⇒ 4x = 24

⇒ x = 6

Thus, The age of Julia is,

⇒ 6 years

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Answer:

(-4,1)

Step-by-step explanation:

First, subtract 1-5. (When you move left or down you subtract. When you move right or up you add.) Left and right affect the x-axis

Second, subtract 4-3. Up and down Affect the y-axis

It would look like this:

(1,4)

=(1-5,4-3)

=(-4,1)

Answer:

here you go(image included)

Step-by-step explanation:

Answer:

-21.6 z^3 - 2 z + 2

Step-by-step explanation:

(-12.7z³ - 14z) + (-8.9z³ + 12z + 2)

I like to line them up vertically

  (-12.7z³ - 14z)

+ (-8.9z³ + 12z + 2)

---------------------------------

-21.6 z^3 - 2 z + 2

Answer:

Step-by-step explanation:

[tex]|a|=a\ \text{for}\ a\geq0\\\\|a|=-a\ \text{for}\ a<0[tex]|x|+7<4\qquad\text{subtract 7 from both sides}\\\\|x|+7-7<4-7\\\\|x|<-3\to x\in\O\ \text{because}\ |x|\geq0\ \text{for any value of }\ x.[/tex]===================[/tex]

Answer:

D) x < -15

Step-by-step explanation:

-3x - 42 >3

Add 42 to each side

-3x - 42+42 >3+42

-3x > 45

Divide each side by -3.  Remember to flip the inequality since we are dividing by a negative

-3x/-3 < 45/-3

x < -15

Explanation:

400 ft/ 4 m

= 100 ft/ 1 m

Answer:

it would take her 12 minutes to run 1200 ft.

she would run 1000 ft in 10 minutes given she does not slow down from fatigue

12weeks-15 books

4 weeks-5 books

8 weeks-10 books

Answer:

4 to 5

8 to 10

Step-by-step explanation:

The expression[tex]\(2n^{-4}\)[/tex] rewritten without a negative exponent is [tex]\(\frac{2}{n^4}\)[/tex]. This means the same as [tex]\(2\)[/tex] times the reciprocal of [tex]\(n\)[/tex] raised to the fourth power.

To rewrite the expression [tex]\(2n^{-4}\)[/tex] without using a negative exponent, we'll follow these steps:

1. Understand the Negative Exponent Rule: The rule states that [tex]\(a^{-b} = \frac{1}{a^b}\)[/tex]. It means that to convert a negative exponent to a positive one, you flip the base to the denominator of a fraction.

2. Apply the Rule to the Given Expression: We apply this rule to[tex]\(2n^{-4}\)[/tex].

3. Simplify the Expression: We simplify the expression to its final form without a negative exponent.

Let's apply these steps:

Step 1: Understand the Negative Exponent Rule

- The rule [tex]\(a^{-b} = \frac{1}{a^b}\)[/tex] tells us that to eliminate a negative exponent, we place the base with the positive exponent in the denominator of a fraction.

Step 2: Apply the Rule to the Given Expression

- Apply this to [tex]\(2n^{-4}\)[/tex]. It becomes [tex]\(2 \times \frac{1}{n^4}\)[/tex].

Step 3: Simplify the Expression

- Simplify [tex]\(2 \times \frac{1}{n^4}\)[/tex] to get the final expression.

Let's simplify it.

Step 3: Simplify the Expression

After applying the negative exponent rule to [tex]\(2n^{-4}\)[/tex], the expression simplifies to [tex]\(\frac{2}{n^4}\)[/tex].

Answer:

See below for explanation

Step-by-step explanation:

Another way to think about this is to think "How many fourths are in 3".  There are 4 fourths in 1, and there are 3 1's in 3, so we have

3(4) = 12 fourths in 3

Algebraically you can write it as.

1(4)x = 3         this means "one fourth time some value is 3"  which is a rewording of what I explained above.  Solve for x by multiplying both sides by 4...we get x = 12, so

one fourth, 12 times gives us 3

The fraction 12/4 simplifies to 3 because the numerator and denominator can both be divided by their greatest common divisor, which is 4.

The question is related to the conversion of a fraction to a simpler form. The fraction 12/4 can be converted into a simpler form by dividing both the numerator and the denominator by their greatest common divisor. The greatest common divisor of 12 and 4 is 4. So, we can divide the numerator 12 and the denominator 4 by 4.

Here's how to do it:

As a result, the fraction 12/4 reduces to the whole number 3. Thus, 12 fourths is represented as 3 in its simplest form.

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Answer:

Volume of the sphere model of earth is 321m³

Step-by-step explanation:

Parameter given:

    diameter of the sphere = 8.5m

      π = 3.14

   Volume of a sphere is given as = 4/3 π r³

      Where r is the radius of the sphere.

  From given diameter, radius = 8.5/2 = 4.25m

Therefore, imputing the parameters in the formular we have:

                           ⇒4/3 × 3.14 × 4.25³

                            ⇒1.333 ×3.14 × 76.766

Volume of the sphere model = 321.31m³ ≅ 321m³

Answer:

a) 2 minutes 48 seconds

b) The time would decrease as it takes less time for Lara to finish the race.

Step-by-step explanation:

Speed = Distance / Time

Speed = 475 / 114

Speed = 4.16m/s

Distance = 700m

Time = Distance/Speed

Time = 700/4.16

= 168 seconds

= 2 minutes and 48 seconds

Answer:

7.8 miles

Step-by-step explanation: