What does the initial point, or y-intercept, represent for Smokey Joe's?
Describe the rate of change for "Smokey Joe's" catering and what it represents in the context of the situation.
Would this relationship best be described as proportional or non-proportional? Justify your answer.
If Smokey Joe's charges a $25.00 delivery fee, how will this impact the pricing?

Answer: 56 inches

Step-by-step explanation:

To find the length of each side, use Pythagorean's Theorem, a² + b² = c²

Note the bottom sides are the same length and the top two are the same length.

Bottom sides:

5² + 12² = c²

25 + 144 = c²

169 = c²

13 = c

Top sides:

9² + 12² = c²

81 + 144 = c²

225 = c²

15 = c

Add it all together

13 + 13 + 15 + 15 = 56

The perimeter is 56 inches.

Hope this helps!

To further analyze the function f(x)=1.3x^(4)-5.7x^(2)+3.71 on the interval [-4,4,-8,14], we can find the critical points, relative extrema, and inflection points of the function.

First, let's find the critical points by taking the derivative of the function and setting it equal to zero:
f'(x)=5.2x^(3)-11.4x
0=5.2x^(3)-11.4x
0=x(5.2x^(2)-11.4)
x=0, x=±√(11.4/5.2)
So the critical points are x=0, x=±1.4656

Next, let's find the relative extrema by using the second derivative test:
f''(x)=15.6x^(2)-11.4
f''(0)=-11.4<0, so x=0 is a relative maximum
f''(1.4656)=11.4>0, so x=1.4656 is a relative minimum
f''(-1.4656)=11.4>0, so x=-1.4656 is a relative minimum

Finally, let's find the inflection points by setting the second derivative equal to zero:
0=15.6x^(2)-11.4
x=±√(11.4/15.6)
x=±0.8544

So the inflection points are x=±0.8544

Overall, the function f(x)=1.3x^(4)-5.7x^(2)+3.71 has a relative maximum at x=0, relative minimums at x=±1.4656, and inflection points at x=±0.8544 on the interval [-4,4,-8,14].

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13 inches of wire will cost 52 cents at the same rate as 18 inches of wire costs 72 cents.

To solve this word problem on proportions using a unit rate, we need to first find the unit rate for the cost of the wire. The unit rate is the cost per one inch of wire.

We can find this by dividing the cost by the number of inches:

Unit rate = 72 cents / 18 inches = 4 cents per inch

Now that we have the unit rate, we can use it to find the cost of 13 inches of wire.

We simply multiply the unit rate by the number of inches:

Cost = 4 cents per inch × 13 inches = 52 cents

Therefore, 13 inches of wire will cost 52 cents at the same rate as 18 inches of wire costs 72 cents.

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Answer:

Day 24 will be the day she'll reach $300

Step-by-step explanation:

Answer20th

Step-by-step explanation:

Answer:

103,92,81,70,59,48,37,36,15,4

Step-by-step explanation:

every number has difference of 11

the answer to the question Simplify. Express your answer z^(4)*z*z" is z^(6).

To simplify the expression z^(4)*z*z, we need to use the rules of exponents. Specifically, we need to use the rule that states that when we multiply expressions with the same base, we can add the exponents. In other words, a^(b)*a^(c) = a^(b+c).

Using this rule, we can simplify the given expression as follows:

z^(4)*z*z = z^(4+1+1) = z^(6)

So, the simplified expression is z^(6).

In conclusion, the answer to the question "Simplify. Express your answer z^(4)*z*z" is z^(6).

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Jada has earned a total of 400 points so far.

    141 + 87 + 81 + 91 = 400

There are a total of 450 points possible so far.

    150 + 100 + 100 + 100 = 450

Jada has 400/450 or about 88.89% of the possible points, so no, she does not have 90%.

Adding in a 100-point test, the total number of points would become 550 and 90% of 550 is 495 points.

    0.90 x 550 = 495

To finish the class with an A, Jada needs to have 495 points.  She currently has 400 points.  This means she needs a 95 on the final to finish the class with an A.

Given the box and whiskers plot with the given data, the five number summary would be :

Arrange the numbers in order from smallest to largest:

2, 2, 3, 4, 5, 5, 8, 8, 10, 10, 11, 13, 15, 15, 15

The minimum number is therefore 2.

First Quartile Q1 = 4 :

= ( 15 + 1 ) / 4

= 4 th position

Median :

= ( 15 + 1 ) / 2

= 8 th position which is 8

Third quartile :

= ( 15 + 1 ) x 3 / 4

= 12 th position which is 13.

Maximum value is 15.

Move the box plot to correspond with these figures.

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Answer:

Step-by-step explanation:

the answer is eitehr b or a

x1 = 0.75, x2 = 5, x3 = 0, x4 = 12

To transform the augmented coefficient matrix to echelon form using elementary row operations:

1. Subtract twice the first row from the second row.

2. Subtract the first row from the third row.

3. Subtract the first row from the fourth row.

4. Subtract the third row from the fourth row.

The resulting augmented coefficient matrix in echelon form is:

4x1 - 2x2 - 3x3 + x4 = 3

0x1 - 4x2 - 8x3 = -16

0x1 + x2 + 2x3 + x4 = 17

0x1 + 0x2 + x3 + x4 = 12

To solve the system by back substitution:

1. x4 = 12 (from the last equation)

2. x3 = 12 - x4 = 0 (substitute x4 from step 1 into the third equation)

3. x2 = (17 - x4) / (1) = 5 (substitute x4 from step 1 into the second equation)

4. x1 = (3 - 2*5 - 3*0) / (4) = 0.75 (substitute x2 and x3 from steps 2 and 3 into the first equation)

The solution is x1 = 0.75, x2 = 5, x3 = 0, x4 = 12.

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Answer: 12 [tex]m^{3}[/tex]

Step-by-step explanation:

Volume = length x width x height

Volume = 4 m x 1.5 m x 2 m

Volume = 12 cubic meters

Answer: 4

Step-by-step explanation:

We can start by simplifying each term step by step:

First, the cube root of 1 is 1, so -3 times the cube root of 1 is simply -3.

Second, the square root of 49 is 7, so 49 divided by the square root of 49 is also 7.

Putting it all together, we have:

-3 × ∛1 + 49 ÷ √49 = -3 + 7 = 4

Therefore, the value of the expression is 4.

The solutions for θ in the interval [0, 2π) where cos(θ) = -√3/2 are θ = 2π/3 and θ = 4π/3.

The graph of f(θ) is shifted and stretched when compared to the graph of f(2θ).

What is Trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles, and the trigonometric functions that describe those relationships.

Part A:

To find when the pogo stick's spring will be equal to its non-compressed length, we need to solve for when f(θ) = 0.

f(θ) = 2cos(θ) + √3 = 0

2cos(θ) = -√3

cos(θ) = -√3/2

The solutions for θ in the interval [0, 2π) where cos(θ) = -√3/2 are θ = 2π/3 and θ = 4π/3.

Part B:

If we double the angle, θ becomes 2θ, and the function becomes:

f(2θ) = 2cos(2θ) + √3

Using the double angle formula for cosine, we can rewrite this as:

f(2θ) = 2(2cos²(θ) - 1) + √3

f(2θ) = 4cos²(θ) - 2 + √3

Substituting cos(θ) = -√3/2, we get:

f(2θ) = 4(-3/4) - 2 + √3

f(2θ) = -3 + √3

So the solutions for 2θ in the interval [0, 2π) where f(2θ) = 0 are:

2θ = π/6 and 2θ = 11π/6

Dividing by 2, we get the solutions for θ:

θ = π/12 and θ = 11π/12

These solutions are different from the solutions in Part A, and the graph of f(θ) is shifted and stretched when compared to the graph of f(2θ).

Part C:

To find when the lengths of the springs are equal, we need to solve the equation f(θ) = g(θ).

2cos(θ) + √3 = 1 - sin²(θ) + √3

2cos(θ) = 1 - sin²(θ)

Using the identity sin²(θ) + cos²(θ) = 1, we can rewrite this as:

2cos(θ) = cos²(θ)

cos(θ)(cos(θ) - 2) = 0

The solutions for θ in the interval [0, 2π) where the lengths of the springs are equal are:

θ = 0, θ = π/3, θ = 2π/3, θ = π, θ = 4π/3, θ = 5π/3

We can check that f(θ) = g(θ) at each of these values.

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The following values represent the rollercoaster graph scenario most accurately:

is, Red (x) = 6+4 × cos(πx/6) if 0 ≤ x < 6

Green (x) = -2.5 × cos (π(x - 6)/4) + 4.5

Purple (x) = 3.5 - 3.5 × sin (π(x - 12.5)/5)

For Red (x) = 6 + 4 × cos(πx/6) if 0 ≤ x < 6

The graph is simply a structured representation of the data. It facilitates our understanding of the facts. The numerical information gathered through observation is referred to as data.

The Latin word Datum, which meaning "something provided," is where the word data first appeared.

In the question, where at x = 0, Red(x) = 10,

at x = 5, Red(x) = 2.5

For Green (x) = -2.5 × cos (π(x - 6)/4) + 4.5       if    6 ≤ x < 10

Given, where at x = 10, Green (x) = 7,

So, at x = 6, Green (x) = 2.0

For Purple (x) = 3.5 - 3.5 × sin (π(x - 12.5)/5) if 10 ≤ x ≤ 15

Given, where at x = 10, Purple (x) = 7,

at x = 15, Purple (x) = 0

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The complete question is:

The above rollercoaster graph needs a function to go with it. Select the correct functions that begins at (0,12) and ends at (12,0) with a local minimum at (5,1) and a local maximum at (9,6). You need to select one function for the red piece, one function for the green piece, and one function for the purple piece.

Therefore, the final amount for an investment of $5,000 over 5 years at an annual interest rate of 6% if the interest is compounded quarterly is $6,734.27.

SI unit is defined as (P, R, and T) / 100.

SI stands for Straightforward Interest in this instance. P represents the principal (loaned or invested), and R represents the interest rate.

To solve this problem, we need to use the formula for compound interest:

A = P (1 + r/n)^(nt)

Where:

A = the final amount

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time (in years)

Here, we have:

P = $5,000

r = 6% = 0.06 (annual interest rate)

n = 4 (compounded quarterly)

t = 5 years

Plugging these values into the formula, we get:

A = 5000 (1 + 0.06/4)^(4*5)

A = 5000 (1.015)^20

A = 5000 (1.349858807)

A = $6,734.27 (rounded to the nearest cent)

Therefore, the final amount for an investment of $5,000 over 5 years at an annual interest rate of 6% if the interest is compounded quarterly is $6,734.27.

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The fourth term in the geometric sequence is -81.

What is a geometric sequence?

In mathematics, a geometric progression, also known as a geometric sequence, is a set of non-zero numbers where each term after the first is derived by multiplying the previous one by a fixed, non-zero amount called the common ratio.

We are given a sequence as 3, –9, 27, ...

We can observe that each term is being multiplied by -3.

So, the common ratio i.e. r = -3

Here x = 4 and a₁ = 3.

Now, using aₓ = a₁ r⁽ˣ⁻¹⁾ , we get

⇒a₄ = a₁ r⁽⁴⁻¹⁾

⇒a₄ = a₁ r³

⇒a₄ = 3 (-3)³

⇒a₄ = 3 * -27

⇒a₄ = -81

Hence, the fourth term in the geometric sequence is -81.

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The system of inequalities that describes the graph is given as follows:

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

For the lower bound of the inequality, we have that:

Hence:

y ≥ -4/3x + 8

4x/3 + y ≥ 8

4x + 3y ≥ 24.

For the upper bound of the inequality, we have that:

Hence:

y ≤ -5x/8 + 5

5x/8 + y ≤ 5

5x + 8y ≤ 40.

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The average amount spent per person on healthcare in 2019 in the United States of America is $1.09×10⁴.

The average can be defined as the sum of all numbers divided by the total number of values. The mean can be defined as the mean of the values ​​of a sample of data. That is, the average is also called the arithmetic mean.

Solution according to the information given in the question:

Given, Population of USA = 328.2 million = 3282 × 10⁵

           Total Healthcare costs = $3.6 trillion = 3.6 × 10¹²

∴ Average amount spent = Total Healthcare costs/Population of USA

                                          = (3.6 × 10¹²)/(3282 × 10⁵)

                                          = (36 × 10¹¹)/ (3282 × 10⁵)

                                          = (36/3282) × (10¹¹/10⁵)

                                          = 0.0109 × 10⁶

                                          = $1.09 × 10⁴

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The average amount spent per person on healthcare in the United States in 2019 was $10,918.98.

What is average in mathematics?

Average in mathematics is a measure of the central or typical value in a set of numbers. It is computed by adding all the values together and dividing the total by the number of values in the set. In statistics, the average is the most commonly used measure of central tendency.

The average amount spent per person on healthcare in the United States in 2019 was $10,918.98. This figure is calculated by taking the total healthcare costs of $3.6 trillion and dividing it by the population of 328.2 million people. This figure represents the amount of money each person in the country spent on healthcare in 2019, ranging from medical services and prescriptions to insurance premiums and other costs. It is important to note that this figure does not take into account any out-of-pocket expenses that individuals may have incurred during the year.

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The solution for c in the equation is 35/3

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

\(c = 5\frac{5}{6} \times 2 \)

Express the equation properly

So, we have the following representation

c = 5 5/6 * 2

Convert the fraction to improper​ fraction

So, we have the following representation

c = 35/6 * 2

Evaluate the products

c = 35/3

Hence, the solution is 35/3

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the height of the cylinder is 12/π inches. This is an exact value, but if you want an approximate decimal value, you can use a calculator and substitute 3.14 or 22/7 for π. For example, if we use π ≈ 3.14, we get:

h ≈ 12/3.14

h ≈ 3.822 inches (rounded to three decimal places)

The answer of the question based on the probability  that The spinner shows has 4 equal sized sections. Jackson spins the spinner 32 times the answer is 8 times.

A event is any outcome or the set of outcomes of experiment or random process.

An event can be as like as a single outcome or as complex as a combination of the outcomes. For example, flipping a coin and getting heads is an event, as is rolling a die and getting a 6.

The spinner has 4 equal sized sections, then each section has a probability of 1/4 or 25% of being landed on when the spinner is spun.

If Jackson spins the spinner 32 times, we can find the expected number of times each section will be landed on by multiplying the probability of landing on each section by the total number of spins:

Expected number of times to land on each section = (Probability of landing on section) x (Total number of spins)

Expected number of times to land on each section = (1/4) x (32)

Expected number of times to land on each section = 8

Therefore, we can expect each section to be landed on approximately 8 times out of the 32 spins.

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The equation of the line through the point (3, -7) that is parallel to the line 4x + 7y - 10 = 0 is y = (-4/7)x - (37/7) in the point-slope form

To find the equation of the line through the point (3, -7) that is parallel to the line 4x + 7y - 10 = 0, we first need to find the slope of the given line. We can do this by rearranging the equation to the slope-intercept form, y = mx + b, where m is the slope.

4x + 7y - 10 = 0

7y = -4x + 10

y = (-4/7)x + (10/7)

The slope of the given line is -4/7. Since we want a line that is parallel to this one, the slope of our new line will also be -4/7.

Now we can use the point-slope form of a line, y - y1 = m(x - x1), to write the equation of the new line. We plug in the given point (3, -7) for (x1, y1) and the slope -4/7 for m.

y - (-7) = (-4/7)(x - 3)

y + 7 = (-4/7)x + (12/7)

y = (-4/7)x + (12/7) - 7

y = (-4/7)x - (37/7)

So the equation of the line through the point (3, -7) that is parallel to the line 4x + 7y - 10 = 0 is y = (-4/7)x - (37/7) in the point-slope form.

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There are 360 permutations of 4 item programs for a teacher's program.

A permutation is an arrangement of items in a specific order. To find the number of permutations of 4 items from a set of 6 items, we can use the formula:

nPr = n! / (n-r)!

Where n is the total number of items, r is the number of items we want to choose, and n! is the factorial of n (n * (n-1) * (n-2) * ... * 1).

Plugging in the given values, we get:

6P4 = 6! / (6-4)!

= 6! / 2!

= (6 * 5 * 4 * 3 * 2 * 1) / (2 * 1)

= 720 / 2

= 360

Therefore, there are 360 permutations of 4 item programs for a teacher's program.

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Answer: The system of equations is:

3x + y = 18

3x + y = 16

To determine how many solutions this system has, we can subtract the second equation from the first:

(3x + y) - (3x + y) = 18 - 16

0 = 2

This is a contradiction, since 0 can never be equal to 2. Therefore, there are no solutions to this system of equations. Geometrically, these two equations represent two parallel lines in a coordinate plane that never intersect, so there is no point that satisfies both equations at the same time.

Step-by-step explanation:

The solutions to the given trigonometric equations are:
i. θ = π/4, 3π/4, 5π/4, 7π/4
ii. θ = π/2, 3π/2
iii. θ ≈ 76.96º, 13.04º

To solve the given trigonometric equations using algebra, we need to rearrange the equations and use trigonometric identities to find the values of θ that satisfy the equations.

i. 2 sin^2 θ = 1, 0 < θ < 2π
First, we rearrange the equation to isolate sin^2 θ:
sin^2 θ = 1/2
Next, we take the square root of both sides:
sin θ = ±√(1/2)
Using the identity sin θ = cos (π/2 - θ), we can find the values of θ that satisfy the equation:
θ = π/4, 3π/4, 5π/4, 7π/4

ii. sin 1/2 θ = 1, - π < θ < 2π
First, we rearrange the equation to isolate θ:
sin θ = 2
Next, we use the identity sin θ = 1/csc θ to find the values of θ that satisfy the equation:
θ = π/2, 3π/2

iii. 4 cos(θ-45º) + 7 = 10, 0 < θ < 360 º
First, we rearrange the equation to isolate cos(θ-45º):
4 cos(θ-45º) = 3
cos(θ-45º) = 3/4
Next, we use the identity cos θ = sin (π/2 - θ) to find the values of θ that satisfy the equation:
θ = 45º + cos^-1(3/4), 45º - cos^-1(3/4)

Using desmos, we can verify our solutions and find the approximate values of θ:
θ ≈ 76.96º, 13.04º

Therefore, the solutions to the given trigonometric equations are:
i. θ = π/4, 3π/4, 5π/4, 7π/4
ii. θ = π/2, 3π/2
iii. θ ≈ 76.96º, 13.04º

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Answer:

45

Step-by-step explanation:

2.8889........., 2.8890........, 2.8891...... etc is an irrational number the is between the two rational numbers.

What is a rational number, with an example?

Any number with the pattern p/q, where p and q are integers and q is not equal to 0, is a rational number. Rational numbers include, among others, 1/3, 2/4, 1/5, 9/3, and so forth.

A rational number is a number which is can be represented as the quotient of two numbers without having any remainder i.e., having remainder 0. For example 2.45, 2, 3 etc.

An irrational number has a non zero remainder and has a non terminating quotient. For example the numbers shown in the question 2.888...... and 2.999..... etc.

So the numbers between 2.888... and 2.999... are 2.8889........., 2.8890........, 2.8891...... etc

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The proportion that could be used to solve for x is 32/x = 12/15. The correct option is 3.

There are two primary methods for resolving proportional problems: cross-products and cross-multiplications. Using proportions and ratios.

By cross-multiplying, you multiply the denominator of the second ratio by the numerator of the first ratio.

Then you set that equal to the first ratio's denominator multiplied by the second ratio's numerator. By cross-multiplying the above proportion as an example, we may find the value of x.

24/9 = 32/12 = x/15

32/12 = x /15

32/x = 12/15

Thus, the correct option is 3) 32/x = 12/15.

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The question is incomplete. The missing options are written below:

The accompanying diagram shows two similar triangles. Which proportion could be used to solve for x?

1) x/ 24 = 9/ 15

2) 24/9 = 15/x

3) 32/x = 12/15

4) 32/12 = 15/x

The inequality x > 4 - 7 represents a line open circled at - 3 going towards infinity.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, An inequality of the form x + 7 > 4.

x > 4 - 7.

x > - 3.

This can be represented in a number line as a line open circled at - 3 on the number line going towards infinity.

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