Suppose you take a survey of all the schools in your state. What would you expect the relationship between the number of students and the number of teachers in each school to be?

an = an - 1 . 7; 4,802 is the recursive formula for the geometric sequence.

What exactly is a geometric series?

A geometric sequence is a set of integers that follows a pattern where each term is multiplied by a fixed number called the common ratio, or r, to find the following term.

                             2, 4, 8, 16, 32, 64,..., which has a common ratio of 2, is an illustration of a geometric sequence.

2, 14, 98, 686, ...

as shown in total

2 * 7 = 14             14 * 7 = 98          98 * 7 =   686

So   aₙ = aₙ₋¹

     a₅   =   a₄  . 7

           =    686  . 7  =  4802

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To complete the table, we need to calculate the value resulting from the $14,000 investment with a 4% interest rate for 5 years under the given compounding options.

a. Daily compounding:

To calculate the value with daily compounding, we use the formula:

Value = Principal × (1 + (Rate / n))^(n × Time)

In this case, the principal (P) is $14,000, the rate (R) is 4% (or 0.04), the time (T) is 5 years, and the compounding period (n) is 365 (since it's daily compounding).

Value = 14000 × (1 + (0.04 / 365))^(365 × 5)

Calculating this value will give you the result for the daily compounding option.

b. Continuously compounding:

To calculate the value with continuous compounding, we use the formula:

Value = Principal × e^(Rate × Time)

In this case, the principal (P) is $14,000, the rate (R) is 4% (or 0.04), and the time (T) is 5 years.

Value = 14000 × e^(0.04 × 5)

Calculating this value will give you the result for the continuously compounding option.

Please note that e represents the mathematical constant approximately equal to 2.71828.

Answer:

x = 1, XZ = 48

Step-by-step explanation:

So you already have the diagram with the number labeled,

4(x + 5) and 2(x + 11)

We know that Y is the midpoint between X and Z so we know that XY = YZ:

4(x + 5) = 2(x + 11)

Let's solve the equation for x:

4x + 20 = 2x + 22 (Distributive Property)

Subtract 20 from both sides:

4x = 2x + 2

Subtract 2x from both sides:

2x = 2

Divide both sides by 2:

x = 1

So now we know that x = 1, we want to find XZ:

XZ = 4(x + 5) + 2(x + 11)

We can plug in x (1):

XZ = 4(1 + 5) + 2(1 + 11)

Simplify:

XZ = 4(6) + 2(12)

XZ = 24 + 24

XZ = 48

Answer:

5

Step-by-step explanation:

1.) Order the numbers from least to greatest (1,2,4,4,6,7,9,12) then find the HIGHEST and LOWEST #.

2.)  Find the number in the very middle, which would be 4 and 6. Since it's not one number, add them both together and divide by 2 (4+6=10, 10/2=5). This will be your MEDIAN.

3.) Similar to step 2, find the number in the middle of the median and lowest number. Ignore the median in this. Since it's 2 numbers again, add both together and divide by 2 (2+4=6, 6/2 = 3, making the first interquartile 3).

4.) Repeat step 3, but instead of finding the number in the middle of the median and lowest number, use the highest number instead of the lowest. Since this also happens to be 2 numbers, repeat the same step of adding the numbers and then dividing by 2 (7+9=16, 16/2=8, making the second interquartile 8).

5.) Now, subtract both interquartiles. This should give you your answer (5).

Answer:

The answer is $0.07 cents per inch

Step-by-step explanation:

If you take 6 feet into inches (72)

and divide the total cost by the amount of inches (5.04 / 72)

You get the answer

Answer:

483

Step-by-step explanation:

A=1/2(a+b)h

A = 96.6

V = A x h

V = 96.6 x 5

V=483

The list price of the house is $260,869.57

What is a list price?

This is the price the property is valued to sell at in an arm's length transaction in a transaction that occurs between independent parties.

In this case, the property was sold for 92% of its list price, which means the sales price is 92% multiplied by the list price.

sales price=92%* list price

sales price=$240,000

list price=unknown(assume it is X)

$240,000=92%*X

X=$240,000/92%

X=$260,869.57

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Inequalities are used in various branches of mathematics, as well as in real-world applications such as economics, physics, and social sciences, to describe relationships, make comparisons, and analyze data.

Inequalities are mathematical statements that describe a relationship between two values or expressions, indicating that one is greater than, less than, or not equal to the other. Inequalities are used to compare quantities and express their relative sizes or order.

The most common symbols used in inequalities are:

">" (greater than): indicates that the value on the left side is larger than the value on the right side.

"<" (less than): indicates that the value on the left side is smaller than the value on the right side.

"≥" (greater than or equal to): indicates that the value on the left side is greater than or equal to the value on the right side.

"≤" (less than or equal to): indicates that the value on the left side is less than or equal to the value on the right side.

"≠" (not equal to): indicates that the values on both sides are not equal.

Inequalities can be represented using variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Solutions to inequalities are often expressed as intervals or sets of values that satisfy the given inequality.

Inequalities are used in various branches of mathematics, as well as in real-world applications such as economics, physics, and social sciences, to describe relationships, make comparisons, and analyze data.

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Answer:(0,10)

Step-by-step explanation:

The points On circle with a center at (0, 0) that includes the point (-1, -3) would be (0, 10).

If a circle O has a radius of r units length and that it has got its center positioned at (h, k) point of the coordinate plane,

then, its equation is given as:

\((x-h)^2 + (y-k)^2 = r^2\)

We have given On circle with a center at (0, 0) that includes the point (-1, -3).

So the equation form

\((x-h)^2 + (y-k)^2 = r^2\)

\((x-0)^2 + (y-0)^2 = r^2\\\\x^{2} +y^{2} =r^{2} \\\\(-1)^{2} +(-3)^{2} =r^{2} \\\\r^{2} = 10\)

So, the other point that satisfies the equation would be (0, 10).

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ANSWER:

True

STEP-BY-STEP EXPLANATION:

Sampling bias occurs when some members of a population are systematically more likely to be selected in a sample than others. The statement tells us that the selection method makes the sample differ from the population, that is to say that the sample does not represent the population, since members were selected according to what is needed, that is to say there is a sampling bias.

This means that the statement is true.

Answer:y= 3x-4

Step-by-step explanation:

Use the equation: y-y1=m(x-x1)

Here, y-2=3(x-6)

y=3x-4

Therefore , the solution of the given problem of probability comes out to be rotating blue has two positive results.

Each of the procedure's criteria-based methods have as their main objective determining the likelihood that a statement is accurate or that an event will take place. Any number from zero to one, where 0 typically represents percentage and 1 typically reflects degree of certainty, can be used to symbolize chance. A probability illustration shows the likelihood that a particular occurrence will occur.

Here,

A. The number of potential outcomes for each spin can be multiplied to determine the number of outcomes in the sample space. Since there are two potential outcomes for each spin in this scenario, there are a total of:

=> 2 x 2 = 4

There are four potential outcomes in the sample space as a result.

B. There are two of these branches: blue-blue and red-red. Therefore, spinning the same hue twice in a row has two positive results.

C. Counting the number of branches that lead to blue on either spin will allow us to determine how many good outcomes there are for spinning blue. These stems come in two varieties: blue-red and blue-blue. Therefore, rotating blue has two positive results.

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Answer: 4/5

Step-by-step explanation:

Answer: 69/85 is the simplified form. You can't simplify it.

Step-by-step explanation:

Answer:

7.5 * 10^18

Step-by-step explanation:

We know, as a general fact, scientific notation is written with a decimal multiplied by a power of ten. There are 17 zeroes after the 5, so that makes it 75 * 10^17. However, scientfic notation has a decimal. To get to a decimal, we need to move one place to the left. So add 1 to 17 for 7.5 * 10^18.

Answer:

7.5 x 10¹⁹

Step-by-step explanation:

I took the test.

Answer:

Step-by-step explanation:

Answer: Divide Kayak budget by rental rate

Step-by-step Explanation:

As Joshua is renting for himself alone, the two available options would be the Single Kayak and the Single Sea Kayak.

He can determine the number of hours to rent a Kayak for by dividing his Kayak Budget by the rental rate per hour of the 2 options available to him.

Single Kayak

Budget available = $50

Rental rate = $15 per hour

Hours he can rent = 50/15

= 3.33 hours

Single Sea Kayak

Budget available = $50

Rental rate = $18 per hour

Hours he can rent = 50/18

= 2.78 hours

ANSWER

C = 28 degrees

D = 28 degrees

E = 124 degrees

EXPLANATION

We have the three angles of the triangle are given as:

The angles in a triangle sum up to give 180 degrees. This implies that:

C + D + E = 180

=> (x + 3) + (x + 3) +(5x - 1) = 180

Collect like terms:

x + x + 5x + 3 + 3 - 1 = 180

7x + 5 = 180

7x = 180 - 5 = 175

x = 175 / 7

x = 25 degrees

Therefore, the three angles are:

C = 25 + 3 = 28 degrees

D = 25 + 3 = 28 degrees

E = 5(25) - 1 = 125 - 1 = 124 degrees

Answer:

15 ° is correct answer

Answer:

no cuz if u work for 4 hours and get $12 then if u work for 7 hours u get $21

Step-by-step explanation:

Based on the amount deposited by Nancy into the account and the interest it paid, the ending balance after 1 year is $1,220.40

The ending balance of the amount that Nancy deposited which was $1,200 is based on the interest compounded on the amount over the investment year.

The ending balance can be found as:
= Amount deposited x ( 1 + rate) ^ number of years

Solving for the ending balance gives:
= 1,200 x (1 + 1.7%) ^ 1

= 1,200 x 1.017

= $1,220.40

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The value of x when lines MN and PQ are equal is 7

Let take note of the properties of a quadrilateral, they include;

From the information given in the diagram, we have that;

Line MN = Line PQ

Also, the expressions are;

MN = 7x + 13

PQ = 10x - 8

Now, equate the values, we get;

7x + 13 = 10x - 8

collect the like terms

7x - 10x = -8 - 13

subtract the like terms

-3x = -21

Divide both sides by the coefficient of x, we get

x = 7

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Answer:

D, g(x) = 1/4 x^2

Step-by-step explanation:

You can try plugging in the x and y values into each equation. The answer to this would be D, where if you plug in 2 as the x value, you get 1/4 * 4 which equals 1. This also makes sense because 2x would have a narrower curve while 1/2x would have a wider curve.

Answer:

x = g + c - y

Step-by-step explanation:

g = x - c + y

g + c - y = x

therefore; x = g + c - y

Answer:

(a) Equation of parallel line is y = x + 4

(b) Equation of perpendicular line is y = - x + 8

Step-by-step explanation:

Given line is

x - y = 4

Rewrite this as

x - 4 = y

or

y = x - 4

This is the equation of a line in slope intercept form which is generally

y = mx + b

where m is the slope and b the y-intercept

Here m = 1, b = -4

(a) A parallel line will have the same slope but a different y-intercept
So for starters we can write the equation of the parallel line as
y = x + b

Since this passes through (2,6) sub 2 for x and 6 for y to get

6 = 2 + b

==> b = 4

Equation of the line is
y = x + 4

(b) A perpendicular line will have as slope -1/m where m is the slope of the original line

Here m = 1, so -1/m = -1/1 = -1

Equation will be of the form
y = -x + b

Since this also passes through (2,6)
6 = -2 + b

==> b = 6 + 2 = 8

Equation of perpendicular line is
y = -x + 8

Let's develop a synthetic division

As you can observe, the division is exact because its reminder is zero.

Hence, the answer is-

Solution

Observe that as you move to the left, we have

Therefore, as well move to the left, we multiply by 10

OptionB

\(\huge\underline\mathcal{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}\)

the question asks us to find the values of y.

the question can be solved as follows ~

\(\longrightarrow \: 5y {}^{2} - 17y = - 6\)

let's first convert the equation into its general formula , i.e. , ax² + bx + c = 0

\(\longrightarrow \: 5y {}^{2} - 17y + 6 = 0\)

using splitting the middle term , let's find out the factors of the given equation ~

\(\longrightarrow \: 5y {}^{2} - 15y - 2y + 6 = 0 \\ \\ \longrightarrow \: 5y \: (y - 3) - 2 \: (y - 3) = 0 \\ \\ \longrightarrow \: 5y - 2 = 0 \: \: \: or \: \: \: y - 3 = 0 \\ \\ \longrightarrow \:\boxed{ y = \frac{2}{5}} \: \: \: or \: \: \: \boxed{y = 3}\)

hope helpful ~

\( \: \: \: \: \: \: \: \: \: \: \: \: \purple\diamond{\boxed{\boxed{\boxed{\sf{{ \pink{ANSWER}}}}}}}\)

\(5y^2- 17y=-6\)

Move terms to the left side

\(5y^2- 17y=-6 \)

\(5y^2- 17y-(-6) = 0\)

Use the sum-product pattern

\(5y^2-17y+6=0\)

\(5y^2-2y-15y+6=0\)

Common factor from the two pairs

\((5y^2-2y)+(-15y+6) = 0\)

\(y(5y-2)-3(5y-2) = 0\)

Rewrite in factored form

\(y(5y-2)-3(5y-2) = 0\)

\((y-3)(5y-2) = 0\)

Create separate equations

\((y-3)(5y-2) = 0\)

\(y-3=0\)

\(5y-2=0\)

Solve :

Rearrange and isolate the variable to find each solution

\(y = 3\)

\(y = \frac{2}{5}\)

Answer:

36 < (x - 2)² + (y + 3)² and 16 > (x - 4)² + y²

Step-by-step explanation:

This is because the shaded area is inside the first circle (centered at (4, 0) with a radius of 4) but outside the second circle (centered at (2, -3) with a radius of 6). The inequalities reflect these conditions by setting the inequality signs accordingly. The inequality with "<" for the first circle ensures that the shaded area is within the circle, and the inequality with ">" for the second circle ensures that the shaded area is outside the circle.