Determine whether the
data in the table can be modeled by a linear
function or an exponential function and write the
function. Write “neither” if the data are not linear
or exponential

Answer:

P = 0.232

Step-by-step explanation:

In the cooler, we have 12 bottles of apple juice and 18 bottles of orange juice.

This adds up to a total of 30 bottles.

Now we want to find the probability of pulling a bottle of apple juice after you pulled one bottle of apple juice.

The probability of pulling a bottle of apple juice at the beginning is equal to the quotient between the number of apple juice bottles in the cooler and the total number of bottles in the cooler,

This means that 12 out of 30 are apple juice, then the probability of getting first a bottle of apple juice is:

p = 12/30

Now, we want to find the probability of getting another, we will do the same calculation than above, but now the number of bottles of apple juice is 11 (because we took one) and the total number of bottles is 29.

In this case, the probability is:

q = 11/29

The joint probability (the probability of both events happening) is equal to the product of the individual probabilities.

Then the probability of pulling apple juice and then pulling another apple juice is:

P = p*q = (12/30)*(11/29) = 0.232

Step-by-step explanation:

Questions about equivalent expressions usually feature both simple expressions and complex expressions. To check which complex expression is equivalent to the simple expression:

Distribute any coefficients: a(bx\pm c)=abx\pm aca(bx±c)=abx±aca, left parenthesis, b, x, plus minus, c, right parenthesis, equals, a, b, x, plus minus, a, c.

Combine any like terms on each side of the equation: xxx-terms with xxx-terms and constants with constants.

Arrange the terms in the same order, usually xxx-term before constants.

If all of the terms in the two expressions are identical, then the two expressions are equivalent.

Example

How do we solve for unknown coefficients?

Some questions will present us with an equation with algebraic expressions on both sides. On one side, there will be an unknown coeffient, and the question will ask us to find its value.

For the equation to be true for all values of the variable, the two expressions on each side of the equation must be equivalent. For example, if ax+b=cx+dax+b=cx+da, x, plus, b, equals, c, x, plus, d for all values of xxx, then:

aaa must equal ccc.

bbb must equal ddd.

To find the value of unknown coefficients:

Distribute any coefficients on each side of the equation.

Combine any like terms on each side of the equation.

Set the coefficients on each side of the equation equal to each other.

Solve for the unknown coefficient.

Example

How do we rearrange formulas?

Formulas are equations that contain 222 or more variables; they describe relationships and help us solve problems in geometry, physics, etc.

Since a formula contains multiple variables, sometimes we're interested in writing a specific variable in terms of the others. For example, the formula for the area, AAA, for a rectangle with length lll and width www is A=lwA=lwA, equals, l, w. It's easy to calculate AAA using the formula if we know lll and www. However, if we know AAA and www and want to calculate lll, the formula that best helps us with that is an equation in which lll is in terms of AAA and www, or l=\dfrac{A}{w}l=

w

A

l, equals, start fraction, A, divided by, w, end fraction.

Just as we can add, subtract, multiply, and divide constants, we can do so with variables. To isolate a specific variable, perform the same operations on both sides of the equation until the variable is isolated. The new equation is equivalent to the original equation.

The value of equivalent expression is,

⇒ 5x - 29

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

Given that;

The expression is,

⇒ 6x + 7 - 12 × 2 - (3² + 3) - x

Now, We can simplify as;

⇒ 6x + 7 - 12 × 2 - (3² + 3) - x

⇒ 6x + 7 - 24 - (9 + 3) - x

⇒ 6x + 7 - 24 - 12 - x

⇒ 5x - 29

Thus,  The value of equivalent expression is,

⇒ 5x - 29

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Answer:

Slope = 2

Y-intercept = -4

Step-by-step explanation:

The slope of a function is found by finding the change in the y-values and dividing it in the change in x-values.

The change in y-values is 2 because that is the difference between each given data point. The change in x-values is 1 for the same reason.

The slope would be 2/1 which is just 2.

The y-intercept can be found by setting up the function in slope-intercept form (y=mx+b) and using the given data to solve for b. The point I chose to do this with was (2,0)

y=mx+b

y=2x+b

0=(2*2)+b

0=4+b

b=-4

So the slope is 2 and the y-intercept is -4.

Answer:

I'm not sure about this, sorry!

Step-by-step explanation:

\(648 \div 36 = 18\)

18 gallons of water flowed into the tank each minute.

Answer: the answer is 18 gallons

Step-by-step explanation: all you have to do is divide 648 by 36 and you should recieve an answer of 18

Answer:

character

Step-by-step explanation:

I think Character because character is basically position and who you're playing as

Answer:

1/8, or 12.5%.

Step-by-step explanation:

Answer:

\(\frac{1}{8}\)

Step-by-step explanation:

Answer:

The nth term is Tn = 2[T(n- 1) -2]

The next term is 356

Step-by-step explanation:

Given

Terms: 15,26,48,92,180

Solving (a) : The recursive n term

We have:

T1 = 15

T2 = 26 = 13 * 2 = (15 - 2) * 2

T3 = 48 = 24 * 2 = (26 - 2) * 2

T4 = 92 = 46 * 2 = (48 - 2) * 2

T5 = 180 = 90 * 2 = (92 - 2) * 2

So, the nth term can be represented as:

Tn = [T(n-1) - 2] * 2

Tn = 2[T(n-1) - 2]

The next term is the 6th term.

So, substitute 6 for n in the above formula.

T6 = 2 * [T(6 - 1) - 2]

T6 = 2 * [T5 - 2]

Substitute 180 for T5

T6 = 2 * (180 - 2)

T6 = 2 * 178

T6 = 356

Answer:

Dustin Earns $14,000 in a year but in the question, we are given the salary of a month

Monthly salary of dustin:

14000 / 12 = $1,166 (approx)

Hence,

The actual monthly salary of Dustin is $1166, excluding the commissions

For a specific month, the salary of Dustin including the commissions is $2,400

Money earned in commissions:

Salary earned  - Actual monthly salary

2400 - 1166 = $1,234

We are given the sales of Dustin for that specific month = $ 18,000

Hence, Dustin Earned a commission of $1,234 for sales of $18,000

Commission rate of Dustin:

Commission Earned * 100 / Sales made

1234 * 100 / 18000

6.856 %

Therefore, the commission rate of Dustin is 6.856%

Answer:

14

Step-by-step explanation:

56 divided by 4 is 14

STEP 1: a1 = 6.

STEP 2:  r = 0.75

STEP 3: The common ratio is less than one.

STEP 4: The sum of the  Sum of the Infinite Geometric series is Sn = 24

Since we have the expression for the sum of the infinite geometric series

\(\[ \sum_{n=0}^{\infty} 6(0.75)^{n} \]\)

STEP 1:

The first term of the infinite geometric series is 6. Thus, a1 = 6.

STEP 2:

The common ratio of the infinite geometric series is 0.75. Thus, r = 0.75

STEP 3:

The common ratio is less than one.

Because Sn = a/(1 - r)  is the formula we use when the common ratio is less than 1.

STEP 4:

Sn = a/(1 - r)

Sn = 6/(1 - 0.75) = 24

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Answer:

use \(y^{2}\)~\(mx_{1}\)+b to answer your question

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

The cruise ship will travel approximately 15 nautical miles in 345 minutes.

Use a proportion to solve this problem. Let "d" be the number of nautical miles the cruise ship will travel in 345 minutes. Then:

19 nautical miles / 437 minutes = d nautical miles / 345 minutes

To solve for "d", cross-multiply:

19 nautical miles x 345 minutes = d nautical miles x 437 minutes

Then, divide both sides by 437 minutes to isolate "d":

d nautical miles = (19 nautical miles x 345 minutes) / 437 minutes

Simplifying this expression, we get:

d nautical miles = 15 nautical miles (rounded to the nearest whole number)

Therefore, the cruise ship will travel approximately 15 nautical miles in 345 minutes.

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Answer:

The value is   \(P( X < 0.09) = 0.070781\)

Step-by-step explanation:

From the question we are told that

   The population proportion is  p =  0.11

   The sample size is n =  529

Generally given that the sample size is large enough (i.e n > 30), then the mean of this sampling distribution is mathematically represented as

      \(\mu_{x} = p = 0.11\)

Generally the standard deviation of this sampling distribution is

        \(\sigma = \sqrt{ \frac{ p (1 - p )}{n} }\)

=>     \(\sigma = \sqrt{ \frac{ 0.11 (1 - 0.11 )}{529} }\)

=>     \(\sigma = 0.01360\)

Generally the probability that the proportion of defective bottles in a sample of 529 bottles would be less than 9% (0.09) is mathematically represented as

     \(P( X < 0.09) = P(\frac{X - \mu_{x}}{\sigma} < \frac{0.09 -0.11}{ 0.01360} )\)

\(\frac{X -\mu}{\sigma }  =  Z (The  \ standardized \  value\  of  \ X )\)

     \(P( X < 0.09) = P(Z< -1.47 )\)

Generally from the z table  the  area under the normal curve to the left corresponding to -1.47 is  

       \(P(Z< -1.47 ) = 0.070781\)

So

       \(P( X < 0.09) = 0.070781\)

The solution to the algebraic statement Negative six i equals eighteen is i  = -3

The statement is given as:

Negative six i equals eighteen

Rewrite the above equation properly.

This is represented as follows:

-6i  = 18

Divide both sides of the equation by -6.

So, we have:

-6i/-6  = 18/-6

Evaluate the quotient of 18 and -6

So, we have:

-6i/-6  = -3

Evaluate the quotient of -6i and -6

So, we have:

i  = -3

Hence, the solution to the algebraic statement Negative six i equals eighteen is i  = -3

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Answer:

18.9

Step-by-step explanation:

Answer:

what do you need help with

Step-by-step explanation:

The sample mean of the number of movies watched by 25 students is 2.8 and the approximate sample standard deviation is 1.15.

(a) The sample mean X can be calculated by taking the average of the number of movies watched by all 25 students.

Step 1: Sum up the number of movies watched by all 25 students:

\(0 * 1 + 1 * 2 + 2 * 4 + 3 * 10 + 4 * 6 + 3 * 2 = 0 + 2 + 8 + 30 + 24 + 6 = 70\)

Step 2: Divide the sum from Step 1 by the number of students (25):

70 / 25 = 2.8

So the sample mean X = 2.8

(b) The sample standard deviation s can be calculated using the formula:

\(s = \sqrt{\frac{ \sum(X - X_{mean})^2}{(n-1)} }\)

Where \(X_{mean}\) is the sample mean, n is the sample size, and Σ represents the sum of all values.

Step 1: Calculate \((X - X_{mean})^2\)for each data point and sum up the values:

\((0 - 2.8)^2 * 1 + (1 - 2.8)^2 * 2 + (2 - 2.8)^2 * 4 + (3 - 2.8)^2 * 10 + (4 - 2.8)^2 * 6 + (3 - 2.8)^2 * 2\\ = 7.84 + 3.24 + 0.64 + 9.6 + 1.44 + 7.84\\ = 31.36\)

Step 2: Divide the sum from Step 1 by (n - 1) = 24:

31.36 / 24 = 1.31

Step 3: Take the square root of the result from Step 2:

\(\sqrt{1.31} = 1.15\)

So the approximate sample standard deviation s = 1.15 (rounded to two decimal places).

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Answer:

3/2y-5

Step-by-step explanation:

Yes, the given set of the sides of a triangle follows the Pythagorean Triple and the acute angles are 61.92° and  28.08°.

Pythagorean triples are a²+b² = c² where a, b and c are the three positive integers. These triples are represented as (a, b, c). Here, a is the perpendicular, b is the base and c is the hypotenuse of the right-angled triangle.

Given that, A triangle has sides with lengths 8, 15, and 17.

1) Checking for Pythagorean triples;

17² = 289

8²+15² = 225+64 = 289 = 17²

∴ 17² = 8²+15²

Since, they are following the Pythagoras theorem so, they are  Pythagorean triples.

2) Calculating the acute angles:-  [please refer to attached figure]

Let 15 be the perpendicular, 8 be the base and 17 is the hypotenuse,

sinC = 15/17 (sine of an angle is ratio of perpendicular to hypotenuse)

∠ C = sin⁻¹(15/17)

∠ C = 61.92°

∠ A = 90°-61.92°

∠ A = 28.08°

Hence, the given set of the sides of a triangle follows the Pythagorean Triple and the acute angles are 61.92° and  28.08°.

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The effect of increasing the distance e between charged object is that , the electric force decreases because the distance has an indirect relationship to the force.

Coulomb's law states that the force between two charged bodies is directly proportional to the product of the charge and inversely proportional to the square of the distance between them.

Coulomb's law can therefore be expressed mathematical as;

F = Q1Q2/r²

where r is the distance between charge Q1 and Q2

This means that since the force is inversely proportional to the square of distance, force will decrease as distance is increasing.

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Answer:

Subtract fractions: 7/15 - 4/9 = ? Subtraction of ordinary (simple, common) fractions, result explained

The executed operation (with ordinary fractions):

7/15 - 4/9

Step-by-step explanation:

Answer:

To calculate the periodic interest rate for an account billed monthly with an APR of 21.99%, we need to divide the APR by the number of billing periods in a year.

Since there are 12 months in a year for a monthly billing cycle, we can divide 21.99% by 12 to get the monthly periodic interest rate.

Periodic Interest Rate = APR / Number of Billing Periods in a Year

Periodic Interest Rate = 21.99% / 12

Periodic Interest Rate = 1.8325%

Rounding this answer to the nearest hundredth, we get a periodic interest rate of 1.83%.

Answer:

b) H0:μ=90, H1:μ≠90

Step-by-step explanation:

The corporation wants to know if the mean number of days is different from the 90 days claimed.

This means that at the null hypothesis, we test if the mean number is the claimed value of 90, and so:

\(H_0: \mu = 90\)

The corporations wants to know if the mean number is different, and thus, at the alternate hypothesis, we test if the mean number is different from 90, that is:

\(H_1: \mu \neq 90\)

This means that the correct answer is given by option b.

The total number of stamps used is z, then we have:

38x + 7z = 198

Let's solve this problem using a system of equations. Let's assume Scott used x 45-cent stamps and y 7-cent stamps.

The value of x 45-cent stamps is 45x cents.

The value of y 7-cent stamps is 7y cents.

According to the problem, Scott used a total of $1.98 in postage, which is equal to 198 cents.

So we can set up the following equation based on the value of the stamps used:

45x + 7y = 198 ...(Equation 1)

We also know that Scott used a total of x + y stamps.

We can set up another equation based on the total number of stamps used:

x + y = Total Number of Stamps ...(Equation 2)

We need to solve this system of equations to find the values of x and y.

From Equation 2, we can rewrite it as:

y = Total Number of Stamps - x

Substituting this into Equation 1:

45x + 7(Total Number of Stamps - x) = 198

45x + 7Total Number of Stamps - 7x = 198

38x + 7Total Number of Stamps = 198

Let's assume the total number of stamps used is z, then we have:

38x + 7z = 198 ...(Equation 3)

Now, we need more information to solve the system of equations. We need to know the total number of stamps used or the values of x and y.

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The equation of the line containing the paints A and B is y = -1/3x + 4

from the question, we have the following parameters that can be used in our computation:

The graph

Where, we have

(6, 2) and (0, 4)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 4

Using the other points, we have

6m + 4 = 2

So, we have

6m = -2

Evaluate

m = -1/3

So, we have

y = -1/3x + 4

As an equation, we have

y = -1/3x + 4

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