Robert has a job transporting soft drinks by truck. His truck is filled with cans that weigh 16 ounces each
and bottles that weigh 54 ounces each. There is a combined total of 280 cans and bottles in his truck.
Let c be the number of cans in his truck. Write an expression for the combined total weight (in ounces)
of the cans and bottles in his truck.


O Total weight in ounces = 70c + 280
O Total weight in ounces = -54c + 15, 120
O Total weight in ounces = 38c + 280
O Total weight in ounces = -38c + 15, 120

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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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:

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.

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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Tone is the feeling the author wants the reader to have when reading his or her work. Anaya employs tone to generate the texts "Take the Tortillas out of your poetry" and "Speaking Arabic."

Both authors explore regional cuisine and make use of terminology from various languages.

While Nye's tone is welcoming of mixed cultures, Anaya's tone is sincere towards culture and indignant towards suppression.

The funny tone of Anaya's writing reflects his intention to draw attention to the subject. The laid-back nature of Anaya's delivery is evident.

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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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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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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 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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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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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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Step-by-step explanation:

It's a long answer. You have to find the area of the large triangle, the small triangle than subtract the two

A = 1/2(b)(h)

For the big triangle

A = 1/2(16)(4) = 1/2(64) = 32

For the small triangle

A = 1/2(8)(2)

We use 8 and 2 because that's half of 16 and 4, since at the bottom it says A and B are midpoints

A = 1/2(8)(2) = 1/2(16) = 8

Now we subtract

32-8 = 24 units

Answer:

[tex]sin(P)=\frac{\sqrt{55}}{10}[/tex]

Step-by-step explanation:

The sine function is defined as a ratio of sides: [tex]sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}[/tex]

where the "opposite" side is quite literally the opposite side, if you went straight from the angle, whatever side it's pointing towards is the opposite angle. The hypotenuse... is as the name implies, the hypotenuse. The symbol inside the parenthesis next to the sine is called theta and is just used to represent some angle.

We of course don't know the hypotenuse as it's not given, but we can use the Pythagorean Theorem to solve for the hypotenuse:

[tex]c^2=\sqrt{45}^2+\sqrt{55}^2\\c^2=45+55\\c^2=100\\c=10[/tex]

We do know the opposite side though, it's just the square root of 55, it's directly opposite of the angle P. Plugging in known values we get the following: [tex]sin(P)=\frac{\sqrt{55}}{10}[/tex] and we can't simplify this any further as 45 has no factors which are perfect squares.

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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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 information regarding the addition is explained below.

Adding 29 + 46:

Student 1: May use the traditional column addition method, lining up the digits in the ones, tens, and hundreds place and carrying over if necessary.

Student 2: May use the breaking apart method, where they break apart the numbers into smaller parts (e.g. 20 + 40) and then add the pieces together.

Student 3: May use a number line, counting up from 29 by the increments of 46 until they reach the sum.

Subtracting 54 - 28:

Student 4: May use the traditional column subtraction method, lining up the digits in the ones, tens, and hundreds place and borrowing if necessary.

Using bundled things to explain regrouping in the addition problem 167 + 59:

First, separate the numbers into bundles of ten.

Next, show how you can regroup the ones as ten ones to make a bundle of ten.

Then add the tens and hundreds place to get the answer 226.

Using bundled things to explain regrouping in the subtraction problem 231 - 67:

First, separate the numbers into bundles of ten.

Next, show how you can regroup the tens as ten tens to make a bundle of a hundred.

Then subtract the hundreds place and the tens place to get the answer 164.

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The triangles given can be determined to be :

You can use the Pythagorean Theorem and its Converse to determine the type of triangle.

The Pythagorean Theorem and its Converse are basically :

c ² = a² + b ²   This is a right angled triangle

c ² > ( a² + b ² ) This is an obtuse triangle

c ² < ( a² + b ² )

The triangles are :

13 :

26 ² = 24 ² + 10 ²

676 = 676

Right - angled

14 :

20 ² = 13 ² + 6 ²

400 > 205

Obtuse triangle

15 :

17 ² = 16 ² + 3 ²

289 > 265

Obtuse triangle

16 :

32 ² = 29 ² + 24 ²

1, 024 < 1, 417

Acute triangle

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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

Answer:

The answer

Step-by-step explanation:

Figure 1 figure

3/4

The Expression with coefficient 4 and -9 is 4j and -9j.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

We have to write the coefficient as 4 and -9.

As, coefficient is the number which is just before the variable like in 2x 'x' is the variable and '2' is the coefficient.

So, with coefficient 4 the expression is 4j

and, with coefficient  -9 the expression is -9j.

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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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The steps that she could use to solve the quadratic equation is determined as 2(x² + 6x + 9) = 18 + 3.

Solution to the quadratic equation

The solution to the quadratic equation is determined as follows;

2x² + 12x - 3 = 0

2x² + 12x = 3

divide through by 2

x² + 6x = ³/₂

take half of coefficient of x, square it and add it both sides of the equation

(x + 3)² = ³/₂ + 3²

x² + 6x + 9 = 9 + ³/₂

2(x² + 6x + 9) = 18 + 3

Thus, the steps that she could use to solve the quadratic equation is determined as 2(x² + 6x + 9) = 18 + 3.

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Answer:

Let's call the number of cubic yards of mix A that the farmer buys "x", and the number of cubic yards of mix B that the farmer buys "y".

We can write the following constraints based on the minimum monthly requirements:

20x + 10y >= 460 (for acid)

30x + 30y >= 939 (for nitrogen)

5x + 10y >= 200 (for potash)

We also want to minimize the cost, which is given by 25x + 49y.

This is a linear programming problem, which can be solved using simplex method or the graphical method.

By using the graphical method, we find that the optimal solution occurs at x = 11.75 and y = 4.5. This means that the farmer should buy 11.75 cubic yards of mix A and 4.5 cubic yards of mix B to meet the minimum monthly requirements at a minimum cost.

So, the answer to the question is: If mix A costs $25 per cubic yard and mix B costs $40 per cubic yard, the farmer should blend 11.75 yd of mix A & 4.5 yd of mix B to meet the minimum monthly requirements at a minimum cost.

Answer:

The correct answer is:

e = 0.25 t + 1.75 .

The relationship between the number of gallons of gas and the cost in dollars is: C. The cost of gas is $3.75 per gallon.

In Mathematics, a proportional relationship is a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the relationship between the number of gallons of gas and the cost in dollars on this graph as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 7.5/2

Constant of proportionality, k = $3.75.

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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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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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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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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

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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.