Simplify the fraction 112 144 as much as possible.

Answer:

$2,875

Step-by-step explanation:

Interest = Principal x rate x time

Interest = $2500 x 0.03 x 5

Interest = $375

Original value + interest = Total amount

$2,500 + $375 = $2,875

Answer

Step-by-step explanation

Given the polynomials:

To add them we need to add the similar terms (terms with the same variable and degree), as follows:

The variable represents time. The time in which a person runs a mile will depend on the speed of that person, and that can take almost any value, thus, here the variable is continuous.

First, when a variable is discrete and when it is continuous?

A variable is discrete if it only can take some selected values on a given interval, while a variable is continuous if it can take any value (or at least a dense set) of values in that interval.

For example, the numbers that one can roll on a dice form a discrete set, because the values can only be {1, 2, 3, 4, 5, 6}, just to given an example.

Now, in this case, the variable represents time. Time almost always is a continuous variable, in this case, the time is the time in which a person runs a mile. So that variable can take almost any value (depends on the speed of the person).

So we conclude that this is a continuous variable.

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Since [tex]x[/tex] is approaching 1 from the left/below, we take the part of [tex]f(x)[/tex] that is defined over [tex]x<1[/tex], for which we have

[tex]f(x) = \dfrac{x-1}{\sqrt{x-1}}[/tex]

Since [tex]x\neq1[/tex], we can simplify this to

[tex]f(x) = \dfrac{x-1}{(x-1)^{1/2}} = (x-1)^{1/2} = \sqrt{x-1}[/tex]

and this is continuous at [tex]x=1[/tex], so we can evaluate the limit by directly substituting [tex]x[/tex].

To summarize:

[tex]\displaystyle \lim_{x\to1^-} f(x) = \lim_{x\to1} \frac{x-1}{\sqrt{x-1}} = \lim_{x\to1} \sqrt{x-1} = \sqrt{1-1} = \boxed{0}[/tex]

Answer:

64 = x

Step-by-step explanation:

The angles are alternate interior angles and alternate interior angles are equal when the lines are parallel

128 = 2x

Divide each side by 2

128/2 = 2x/2

64 = x

Answer:

x = 64

Step-by-step explanation:

We know that,

If lines are parallel, the alternate angles are also equal.

Therefore,

[tex] \sf2x = 128[/tex]

Now, let us solve for x.

For that, divide both sides by 2.

[tex]x = 64[/tex]

Step-by-step explanation:

which can also be said as 5×5=25

2. perimeter is addition of all sides which is solved as L+L+L+L= 28cm

also: 7+7+7+7= 28cm

Given

The three sides are given 24, 30 and 18.

Explanation

To find the triangle is acute, obtuse or right triangle.

To determine whether the triangle is acute, right, or obtuse.add the squares of the two smaller sides, and compare the sum to the square of the largest side. Since this sum is greater, the triangle is acute.

A

If the sum of the squares of the two smaller sides is equal to the square of the largest side , then it is right triangle.

Now c.

Answer

Hence the sum of the squares of the two smaller sides is equal to the square of the largest side , then it is right triangle.

The correct option is A.

SOLUTION

For the image point A has the coordinates (-3, 6) and A' is (3, -6) so with a translation of

We see A(-3, 6) as

And B(-2, 2) as

Therefore the correct translation is

Option B is the correct answer.

7-(x^2+14x+49)

7-x^2-14x-49

-x^2-14x-42

The most appropriate choice for expectation will be given by-

Amount of money the company expected to pay = $10400

What is expectation?

At first it is important to know about probability of an event.

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Suppose x is a random variable with the probability function f(x). suppose [tex]x_1[/tex], [tex]x_2[/tex],....., [tex]x_n[/tex] are the values corrosponding to the actual occurance of the event and [tex]p_1,[/tex] [tex]p_2,[/tex]....,[tex]p_n[/tex] be the corrosponding probabilities.

Expectation is given by the formula

[tex]p_1x_1 + p_2x_2....+p_nx_n[/tex]

Here,

Amount of money the company expected to pay =

$[tex](0 \times 0.70 +20000 \times 0.16+ 40000 \times 0.09 + 60000 \times 0.03 + 80000 \times 0.01 + 100000 \times 0.01)[/tex]

                                                                                  = $10400

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Answer:

  (c)  32

Step-by-step explanation:

Given a map between x, g(x), and f(g(x)), you want to find f(g(13)).

You want the function value that results when 13 is the argument of g(x), and g(x) is the argument of f(x).

Locate the input (13) in the left column of the diagram. Follow the arrow to find g(13) = 16. Follow the arrow again to find f(16) = 32.

  f(g(13)) = 32

The product of the multiplication of (2056 * 18394) is 37818064.

As per the question statement, we are provided with the multiplicative statement of two numbers, 2056 and 18394.

We are required to perform the above mentioned multiplication and determine the product in the simplified form a number.

To solve this question, we simply need to multiply 2056 and 18394, and mention the upcoming product as our required answer, i.e.,

(2056 * 18394) = 37818064.

Hence, The product of the multiplication of (2056 * 18394) is 37818064.

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The transformation that took f(x) = 3x+1 to g(x) = −3x−5 is reflection and translation 4 units downwards

given data

f(x) = 3x+1

g(x) = −3x−5

Reflection

Reflections changes the sign of the both coordinates

from                                      to

f(x) = 3x + 1                          f'(x) = -3x - 1

Translation

Translation downwards leads to subtraction with the required units in the y coordinates. In this case 4 units

from                                     to

f'(x) = -3x - 1                          f''(x) = -3x - 5

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Answer:

Either of ...

Step-by-step explanation:

You want the transformations that take f(x) = 3x+1 to g(x) = -3x-5.

The x-term of the transformed function has a sign opposite that of the original function. That can be accomplished by either of (a) reflection across the y-axis (replaces x by -x), or by (b) reflection across the x-axis (replaces f(x) by -f(x)).

Either way, an additional translation is required. That translation can be either vertical or horizontal, and may be done either before or after the reflection.

Reflecting f(x) across the y-axis means it becomes ...

  f(-x) = 3(-x) +1 = -3x +1

In order to make that into -3x-5, we must add -6 to the function value:

  g(x) = f(-x) -6 = (3(-x)+1) -6 = -3x -5

F(x) will be taken to g(x) = -3x-5 by reflection across the y-axis and translation down 6 units.

Reflecting f(x) across the x-axis means it becomes ...

  -f(x) = -(3x +1) = -3x -1

In order to make that into -3x-5, we must add -4 to the function value:

  g(x) = -f(x) -4 = -(3x +1) -4 = -3x -5

F(x) will be taken to g(x) = -3x-5 by reflection across the x-axis and translation down 4 units.

__

Additional comment

As noted above, the translation can be either horizontal or vertical. For example, translating the function 2 units to the right makes it f(x-2). Then reflection across the y-axis replaces x by -x, so we have ...

  g(x) = f(-x-2) = 3(-x-2)+1 = -3x -6 +1 = -3x -5

To get g(x), we could translate right 2 units, then reflect across the y-axis.

We also note that point (-1, -2) is shared by f(x) and g(x), so reflection horizontally across the line x=-1, or vertically across the line y=-2 would also give the required transformation.

[tex]\textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &400\\ t=\textit{elapsed time}\dotfill &20\\ h=\textit{half-life}\dotfill &4 \end{cases} \\\\\\ A=400\left( \frac{1}{2} \right)^{\frac{20}{4}}\implies A=400\left( \frac{1}{2} \right)^5\implies A=12.5[/tex]

The function 1 is,

So rate of function is 1/3.

From the table function 2 it can be observed that the value of y is one third of x. The mathematical expression of function 2 is,

So rate of function 2 is also 1/3.

Thus function 1 and function 2 have the same rate, 1/3.

Answer: Width x length x height = volume

i think

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Based on the fact that Gordon has 1/2 gallons of paint and is able to fill up bowls in 7 tables, the number of gallons of paint each table has is 1/14 gallons of paint

Gordon has 1/2 gallons of paint and knows that this amount of paint can given each bowl in all 7 tables, a full bowl of paint.

The amount of paint that each bowl gets can therefore be calculated by the formula:

= Gallons of paint Gordon has / Number of tables

Solving for the paint each bowl has gives:
= 1/2 ÷ 7

= 1/2 x 1/7

= 1/14 gallons of paint

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The correct answer is [a] m<BCD - m<DBC =10°

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively.

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles. The angle formed by the rays lying perpendicular to the two crossing curves at the point of junction is another property of intersecting curves.

Angle can also refer to the length of a rotation or an angle. This metric represents the relationship between a circular arc's length and radius. The arc is centered at the vertex and defined by the sides in the case of a geometric angle. When there is a rotation, the arc is defined by any other point and the rotation's image, and it is centered at the rotation's center.

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D. The function is neither above nor below its bounds.

An unbounded function is one that is not bounded. The function is referred to as being bounded (from) above by A if it has real values and f(x) A for all x in X. The function is referred to as being bounded by B (from below) if f(x) B for all x in X

A sequence is considered to be constrained if it has bounds above and below. Unbounded sequences exist when a sequence is not bounded. Because 1/n1 for all positive integers n, for instance, the sequence 1/n is confined above. Further, it

If there is an integer 2 such that for all x from the domain D(f), one has f (x) 2, we say that a real function f is bounded from below. If there is a number K such that for every x from the domain D(f), one has f (x) 2, then we say that a real function f is bounded from above.

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Answer:

7 days.  

Step-by-step explanation:

139 = 202 - 9d  subtract 2002 from both sides of the equation

-63 = -9d  Divide both sides of the equation by -9

7 = d

The right information of the circle is as follows:

The line LN is the tangent to the circle O.

Tangent to a circle is a line that touches the circle at one point.

The point where tangent meets the circle is called point of tangency.

The tangent is perpendicular to the radius of the circle, with which it intersects.

Tangent to a circle is always perpendicular to the radius.

Therefore, the correct information from the circle can be found as follows:

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Answer: A) ON is a radius of the circle

Step-by-step explanation:

The line ON starts from the midpoint of the circle showing that it is half of the distance(radius)

ANSWER:

C. point of concurrency

STEP-BY-STEP EXPLANATION:

The only point where these lines cross each other is called the point of concurrency.

Therefore:

The point of concurrency is a point at which three or more lines intersect.

The correct answer then is C. point of concurrency

The equations will be a+ y ≤ 13, since Micaela can't work more than 13 hours and also she needs to earn at least $140 each week, so other equation will be 13a + 10y ≥ 140.

Inequality, a declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.

a = number of hours spent tutoring

y = number of hours spent landscaping

Micaela can't work more than 13 hours, so a + y ≤ 13.

Also, she needs to earn at least $140 each week, so 13a + 10y ≥ 140.

Using intercepts, you may graph things in this format on paper. They must be transformed into slope-intercept form in order to be graphed on a standard graphing calculator.

For instance, if a = 12 and y = 2, then a + y = 13 hours, and 12(13) + 2(10) = $176. Micaela puts in her maximum number of hours and earns more than she should.

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Answer:

$3.33 (rounded) per hour

Step-by-step explanation:

The sprinklers run 5 hours each day. The monthly (30 days) water bill is $500. How much does it cost to run the sprinklers for an hour? Round your answer to the nearest cent.

hours run per month = daily hours × days in month

hours run per month = 5 × 30

hours run per month = 150

if the total bill was $500 for 150 hours then:

$500 ÷ 150 = $3.33 (rounded) per hour.

Answer:

The number of cells that will be present is;

Explanation:

Given that the function f(x) models the number of virus cells present in a sample after x minutes.

Aftere 1 1/2 minutes, the number of cells present can be calculated by substituting;

In the model.

Substituting, we have;

Therefore, the number of cells that will be present is;

The inequality that represents this situation is Option(A.) 3c - 75 ≤ 3.

Given:

Darla wants to buy 3 identical gift cards.

The total cost is no more than $3 above or below $75.

Let's assume that the cost of one gift card is $c.

Total Cost of 3 gift cards = $3c

Also, the total cost is no more than $3 above or below $75.

Hence, it would be -75 and less than 3.

Therefore, the inequality is 3c - 75 ≤ 3.

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Answer:

Y/n had nothing in his hand. His friend gave him 8 oranges for him to eat. But on his way home he saw a hungry child and decided to give away 4 oranges to the child. How many oranges does he have now?