Piecewise linear relations

The amount of profit that the new coffee shop will make after 6 years is; 35.8 thousand dollars

The quadratic equation that represents the annual profit made by the new coffee shop in thousands of dollars is;

p(t) = 0.3t² + 5.5t - 8

where;

t is the number of years for which the profit is measured

Thus, after 6 years, we will substitute 6 for t in the quadratic equation to get;

p(6) = 0.3(6)² + 5.5(6) - 8

p(6) = 10.8 + 33 - 8

p(6) = 35.8 thousand dollars

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Y = (1/x-3) has been moved 3 units to the right and up one unit. If it is moved to the right, it should look like this: (x-3). It should show up as (x+3) if it were moved to the left. If the result were moved ahead, the outcome would be (1/x-3).

The original function f is horizontally shifted into the new function g(x)=f(xh), where h is a constant. Given a function f. The graph will shift to the right in a positive h situation. If h is negative, the graph will slide to the left.

To move a function left in function notation, add within the function's argument: f(x + b) moves f(x) b units left. In the same way, shifting to the right moves f(x) b units to the right.

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Answer:

[tex]\textrm{Each side = 23.6893 cm}\\\\\\\textrm{Rounded to 2 decimal places = 23.69 cm}\\\\\textrm{Rounded to 1 decimal place = 23.7 cm}[/tex]

You can choose the level of precision as desired from the above

Step-by-step explanation:

The area of an equilateral triangle of side a

is
[tex]A = \dfrac{(a^2 \sqrt{3})}{4}[/tex]

We are given A = 243

Plugging in values we get

[tex]243 = \dfrac{a^2\sqrt{3}}{4}[/tex]

Switch sides so [tex]a^2[/tex] term is on the left

[tex]\dfrac{a^2\sqrt{3}}{4} = 243[/tex]

Multiply by 4 both sides to get rid of the denominator:
[tex]\dfrac{a^2\sqrt{3}}{4} \times 4 = 243 \times 4\\\\a^2\sqrt{3} = 972\\\\[/tex]

Divide by [tex]\sqrt{3}[/tex]  both sides:
[tex]a^2 = \dfrac{972}{\sqrt{3}}\\\\a^2 = 561.18446\\\\a = \pm \sqrt{561.18446}\\\\[/tex]

Taking only positive square root:
[tex]a = \sqrt{561.18446}\\\\a = 23.6893\\\\[/tex]

The quotient is 3x + 7, and the remainder is (28x + 9) / (x^2 - 3x).

A division is a process of splitting a specific amount into equal parts.

We have to find 3x³-2x²+7x+9 divided by x²-3x

3x³-2x²+7x+9 is the dividend and x²-3x is the divisor.

The steps to solve this are given below.

Step 1: Take the first digit of the dividend from the left. Check if this digit is greater than or equal to the divisor.

Step 2: Then divide it by the divisor and write the answer on top as the quotient.

Step 3: Subtract the result from the digit and write the difference below.

Step 4: Bring down the next digit of the dividend (if present).

Step 5: Repeat the same process.

Hence, the quotient is 3x + 7, and the remainder is (28x + 9) / (x^2 - 3x).

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Equations 4 and 5 are not equivalent to any of the other equations.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

The equations that are equivalent are:

2 + x = 5

Negative 5 + x = negative 2

x + 1 = 4

Subtracting 2 from both sides, we get x = 3. Therefore, the equation is equivalent to x = 3.

Adding 5 to both sides, we get x = 3. Therefore, the equation is equivalent to x = 3.

Subtracting 1 from both sides, we get x = 3. Therefore, the equation is equivalent to x = 3.

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The shape of the newly cut cross section is option A. A rectangle, 5 inches by 6 inches.

Rectangle is a two dimensional shape or figure which consists of four sides and four angles and all the angles are right angles.

Opposite sides are equal.

It is clearly seen that the red line is passing along the length of the  block.

So the new cross section cannot have the dimension 15 inches in any part.

And the width and height is not getting cut.

So the dimension will be 5 inches by 6 inches.

A square has all the sides equal.

Since both the dimensions are not equal it is a rectangle and not a square.

Hence the new cross section is A. A rectangle, 5 inches by 6 inches.

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The complete question is as follows and the image for the block is attached below :

Landis cuts a foam block along the red line. When he looks at the newly

exposed face, what is the shape of the cross-section?

A. A rectangle, 5 inches by 6 inches

B. A rectangle, 15 inches by 6 inches

C. A rectangle 5 inches by 15 inches

D. A square, 5 inches by 5 inches

Answer:

1,800 lbs of sand

900 lbs of gravel

600 lbs of cement

Step-by-step explanation: 11*300=3,300. 300*6=1,800, 300*3=900, and 300*2=600. This is correct because if you add 1,800+900+600 you get 3,300.

Answer:

[tex]\frac{1}{22}[/tex]

Step-by-step explanation:

For these time of limit problems, we want to try to rewrite the equation in such a way that we can get some value, because in this case plugging in x=121, we simply get 0/0 which is indeterminate.

One thing you may or may not notice is that 11 and 121 are closely related, as 121 is just the square of 11... something important to solving this.

We have the fraction: [tex]\sqrt{x}-11[/tex], we want to possibly rewrite this into the denominator (x-121) to cancel out the two... well we can use the difference of squares. [tex](\sqrt{x}-11)(\sqrt{x}+11)=x-121[/tex] and we want to multiply the bottom by this amount as well, giving us the fraction:

[tex]\frac{x-121}{(x-121)(\sqrt{x}+11}[/tex]

Now we can cancel out the x-121 from the numerator and denominator, leaving us with:

[tex]\frac{1}{\sqrt{x}+11}[/tex]

and now we can directly plug in 121

[tex]\frac{1}{\sqrt{121}+11}=\frac{1}{11+11}=\frac{1}{22}[/tex]

Answer:

0.075 is a hundred times smaller than 7.5

Step-by-step explanation:

Answer:

x=-13

Step-by-step explanation:

Since the two angles given are equivalent, you set up the equation as 7x+205=114.

7x+205=114

7x=114-205

7x=-91

7x/7=-91/7

x=-13

Hope this helps! Please give brainliest!

Answer:

Step-by-step explanation:

The solution to this problem involves calculating the monthly interest and reducing the balance accordingly each month until the balance reaches zero. Here are the steps:

Calculate the monthly interest: First, we need to calculate the monthly interest rate. We can do this by dividing the APR by 12. The monthly interest rate is 9.5% / 12 = 0.7917%.

Calculate the interest charge for the first month: The interest charge for the first month is the balance multiplied by the monthly interest rate. In this case, the interest charge is $1,367.90 x 0.7917% = $10.87.

Calculate the new balance: Next, we need to subtract the payment from the balance and add the interest charge to determine the new balance. The new balance after the first payment is $1,367.90 - $400.00 + $10.87 = $978.87.

Repeat the steps for subsequent months: Repeat the process of calculating the monthly interest charge and the new balance for each subsequent month until the balance reaches zero.

Keep track of the number of months: As we repeat the steps, keep track of the number of months it takes to pay off the card.

Here is a summary of the calculations:

Month Balance        Interest Payment    New Balance

1        $1,367.90 $10.87 $400.00       $978.87

2          $978.87          $7.74 $400.00       $586.61

3          $586.61          $4.62 $400.00        $191.23

4           $191.23          $1.50 $400.00      $-208.27

It takes 4 months to pay off the card, and the total amount paid including interest is $1,367.90 + $10.87 + $7.74 + $4.62 + $1.50 = $1392.73.

1/2a+6 is the simplified form of the expression  3/4a + 8 - 1/4a - 2

An expression is combination of variables, numbers and operators.

The given expression is 3/4a + 8 - 1/4a - 2

Three by four times of a plus eight minus one by four times of a minus 2.

In the given expression a is a variable and plus and minus signs are the operators.

3/4a + 8 - 1/4a - 2

3/4a and  - 1/4a are the like terms

Add the like terms

3/4a   - 1/4a +8 - 2

2/4 a +6

1/2a+6

Hence, 1/2a+6 is the simplified form of the expression  3/4a + 8 - 1/4a - 2

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Answer: d. Triangle with angle measures: 8·, 17·, and 152·

Step-by-step explanation: i did the test

The triangle not possible is option

A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.

Sum of the interior angles of a triangle is 180 degrees.

Let us find the sum of the angles for each triangle given.

(a) Triangle with angle measures: 26°, 19°, and 135°·

Sum = 26° + 19° + 135° = 180°

(b)Triangle with angle measures: 14°, 27°, and 139°·

Sum = 14° + 27° + 139° = 180°

(c) Triangle with angle measures: 9°, 18°, and 153°·

Sum = 9° + 18° + 153° = 180°

(d) Triangle with angle measures: 8°, 17°, and 152°·

Sum = 8° + 17° + 152° = 177°, which is not equal to 180°.

Hence the option (d) is not possible.

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Two pairs of separate sides are parallel in a quadrilateral with a single arrow once per pair of opposite sides.

A quadrilateral has four straight sides and is a two-dimensional form. Parallelograms, isosceles triangles, rectangles, kites, rectangles, and rhombuses are a few examples of quadrilaterals.

Option (c) illustrates a trapezoid in which one set of opposing sides has arrows indicating how they are parallel to one another. Alternative (d) has both couples of opposing sides indicated with arrows, indicating that all side are parallel, while options (a) and (b) don't even have any linear opposite sides.

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The piecewise function for the given problem is;

C(x) = $61.29                           x ≥ 400

C(x) = $61.29 + 0.6(x - 400) if x ≥ 400

A piecewise function is defined as a function that has different definitions depending on which values of x are being used. Piecewise functions are called "piecewise" due to the fact that they are made of "pieces" with different function definitions. To evaluate a piecewise function for a given value of x, find which interval your value fits in, and then use that definition of the function to evaluate.

First, we will find the monthly cost if the 400-minute monthly limit is not exceeded. Then, the total cost would be;

47.35 + 13.94 = 61.29 with just the plan and taxes. So if x ≤ 400, then;

C(x) = 61.29

Now if the 400 minutes is exceeded, the bill will also include $0.60 per additional minute. To find the number of additional minutes, we can take the total number of minutes x and subtract 400. In general, the cost would be;

C(x) = $61.29 + 0.6(x - 400) if x ≥ 400

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Using addition we can conclude that the total time taken for the setup of the machine would be 11.4 hours.

One of the four fundamental operations in mathematics is addition, along with subtraction, multiplication, and division.

The entire amount or sum of the two whole numbers is obtained by adding them.

The process of addition involves combining two or more numbers to determine their sum.

Mathematicians utilize addition as their main arithmetic operation to determine the sum of two or more numbers.

For instance, 7 + 7 equals 14.

So, we can get the total time using addition as follows:

= 0.6 + 2.4 + 5.2 + 1.4 + 1.8

= 11.4 hours

Therefore, using addition we can conclude that the total time taken for the setup of the machine would be 11.4 hours.

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Using the equation of the arithmetic sequence given, the first four terms are 59, 52, 45 and 38 respectively

In the sequence given, the progression is an arithmetic progression since it increases by a common difference.

The first term of the sequence is 59 while the common difference is -7.

A = 59 - 7(n - 1)

n = 1

a = 59 - 7(1 - 1)

a = 59

n = 2

a = 59 - 7(2 - 1)

a = 52

n = 3

a = 59 - 7(3 - 1)

a = 45

n = 4

a = 59 - 7(4 - 1)

a = 38

The terms are 59, 52, 45 and 38

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Translation:  Find the first four terms of the sequence given the following

A circle graph titled social media usage, with four sections labeled vidtok 17 percent, headbook 48 percent, picturegram 25 percent, and tweeter 10 percent.

What is the division?

Division is an arithmetic operation that is the inverse of multiplication. It involves splitting a quantity into equal parts or determining how many times one quantity is contained within another.

If you add all of the numbers together you get 500, but you need to make it 100 percent so you divide the total number by five. to know what percent out of 100 you need to divide all of the variables by 5.

85 ÷ 5 = 17

240 ÷ 5 = 48

125 ÷ 5 = 25

50 ÷ 5 = 10

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Answer:

BBBBBBBBB

Step-by-step explanation:

The supportive statement regarding the trapezoid based on the information is m∠WKT ≅ m∠TRW.

An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium.

The non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel. The parallel sides may be vertical, horizontal, or angled.

The altitude is the measurement of the angle perpendicular to the parallel sides.

The missing statement to support all other statements would be that m∠WKT ≅ m∠TRW as the angle formed by the pair of the corresponding sides is equal.

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In the image of the trapezoid the value of angle C is 82 degrees

A trapezoid is a quadrilateral with one pair of parallel sides.

Opposite angles of a trapezoid are angles that are located across from each other, with a side of the trapezoid between them.

In a trapezoid, opposite angles are always congruent, meaning they have the same measure. This is a result of the fact that a trapezoid is a parallelogram, which means that its opposite sides are parallel and equal in length.

When opposite sides of a parallelogram are parallel, it follows that opposite angles are congruent.

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The system of equations which has infinitely many solutions as required to be determined is; Choice D; 2x + y = 5 and 4x + 2y = 10.

By the standards of linear geometry, two equations have infinitely many solutions when their graphs coincide and in which case, they have the same slope and y-intercept.

Therefore, the system of equations which satisfy the said criterion is; 2x + y = 5 and 4x + 2y = 10.

Ultimately, the correct answer is; Choice D; 2x + y = 5 and 4x + 2y = 10.

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Answer:

The 3rd and 6th equations

Step-by-step explanation:

Any equation that has a variable with an exponent is nonlinear and the 3rd and 6th equations follow this requirement.

The value of x for the given expression will be 22/3.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.

Given that the expression is triple x less by 10 is at least 12. The mathematical form of the expression can be written as below:-

3x - 10 = 12

3x = 10 + 12

3x = 22

x = 22 / 3

Hence, the value of x for the expression 3x - 10 = 12 is x = 22 / 3.

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Answer:

The correct answer is:

e = 0.25 t + 1.75 .

Note that the Polynomial Expression for to represent the total surface area of the two drums is: 4πrh + 4hr².

A polynomial expression is any expression that consists of variables, constants, and exponents and is combined using mathematical operators such as addition, subtraction, multiplication, and division.

According to the number of terms in the expression, polynomial expressions are classed as monomials, binomials, or trinomials.

Given that the total surface area of one cylinder is:

2πrh + 2πr²,

The total surface area of two drums will therefore be:

(2πrh + 2πr²) * 2

⇒ 4πrh + 4hr²

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We would expect John to weigh approximately 216.4 pounds at the end of week 8.

To answer this question, we need to fit a regression model to the data to determine the relationship between the number of calories burned and John's weight. We can use linear regression to find the line of best fit that represents this relationship.

We can see that there is a negative relationship between the number of calories burned and John's weight, which is consistent with the statement that "the more someone exercises the less they will weigh." We can use linear regression to find the line of best fit that represents this relationship.

Using a linear regression model, we get the following equation:

Weight = 219.9 - 0.0007 * Exercise

We can use this equation to predict John's weight at the end of week 8 based on the number of calories he burned. Plugging in Exercise = 5000, we get:

Weight = 219.9 - 0.0007 * 5000

Weight = 216.4

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Answer:

  1625

Step-by-step explanation:

You want the sum of the first 25 terms of the series 5 +10 +15 +....

The first term is 5, the common difference is 5, so the general term is ...

  an = a1 +d(n -1)

  an = 5 +5(n -1)

The last term of the sum is ...

  a25 = 5 +5(25 -1) = 125

The sum of the series is the average of the first and last terms, multiplied by the number of terms:

  S25 = (a1 +a25)/2 · 25 = (5 +125)/2 · 25 = 65·25 = 1625

The sum of 25 terms of the series is 1625.

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Conclusions drawn from a sample of 50 monarch butterflies tagged from one location in California may not be entirely true for all monarch butterflies.

A sample is a subset of data drawn from a larger population by a researcher using a predetermined selection process. These components are referred to as sample points, sampling units, or observations.

The sample size is relatively small compared to the entire population of monarch butterflies. Additionally, the sample is only taken from one location, so the results may not be representative of the entire migration pattern.

The monarch butterfly is known to have a wide geographic range, migrating across North America, and covering a distance of thousands of miles during their annual migration. Thus, to make conclusions that apply to the entire population of monarch butterflies, a more comprehensive and representative sample size from various locations along their migration route would be needed.

In scientific research, it is essential to have a large and representative sample size to minimize the margin of error and to obtain accurate results. Therefore, a larger sample size and a more diverse geographical representation would provide a better understanding of the migration patterns of monarch butterflies.

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The equation of the tangent plane at the point (5,4,7) on the surface z=f(x,y) is z = -3x + 7y + 8.

In 3-space, the plane tangent to a surface at a point can be imagined similarly to how we can see the line perpendicular to a curve at a point in 2-space.

The equation of the tangent plane at the point (5,4,7) on the surface z=f(x,y) can be found using the following formula:

z - [tex]z_{0}[/tex] = fx([tex]x_{0}[/tex],[tex]y_{0}[/tex])(x - [tex]x_{0}[/tex]) + fy([tex]x_{0}[/tex],[tex]y_{0}[/tex])(y - [tex]y_{0}[/tex])

where ([tex]x_{0},y_{0},z_{0}[/tex]) is the point on the surface at which we want to find the tangent plane, and fx([tex]x_{0}[/tex],[tex]y_{0}[/tex]) and fy([tex]x_{0}[/tex],[tex]y_{0}[/tex]) are the partial derivatives of f with respect to x and y, respectively, evaluated at ([tex]x_{0}[/tex],[tex]y_{0}[/tex]).

In this case, we have [tex]x_{0}[/tex] = 5, [tex]y_{0}[/tex] = 4, [tex]z_{0}[/tex] = f(5,4) = 7, fx(5,4) = -3, and fy(5,4) = 7. Substituting these values into the formula, we get:

z - 7 = (-3)(x - 5) + (7)(y - 4)

Simplifying this equation, we get:

z = -3x + 7y + 8

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The mean of the sampling distribution is given as follows:

37.827 millimeters.

The mean of the sampling distribution is obtained using the Central Limit Theorem.

The mean of the sampling distribution is the same as the population mean, hence it is given as follows:

37.827 millimeters.

(on the problem, we are given the population mean).

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