The table below gives data from a linear function. Find a formula for the function.
Price per shirt, p($) 15 20 25
Number of shirts sold, q = f(p) 1000 750 500
a. f( p) = 1750p − 50 b. f( p) = 1000 − 50p c. f( p) = 1000 + 50 p
d. f( p) = 1750 + 50 p e. f( p) = 1750 − 50p

Expressing the expansion of the logarithm in terms of log y, we can write: log(8x^2) = log(8) + 2*log(y), where y = x

Using the logarithmic identity that states log(a^b) = b*log(a), we can expand log(8x^2) as:

log(8x^2) = log(8) + log(x^2)

Note that a  logarithmic identity is a mathematical relationship or equation that involves logarithms.

We can further simplify log(x^2) as:

log(x^2) = 2*log(x)

Therefore, we can write:

log(8x^2) = log(8) + 2*log(x)

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In order to properly solve a system of linear equations utilizing matrices, you must abide by the below instructions:

First, create a matrix representation of the system of equations.  

Second, generate an augmented matrix by merging the coefficient matrix together with the constant matrix.

Third, apply elementary row operations in order to transform the augmented matrix into either row echelon or reduced row echelon form.

Fourth, use back substitution to accurately determine the variable values.

Ultimately, enter this solution into the original equation in order to obtain the primary variable value.

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Solving linear equations using matrices involves steps ranging from creating an augmented matrix, performing row operations, back substitution, and then interpreting results

To solve a system of linear equations using matrices, follow these step-by-step instructions:

Step 1: Write the system of linear equations in matrix form.
Represent the coefficients of the variables as a matrix (called the coefficient matrix), and the constants on the right side of the equations as another matrix (called the constant matrix).

Step 2: Create the augmented matrix.
Combine the coefficient matrix and the constant matrix into a single matrix by appending the constant matrix as an additional column. This combined matrix is called the augmented matrix.

Step 3: Perform row operations to achieve row-echelon form.
Use row operations (swapping rows, multiplying a row by a constant, or adding/subtracting rows) to manipulate the augmented matrix into row-echelon form. Row-echelon form has zeroes below the diagonal and non-zero elements on the diagonal.

Step 4: Perform back-substitution.
Starting from the last row of the row-echelon form matrix, solve for the variables using back-substitution. Substitute the values of the variables you find into the previous rows to determine the remaining variable values.

Step 5: Interpret the results.
Once you have solved all the variables, you have found the solution to the system of linear equations. If there are infinitely many solutions or no solutions, this will be indicated by the row-echelon form.

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In light of this, the 95% confidence interval for is (100.67, 111.33) as s is the sample standard deviation, n is the sample size.

A collection of information's values' standard deviation serves as a gauge for how much variance or dispersion there is. It is a statistical word used to describe the degree to which the individual data points depart as from mean or average value that is contained in the data set. By taking taking square root of the variance—the sum of the squared deviations amongst each point in the data and the mean—we can determine the standard deviation. While a high standard deviation suggests that the data points are widely dispersed, a modest standard deviation suggests that the statistics are close to the mean.

given

(a) When the sample size, n, is 16, we can apply the following formula to create a 95% confidence interval regarding the population mean, :

x ± tα/2 * (s/√n)

where t/2 is the crucial value from the t-distribution with n-1 degrees of freedom and a confidence level of 95%, and x is the sample mean, s is the sample standard deviation, n is the sample size.

We determine that t0.025,15 = 2.131 using a t-distribution table or calculator.

When we enter the values, we obtain:

106 ± 2.131 * (10/√16)

which is equivalent to:

106 ± 5.33

In light of this, the 95% confidence interval for is (100.67, 111.33) as s is the sample standard deviation, n is the sample size.

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The length of the Green Route in miles is 64 miles.

Miles is a unit of linear measurement. It is traditionally defined as 5,280 feet, or 1,760 yards, and is equivalent to 1.609 kilometers. Miles are commonly used to measure long distances, such as the distance between two cities. They are also used to measure the lengths of roads and other paths. Miles are one of the most commonly used units of measurement in the United States.

The length of the Green Route in miles can be calculated by subtracting the total mileage traveled on the Blue Route from the total mileage traveled on both routes.

Total miles traveled on Monday = 38 miles
Total miles traveled on Tuesday = 80 miles

Total miles traveled on the Blue Route = 5 + 11 = 16 miles

Therefore, the total miles traveled on the Green Route = 80 - 16 = 64 miles

Therefore, the length of the Green Route in miles is 64 miles.

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The area of the triangle is 128 square inches.

To find the area of a triangle, you can use the formula:

Area = (1/2) * base * height

In this case, the base of the triangle is 32 inches and the height is 8 inches.

Plugging these values into the formula, we get:

Area = (1/2) * 32 * 8

Area = 16 * 8

Area = 128 in²

So, the area of the triangle is 128 square inches.

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A triangle is shown in the image. A triangle with a height of 8 inches. The height is perpendicular to the base labeled 32 inches. The side from the top of the perpendicular side to the base is labeled 28 inches. What is the area of the triangle? 256 in2 224 in2 128 in2 112 in2

The price that the insurance company should charge for a one-year extended warranty on a Prego SUV is $402.

To determine the price that the insurance company should charge for a one-year extended warranty on a Prego SUV, the company needs to calculate the expected value of the repair costs and then add their desired profit to it.

Let's assume that the price for the warranty is x dollars. Then, the expected value of the repair costs for the insurance company would be:

(0.50)(0) + (0.35)($500) + (0.12)($1500) + (0.03)($4000) = $352

This means that on average, the insurance company can expect to pay out $352 in repair costs for each policy sold. To make an average profit of $50 per policy, the insurance company should charge:

x = $352 + $50 = $402

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Answer:

30 and 10

Step-by-step explanation:

Main concepts:

Concept 1.  Geometric Sequence

Concept 2. Common ratio

Concept 3. Finding the next terms

Concept 1.  Geometric Sequence

Geometric sequences are a specific type of sequence with a pattern where a specific number is multiplied to each term to get the next term.

For instance, a completely different geometric sequence 1,2,4,8,16,... is geometric because you multiply any term by 2 to get the next term.

Concept 2. Common ratio

In a geometric sequence, this number that you can multiply by to get the next term (in the "1,2,4,8,16,..." example, the number 2) is called the common ratio because taking the ratio of two sequential terms of the sequence (dividing two terms in a row) always gives the same answer:

This process of finding ratios will yield a common ratio only if the sequence is a Geometric Sequence.

Concept 3. Finding the next terms

Since we're told that the sequence we're given in the question is a Geometric sequence, it must have a common ratio (otherwise, it wouldn't be a geometric sequence).

Find the common ratio by dividing sequential terms:

270/810 = 1/3

90/270 = 1/3

So, for the sequence in the question, the common ratio is 1/3.  Each term is multiplied by 1/3 to get the next term in the sequence.  (This is equivalent to dividing each term by 3 to get the next term in the sequence, if you prefer division and/or to avoid fractions)

So, to get the next two terms in the sequence, multiply by the common ratio:

90 * 1/3 = 30

30 * 1/3 = 10

So, the next two terms of the sequence are 30 and 10

the probability that the marble is not green is 0.9 or 90%. This means that if we were to randomly select a marble from the box, there is a 90% chance that it will not be green.

How to solve probability?

To calculate the probability that a marble is not green, we need to first determine the total number of marbles in the box, which is given by:

Total number of marbles = 8 + 6 + 2 + 4 = 20

Next, we need to determine the number of marbles that are not green. Since there are 2 green marbles, the number of marbles that are not green is given by:

Number of marbles that are not green = 20 - 2 = 18

Finally, we can calculate the probability of selecting a marble that is not green by dividing the number of marbles that are not green by the total number of marbles in the box, as follows:

Probability of selecting a marble that is not green = Number of marbles that are not green / Total number of marbles

= 18 / 20

= 0.9 or 90%

Therefore, the probability that the marble is not green is 0.9 or 90%. This means that if we were to randomly select a marble from the box, there is a 90% chance that it will not be green.

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The first term a₁ of the geometric series is equal to 121.5

For a geometric series when the common ratio |r| > 1, then we use the formula for the sum of nth term:

Sₙ = a(rⁿ - 1)/(r - 1)...(1)

The nth term aₙ = arⁿ⁻¹

Thus for Sₙ = 4860 and aₙ = 3280.5, the value of a₁ can be derived as follows:

aₙ = arⁿ⁻¹

aₙ = arⁿ/r = 3280.5

rⁿ = a(r × 3280.5)/a

rⁿ = 9841.5/a

putting 9841.5/a for rⁿ in equation (1) we have;

Sₙ = a[(9841.5/a) - 1]/(r - 1)

Sₙ = (9841.5 - a)/(r - 1)

recall Sₙ = 4860 and r = 3 so;

(9841.5 - a)/2 = 4860

a = 9841.5 - 2(4860)

a = 121.5

Therefore, the first term a₁ of the geometric series is equal to 121.5

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Answer:6.25%

Step-by-step explanation:

Six types of costs are:

For assets attained in exchange for a deferred payment contract, the asset should be documented at its fair worth, which is the prevailing market rate. If establishing the fair value of the asset proves to be impracticable, the asset should be recorded based on the current value of upcoming payments due under the deferred payment agreement, stated using an apposite interest rate.

Generally, assets acquired in exchange of other non-monetary commodities should be appraised at their fair worth. If the truthful appraisal of the exchanged assets is uncertain, the assets should be noted down according to the seized amount of the items provided, including any received or paid cash during the transaction.

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Answer:

it is the opposite way around

Step-by-step explanation:

Answer:

The answer is **D. 30x+15y**.

```

5(6x + 3y) = 5*6x + 5*3y = 30x + 15y

```

Step-by-step explanation:

1. Distribute the 5:

```

5(6x + 3y) = (5 * 6x) + (5 * 3y)

```

2. Simplify:

```

5(6x + 3y) = 30x + 15y

```

Therefore, 5(6x + 3y) is equivalent to 30x + 15y.

The total amount in the acount in 5 years is approximately $13,321.76.

The formula accrued amount in a compounded interest is expressed as;

[tex]A = P( 1 + \frac{r}{n} )^{n*t}[/tex]

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given that:

First, convert R as a percent to r as a decimal

r = R/100

r = 5.75/100

r = 0.0575

Plug the given values into the above formula and solve for A.

[tex]A = P( 1 + \frac{r}{n} )^{n*t}\\\\A = 10000( 1 + \frac{0.0575}{12} )^{(12*5)}\\[/tex]

A = $13,321.76

Therefore, the accrued amount is $13,321.76.

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The calculated area of the triangle B is 1.8 square units

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

Triangle A and B

Where

Area of A = 1/2 base * height

Sp, we have

Area of A = 1/2 * 2 * 5

Next, we have

Area of B = Area of A * Scale factor^2

Using the above as a guide, we have the following:

Area of B = 1/2 * 2 * 5 * (3/5)^2

Evaluate

Area of B = 1.8

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The value of tan A is 0. 667. Option B

To determine the value of the identity, we need to take note of the different trigonometric identities.

these identities are;

We also have that the ratio for the tangent identity is expressed as;

tan θ= opposite/adjacent

From the information given, we have that;

The hypotenuse is 18.03, the side opposite to angle A is 10, and the side adjacent to angle A is 15

Then, for the identity, we have;

tan A = 10/15

Divide the values

tan A = 0. 667

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Answer: 34,650 permutations

a) If two similar solids have a scale factor of 2 : 5, the ratio of their volumes is 8:125, expressed in the lowest terms.

b) If cone with volume 2625 m³ is dilated by a scale factor of 15, the volume of the resulting cone is 10,640,625 m³.

(a) When two solids are similar, their corresponding linear dimensions are in the same ratio, which is known as the scale factor. For example, if two similar solids have a scale factor of 2:5, it means that the corresponding sides of the two solids are in the ratio 2:5.

The volume of a solid is proportional to the cube of its linear dimensions. Therefore, if the linear dimensions of two similar solids are in the ratio 2:5, the ratio of their volumes would be:

(2/5)³ = 8/125

(b) The volume of a cone is given by the formula:

V = (1/3)πr²h

where V is the volume, r is the radius, and h is the height of the cone.

When a cone is dilated by a scale factor of k, its linear dimensions increase by a factor of k, and its volume increases by a factor of k³. Therefore, if the volume of a cone is V and it is dilated by a scale factor of k, the volume of the resulting cone would be:

V' = k³V

In this case, the volume of the original cone is given as 2625 m³, and it is dilated by a scale factor of 15. Substituting these values in the formula, we get:

V' = 15³(2625)

V' = 15³(2625/1)

V' = 10640625

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Ari will need 3.6 pound of seed.

We are Given that total number of pounds of grass seed needed

9

Let number of pounds of Bermuda seeds is x

Let number of pounds of Fescue seeds is y

Then sum of both gives equation:

x+y=9

y=9-x...(i)

Given that cost of 1 pound of Bermuda seed = $4.80

Then cost of x pound of Bermuda seed = $4.80x

The cost of 1 pound of Fescue seed = $3.50

Then cost of y pound of Fescue seed = $3.50y

The total cost will be 4.80x + 3.50y

Now combining all three parts, we get equation:

4.80x+3.50y=4.02 x 9

4.80x+3.50y=36.18...(ii)

4.80x+3.50y=36.18

4.80x+3.50(9-x)=36.18

4.80x+31.5-3.50x=36.18

4.80x-3.50x=36.18-31.5

1.3x=4.68

x=3.6

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The value of the function g(f(-4)) = 536. Option D

From the information given, we have that the functions are;

f(x)= 4x+5

g(x) = 4x^2 -5x - 3

To determine the composite function,  g(f(-4)), we need to first determine the value of the function f(x) at -4

Now, substitute the value, we have;

f(-4) = 4(-4) + 5

expand the bracket, we get;

f(-4) = - 16 + 5

Add the values

f(-4) = -11

Now, substitute the value in the function g(x), we have that;

g(f(-4)) = 4(-11)² - 5(-11) - 3

find the square and expand the bracket

g(f(-4)) =484 + 55 - 3

Subtract the values, we have;

g(f(-4)) = 536

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Julieta's claim about the quadrilateral is false.

The statement is given as:

It is impossible to draw a quadrilateral that is not a trapezoid and not a parallelogram.

The condition for a shape to be a quadrilateral is that the shape must have four sides.

An irregular shape that has four sides is a quadrilateral, but neither a quadrilateral nor a parallelogram

Therefore, Julieta's claim is false

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The number of ways to pick 3 astronauts from 10 candidates can be found using the combination formula, which is:

nCk = n! / (k!(n-k)!)

where n is the total number of candidates, k is the number of candidates to be chosen, and "!" denotes the factorial function.

In this case, we want to choose 3 astronauts from a pool of 10 candidates, so we can plug these values into the formula:

10C3 = 10! / (3!(10-3)!)

= (10 x 9 x 8) / (3 x 2 x 1)

= 120

Therefore, there are 120 ways to pick 3 astronauts to go to the moon out of 10 candidates.

Answer:

120 or 220

Step-by-step explanation:

The solutions to the equation 100+ (n - 2)² = 149 are n = 9 and n = -5

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

The equation 100+ (n - 2)² = 149

Express as

100+ (n - 2)² = 149

Subtract 100 from both sides of the equation

So, we have the following representation

(n - 2)² = 49

Take the square root of both sides

n - 2 = 7 and n - 2 = -7

Add 2 to both sides

n = 9 and n = -5

Hence, the solutions to the equation 100+ (n - 2)² = 149 are n = 9 and n = -5

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Answer:

24

Step-by-step explanation:

10^2+x^2=26^2

x^2=26^2-10^2

x^2=576

x=[tex]\sqrt{576}[/tex]=24

The number of feet of fencing that will be needed ​is illustrated below

The feet of fencing that will be needed ​is the perimeter of the fence

To find the perimeter of a composite figure, we need to add up the lengths of all the sides of the figure.

In this case, we add the side lengths of the rectangle to the side lengths of the right triangle and subtracting the common lengths between both shapes

Take for instance, we have

So, we have

Fencing = 2 * (4 + 5) + 3 + 4 + 5 - 2 * 4

Fencing = 22 units

So, the amount of fencing for the assumed dimensions is 22 units

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The area of the tabletop made by the students in the furniture - making class would be 26 ft ²

We can see that this tabletop made by students in the furniture - making class takes the form of a composite shape with two smaller rectangles and one large rectangle.

The area of the large rectangle is:

= 4 ft x ( 1 + 3 + 1 )

= 4 ft x 5 ft

= 20 ft ²

The area of the two smaller rectangles is:

= 2 x ( 3 ft x 1 ft )

= 2 x 3

= 6 ft ²

The total area of the tabletop is:

= 20 + 6

= 26 ft ²

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The range of the monthly rainfall data for the cities is approximately 7 centimeters.

To find the range of the data from the given box plot, we need to determine the highest and lowest values of the dataset. Looking at the box plot, we can see that the "H" represents the high outlier and the "□" represents the low outlier. The vertical line at the bottom of the box represents the minimum value and the vertical line at the top of the box represents the maximum value of the dataset within the interquartile range.

Using the scale on the x-axis, we can estimate the minimum value to be around 0.5 centimeters and the maximum value to be around 7.5 centimeters. The high outlier is located at around 8 centimeters and the low outlier is located at around 0 centimeters.

Therefore, the range of the data is the difference between the highest and lowest values, which is:

range = maximum value - minimum value = 7.5 - 0.5 = 7 centimeters

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a) The  piecewise function is 80p, if p > 100 b) For p > 100, the graph will be a straight line passing through the point (100, 100 × 80) with a slope of 8

a) We can define a piecewise function f(p) to represent the cost of catering service depending on the number of persons (pax).

f(p) =

120p, if p ≤ 30

105p, if 31 ≤ p ≤ 60

95p, if 61 ≤ p ≤ 100

80p, if p > 100

b) To graph the piecewise function, we can plot the points for each of the four parts of the function, and connect them with line segments. The graph will have four segments, each with a different slope.

For p ≤ 30, the graph will be a straight line passing through the origin with a slope of 120.

For 31 ≤ p ≤ 60, the graph will be a straight line passing through the point (31, 31 × 105) with a slope of 105.

For 61 ≤ p ≤ 100, the graph will be a straight line passing through the point (61, 61 × 95) with a slope of 95.

For p > 100, the graph will be a straight line passing through the point (100, 100 × 80) with a slope of 80.

c) To find how many persons they invite to their wedding, we can use the inverse function of f(p) and plug in the given cost of RM9025.

Let C = RM9025, then

120p, if p ≤ 30

105p, if 31 ≤ p ≤ 60

95p, if 61 ≤ p ≤ 100

80p, if p > 100

Case 1: p ≤ 30

120p = C

p = C/120 = 9025/120 = 75.2083

Since p must be an integer, we round up to the nearest integer. Therefore, if they invite 76 persons, the cost of catering service will be more than RM9025.

Case 2: 31 ≤ p ≤ 60

Let x = p - 30, then

105x + 120 × 30 = C

105x = C - 3600

x = (C - 3600)/105 = (9025 - 3600)/105 = 54.5238

Therefore, if they invite 31 + 54 = 85 persons, the cost of catering service will be RM9025.

Case 3: 61 ≤ p ≤ 100

Let x = p - 60, then

95x + 120 × 30 + 105 × 30 = C

95x = C - 9750

x = (C - 9750)/95 = (9025 - 9750)/95 = 0.7632

Therefore, if they invite 60 + 0.7632 × 100 = 137 persons, the cost of catering service will be RM9025.

Case 4: p > 100

Let x = p - 100, then

80x + 120 × 30 + 105 × 30 + 95 × 40 = C

80x = C - 17700

x = (C - 17700)/80 = (9025 - 17700)/80 = -109.375

Since p must be a positive integer, this case is not possible.

Therefore, Mohammed and Mira should invite 85 persons to their wedding to pay RM9025 for the catering service.

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