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By taking some products, we will see that the average amount processed per day is 1,260 tons.

We know that the recycling plant processes an average of 7/8 tons of cardboard each minute.

In one hour we have 60 minutes, so the amount processed per hour is given by the product:

60*7/8 tons = 52.5 tons.

And in one day we have 24 hours, so the total amount processed in one day is 24 times what we got above, which is:

24*52.5 tons = 1,260 tons.

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y = f(x+2) -1 is the equation which describes the graphed function.

Translation is the act of moving a shape or a figure from one location to another. A figure can move in translation up, down, right, left, or anywhere else in the coordinate system. Only the object's position changes during translation; its size stays the same. In mathematics, a translation is the up, down, left, or right movement of a shape. Because the translated shapes appear to be exactly the same size as the original ones, they are consistent with one another. Just one or more directions have been altered.

Given,

When F crosses the x-axis when it is negative.

-1 indicates a 1 unit down translation.

So, the equation will be y = f(x+2) -1.

y = f(x+2) -1 is the equation which describes the graphed function.

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Answer:

0.02, 0.113, 0.2 0.38 0.4

Step-by-step explanation:

The theorem that would be used to justify that triangles ABC and CDA are congruent is: SAS.

If we can show that the two sides and one included angle in one triangle is congruent to the two corresponding sides and an included angle in another triangle, then we can state that the two triangles are congruent to each other by the SAS congruence theorem.

Triangles ABC and CDA have the following:

Side AD is congruent to side BC [one pair of congruent sides]

Side AC is congruent to side CA based on the reflexive property [one pair of congruent sides]

Angle 1 is congruent to angle 2 [one pair of included congruent angle]

Therefore, the above information satisfies the SAS congruence theorem. Therefore, they are congruent triangles based on the SAS. The theorem that justifies why they are congruent is therefore SAS.

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Note that the data is in ascendinhg order.

We shall find the position of the pth percentile as follows;

We now have;

In the 34th and 35th position we have;

ANSWER:

Answer:

A. 96 U2

Step-by-step explanation:

The cube has 6 faces

Multiply by 6 the area of one face

Surface area = 6 (4)(4) = 96 units2

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The perimeter of the shaded figure is 12 units

The area of the shaded figure is 8 square units

Given,

Length of the shaded figure = 4 units

Width of the shaded figure = 2 units.

The shaded figure resembles a rectangle

So,

Perimeter of the shaded figure = 2( length + width)

Perimeter, P = 2 ( 4 + 2)

P = 2 × 6

P = 12 units

Now,

Area of the shaded figure = length × width

Area, A = 4 × 2

A = 6 square units

Therefore,

The perimeter of the shaded figure is 12 units

The area of the shaded figure is 8 square units

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The general formula to find the midpoint of a line in a 3D space is given by

In this case, we have

So the position vector of the midpoint of the line PQ is

which is option B.

Solution:

Given:

Answer: X=5

Step-by-step explanation: If x is 5 more than y, and y is 3 less than z. Well we already know z=3 so z=3 - 3 less than Y=0. Making Y=0, and if x is five more than Y, 5+0=5. Making x=5

The new coordinates are (-1, 7), (-3, 3) and (-8, 5)

To get the new coordinates after the translation, we will first find the initial coordinates of the three vertices

The three vertices: (3, 3), (1, -1) and (-4, 1)

A translation of 4 units to the left:

A translation of 4 units up:

Plotting the points:

1) [tex]\overline{AB} \cong \overline{CD}[/tex] (given)

2) [tex]\angle BAC \cong \angle ACD[/tex] (given)

3) [tex]\overline{AC} \cong \overline{AC}[/tex] (reflexive property)

[tex]\triangle ABC \cong \triangle CDA[/tex] (SAS)

Expression of the given interval (-4,-1) in inequality notation is -4< x <-1.

As given,

Given interval:

( -4 , -1 )

Let us consider x variable belongs to given interval x ∈ ( -4 , -1 ).

Therefore, the expression of the given interval (-4,-1) in inequality notation is -4 < x < -1.

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We have the sequence:

We rewrite the sequence as:

From the previous equations, we see that the general term is given by:

Replacing n = 19, we get:

Answer

Answer:

Step-by-step explanation:

You want to solve the equations and check the solutions for ...

1. -2a-9=6a+15

2. 14+3n = 5n-6

3. 1/2 x -5=10 - 3/4 x

4. 7/3 y+1=1/6 y+8

Each of these equations has both a variable term and a constant term on each side of the equal sign. The usual 3-step solution is ...

This can be made less error-prone by choosing the variable term in Step 1 that has the smallest (least) coefficient. Then the constant in Step 2 will be the constant on the side of the equation that has the variable term with the largest coefficient.

We can do the subtractions of Step 1 and Step 2 both at the same time, reducing the work slightly. Of course, subtraction is the same as adding the opposite. Then what remains is dividing by the coefficient of the variable (or multiplying by its inverse).

  Add 2a -15 to both sides:

  -24 = 8a

  -3 = a . . . . . . divide by 8

  check: -2(-3)-9 = 6(-3) +15   ⇒   -3 = -3 . . . checks OK

  Add -3n+6 to both sides:

  20 = 2n

  10 = n . . . . . . divide by 2

  check: 14 +3(10) = 5(10) -6   ⇒   44 = 44 . . . checks OK

  Add 3/4x +5 to both sides:

  5/4x = 15

  x = 12 . . . . . . multiply by 4/5

  check: 1/2(12) -5 = 10 -3/4(12)   ⇒   1 = 1 . . . checks OK

  Add -1/6y -1 to both sides:

  13/6y = 7

  y = 42/13 . . . . . multiply by 6/13

  check: (7/3)(42/13) +1 = (1/6)(42/13) +8   ⇒   98/13 +1 = 7/13 +8

  ⇒   8 7/13 = 8 7/13 . . . checks OK

The dividend is

and the divisor is

x+2

We begin by arranging them as follows:

now, we divide the leading term in the dividend by the leading term in the divisor to get the first term of the quotient: 4x^2 / x = 4x.

Then we multiply the divisor by 4x and subtract

the result from the dividend. That is:

We repeat the same procedure: using the last line -3x - 6 as the dividend:

So, the leading term of -3x-6 is -3x, so we have -3x/x = -3. Then we multiply the divisor by -3 and subtract the result from the dividend. That is:

Because the remainder is 0, we have finished the division. So the correct answer will be 4x-3

Expression of the given interval (-4,-1) in inequality notation is -4< x <-1.

As given,

Given interval:

( -4 , -1 )

Let us consider x variable belongs to given interval x ∈ ( -4 , -1 ).

Given interval ( -4 , -1 ) is open interval.

In open interval when we plot it on the real number line , we are not including upper limit and the lower limit of the given interval.

-4 and -1 are exclusive values for the given variable.

Symbol representing open interval is sign of < or >.

Interval (-4,-1) in inequality notation is given by -4 < x < -1.

All values are included between -4 and -1 except -4 and -1.

Therefore, the expression of the given interval (-4,-1) in inequality notation is -4 < x < -1.

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Answer:

24

Step-by-step explanation:

We will use the proportional concept to solve it.

So, 6/13 = x/52

x = 6*4

x = 24

So, height of tree is 24 feet

Answer: a. (-10, 0) u(12, infinity)

b. (negative infinity, -10) u(0, 12)

All of this is assuming that the ends of both functions are continuing in the direction it's going shown in the graph.

Step-by-step explanation:

f(x) and g(x) basically means the y value. So when f(x) is greater than g(x), it's saying the y value for the f(x) line is greater than the y value for g(x). This happens when x = -10 till x = 0 and x = 12 till forever going right.

Side note: (-10, 0) is a way to write the domain, with the first number meaning the start and the second number meaning the end.

Answer:

1/100 or -1/100

Step-by-step explanation:

the two solutions are

0.01 = 1/100

-0.01 = -1/100

a. Sin (θ) = √35 / 6

b. Tan (θ) = Tan θ = √35

c. Sec (θ) = 6

d. Csc (90° -θ) = 6

Note that according to trigonometric identities:

cos θ = Adjacent / Hypotenuse

From the question:

cos θ = 1/6

Comparing this with the given trigonometric identity:

Adjacent, A = 1

Hypotenuse, H = 6

Let us look for the opposite, O

Using the pythagora's theorem

H² = A² + O²

6² = 1² + O²

36 = 1 + O²

36 - 1 = O²

O² = 35

O = √35

Therefore, Opposite = √35

a) Sin θ = Opposite / Hypotenuse

Sin θ = √35 / 6

b) Tan θ = Opposite / Adjacent

Tan θ = √35 / 1

Tan θ = √35

c) Sec θ = 1 / cos θ

Sec θ = 1 ÷ 1/6

Sec θ = 1 x 6

Sec θ = 6

d) Csc ( 90 - θ) = Sec θ

Since Sec θ = 6

Csc ( 90 - θ) = 6

Yes, the probability approaches each time will result in getting a sample that is representative of the population of that group class.

If you are going on and properly conducting the specific research on a specific population, you will totally want to make sure that your taken sample of that population is absolutely representative.

If in any case your sample is a kind of representative of your total population, you will be able to confidently take up and generalize the results of your study to that of the population.

In order to be a representative sample, the sample of the group must represent the total population as a whole.

For instance, if the researcher’s population of absolute interest has 60% of people of total ages 18-25 and 40% of the total people ages from about 26-40, then the representative sample must also absolutely reflect this ratio.

The best way of ensuring a representative sample is to have a complete list (i.e., sampling frame) of all the elements in the present population and know that each and every element (e.g., people or present households) on the list that has a nonzero chance (but then it is not necessarily required to be an equal chance) of being included in the entire sample.

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Population means μ as a tri-linear inequality is given as 58.852< m<61.548 with a confidence interval of 99.5%.

What is a confidence interval?

Mean, x= 60.2

sample size, n= 867

standard deviation=21.9

population mean m as a tri-linear inequality is given by,

The t value for a 99.5% Confidence interval because the sigma is unknown.

From Inverse t Distribution Calculator, the Confidence interval is 0.995 and the degree of freedom is 867-1=866

One-sided t-Score: 1.8125

We can now determine the standard error E:

E=1.8125(21.9/√867)=1.348

We can now create the confidence interval by:

x - E < m< x + E

60.2-1.348< m <60.2+1.348

58.852< m<61.548

Population means μ as a tri-linear inequality is given as 58.852< m<61.548 with a confidence interval of 99.5%.

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The cost of 12.49 is fixed, while the extra cost for toppings is 1.5 per topping.

If we have a total of t topping, the cost of the toppings will by 1.50t, adding the fixed cost, we will have the total cost, which should be equal to d. so we have the equation:

Now, we can manipulate the equation to check which ones are equivalent to it.

As we can see, the first one is missing the 1.50, so it is not equivalent.

The second have the 1.50, it is just inverted:

So, it is equivalent.

The third had the t and d switched, so it is not equivalent.

The fourth get the 1.50t to the other side, but don't change the sign accordingly, so it is not equivalent.

The fifth solved for t let's do that:

So, it is equivalent.

The sixth don;t distribute the denominator correctly, so it is not equivalent.

So, the alternatives that are equivalent are:

The second and fifth.

ANSWER

EXPLANATION

Two lines are perpendicular if they have opposite reciprocal slopes. So, to find the line, first, we have to find the slope of the line tangent to the graph of y = 1/x at x = 2. To do so, we have to find the derivative of the function and evaluate it at x = 2. That is the slope of the tangent line at that point.

The derivative of the function is,

So, the slope of the tangent line at x = 2 is,

Therefore, the slope of the perpendicular line is the opposite reciprocal,

So we have that the perpendicular line we are looking for is,

We have to find the y-intercept, b. We know that this perpendicular line intersects the graph at the tangency point, so with that point, we will find b.

The x-coordinate of the tangency point is x = 2, and the y-coordinate is,

Substitute (x, y) with (2, 1/2) in the equation of the line to find b,

Subtract 8 from both sides,

Hence, the equation of the line perpendicular to the tangent of the graph at x = 2 passing through the tangency point is,

Answer: 1/2

Step-by-step explanation:

1) Find the equation of sin of angle K

Sine is opposite/hypotenuse.

Opposite of K = 5.

the hypotenuse of K = 10

You then get 5/10

2) Simplify the fraction

5/10 = 1/2

Consider that the volume of a rectangular prism is given by the following formula:

V = l·h·w

l: length = 4 cm

w: width = 5.1 cm

h: height = 9 cm

replace the previous values of the parameters into the formula for V:

V = (4 cm)(5.1 cm)(9 cm)

V = 183.6 cm³

Hence, the volume of the rectangular prism is 183.6 cm³

The required expression is f(x) = (3x - 2).

A linear expression is an algebraic equation of highest degree 1 and it contains only one variable. A quadratic expression is an algebraic expression in which the variable has highest degree of 2. In a quadratic equation the two values of variable which satisfies the equation ax² + bx + c = 0 is called the roots of the given equation. According to the given question Square then subtract 5 is expressed as the function f(x) = x² - 5

∴ The function Multiply by 3, then subtract 2 will be expressed as

f(x) = (3x - 2).

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Complete question:

Express the rule in function notation. (For example, the rule "square, then subtract 5" is expressed as the function f(x) = (x2 − 5.)Multiply by 3, then subtract 2.

the sum of the internal angles of the 4-sided polygon is 360, therefore

then

answer: a. y = 116° and z = 61°

The decimal that is equivalent to 9% is:

Then, the decimal which is equivalent to 9% is 0.09.