\( - \frac{2}{3} + 4 \times \frac{1}{3} \)
​

Answer:

1 2/6

Step-by-step explanation:

3 1/2 - 2 and 6 inches

change 6 to 1/6

3 1/2 = 3/6

2 1/6 = 1/6

-

_____

1 2/6

The values are:b = -2i - j + 6k, 2a = 2i + 10j - 8k, 3b = -6i - 3j + 18k, |a| = sqrt(42), |a - b| = sqrt(145).



To find the values of b, 2a, 3b, |a|, and |a - b|, substitute the given values of a and b into the equations.

Given:a = i + 5j - 4k

b = -2i - j + 6k

1. b:

Substituting the values of b:b = -2i - j + 6k

2. 2a:

Multiply each component of a by 2:2a = 2(i + 5j - 4k)

  = 2i + 10j - 8k

3. 3b:

Multiply each component of b by 3:3b = 3(-2i - j + 6k)

  = -6i - 3j + 18k

4. |a|:

Calculate the magnitude of a using the formula:|a| = sqrt((i)^2 + (5j)^2 + (-4k)^2)

   = sqrt(1 + 25 + 16)

   = sqrt(42)

5. |a - b|:

Calculate the magnitude of the vector (a - b):|a - b| = |(i + 5j - 4k) - (-2i - j + 6k)|

        = |3i + 6j - 10k|

        = sqrt((3)^2 + (6)^2 + (-10)^2)

        = sqrt(9 + 36 + 100)

        = sqrt(145)

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Answer:

Seven cups of canned apples are required to make apple pie recipe

Step-by-step explanation:

The weight of one canned apple is 0.45 pounds

Weight of total canned apple required to make the apple pie recipe is 3 pounds.

Total number of cups of canned apples required

\(= \frac{3}{0.45} \\= \frac{300}{45} \\= \frac{20}{3} \\\)

So approximately seven cups of canned apples are required to make apple pie recipe

Answer:

-20, -8, -3, 0, 16, 44

Step-by-step explanation:

The roots of the function f ( x ) are x = 1 and x = 3

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = x⁴ - 13x³ + 38x² - 23x - 3

On simplifying , we get

The possible factors of the constant term (-3) are ±1 and ±3, while the possible factors of the leading coefficient (1) are ±1.

Now, we can test these factors by substituting them into the function and checking if the result is zero:

f(1) = (1)⁴ - 13(1)³ + 38(1)² - 23(1) - 3 = 1 - 13 + 38 - 23 - 3 = 0

f(-1) = (-1)⁴ - 13(-1)³ + 38(-1)² - 23(-1) - 3 = 1 + 13 + 38 + 23 - 3 = 72

f(3) = (3)⁴ - 13(3)³ + 38(3)² - 23(3) - 3 = 81 - 351 + 342 - 69 - 3 = 0

f(-3) = (-3)⁴ - 13(-3)³ + 38(-3)² - 23(-3) - 3 = 81 + 351 + 342 + 69 - 3 = 840

From the above calculations, we can see that f(1) = f(3) = 0. This means that x = 1 and x = 3 are roots of the polynomial function

Hence , the function is solved and x = 1 and x = 3

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The station wagon will be worth approximately $15,122 in 2010.

To calculate the value of the car in 2010, we need to take into account the annual depreciation rate of 9% and the initial purchase price of $24,500 in 2002.

First, let's calculate the depreciation for each year from 2002 to 2010. The depreciation rate is 9%, which means the car's value decreases by 9% each year.

Year 2002:

Value = $24,500

Year 2003:

Depreciation = 9% of $24,500 = $2,205

Value = $24,500 - $2,205 = $22,295

Year 2004:

Depreciation = 9% of $22,295 = $2,007.55 (rounded to the nearest dollar)

Value = $22,295 - $2,007 = $20,288

Continuing this pattern, we can calculate the value for each subsequent year:

Year 2005:

Value = $20,288 - ($20,288 * 0.09) = $18,518

Year 2006:

Value = $18,518 - ($18,518 * 0.09) = $16,904

Year 2007:

Value = $16,904 - ($16,904 * 0.09) = $15,414

Year 2008:

Value = $15,414 - ($15,414 * 0.09) = $14,057

Year 2009:

Value = $14,057 - ($14,057 * 0.09) = $12,821

Finally, in 2010:

Value = $12,821 - ($12,821 * 0.09) = $11,639.89 (rounded to the nearest dollar)

Therefore, the station wagon will be worth approximately $15,122 in 2010.

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Answer:

Taryn charges $12.50, Alastiar charges $17.50, Alastair earns more per hour

Answer:

  a.  0

Step-by-step explanation:

You want the limit of (k(x) -h(x))/k(x) as x approaches 0 when k(x) = sin(x)/x {x≠0} and h(x)=x+1 {x<1}.

Since we're concerned about the limit as x → 0, we don't have to be concerned with the fact that the expression is undefined at x = 0.

The function h(x) is defined as h(0) = 1, so we can just be concerned with the value of ...

  lim[x→0] (k(x) -1)/k(x)

The limit of k(x) as x → 0 is 1, so this becomes ...

  lim[x→0] (k(x) -1)/k(x) = (1 -1)/1 = 0

At x=0, sin(x)/x is the indeterminate form 0/0, so its limit there can be found using L'Hôpital's rule. Differentiating numerator and denominator, we have ...

  lim[x→0] sin(x)/x = lim[x→0] cos(x)/1 = cos(0) = 1

The fact that k(0) = 0 is irrelevant with respect to this limit.

__

Additional comment

We like to use a graphing calculator to validate limit values. The attachment shows the various functions involved. It also shows that as x gets arbitrarily close to 0 from either direction, the value of g(x) does likewise. This is all that is required for (0, 0) to be declared the limit. The lack of definition of g(x) at x=0 simply means the relation has a (removable) discontinuity there.

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Answer:

22% decrease

Step-by-step explanation:

(1100-900)/900 = .22

Answer:

5/6 in fraction form and 1.2 in decimal form

Step-by-step explanation:

4/5 divided by 2/3 is equal to 5/6 in fraction form and 1.2 in decimal form

Each points can be determine as the ordered pair (x, y) with inequalities;

W  ⇒  x ≥ 5 and y < -1

X  ⇒   x ≥ 5 and y > 1

Y  ⇒   x < -5 and y ≥ 5

Z  ⇒   x < -1 and y < -4

A chart in x-y hub plot is a visual portrayal of numerical capabilities or data of interest on a Cartesian direction framework. The horizontal, or independent, variable is represented by the x-axis, while the vertical, or dependent, variable is represented by the y-axis. To demonstrate the connection between the two variables, a line or curve is drawn between the plotted points.

According to the graph each points can be determine with inequalities;

W = (5, -2) ⇒  x ≥ 5 and y < -1

X = (5, 2) ⇒    x ≥ 5 and y > 1

Y = (-6, 5) ⇒   x < -5 and y ≥ 5

Z = (-2, -5) ⇒  x < -1 and y < -4

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A value that is less than 2 1/5% from the given data is 0. 0215. Option A is the correct answer.

A fraction represents a part of a number or any number of equal parts. There is a fraction, containing numerator and denominator.

To find a value that is less than 2 1/5% we need to find the decimal number of a given fraction. to convert the given fraction into decimal form we need to divide the given fraction by 100.

= 2 1/5% / 100

= (2 + (1/5)) / 100

= 0.022

A value that is less than 0.022 from the given data is 0. 0215.

Therefore, a value less than 2 1/5% is 0. 0215.

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Answer:

Step 1

Step-by-step explanation:

Concepts:

Solving:

Let's go through the order of operations to solve the expression, so we can see the mistake in the steps.

(24 + 3 + 10) - 14 + 2

1. Add 24 and 3 together

2. Add 27 and 10 together

3. Subtract 14 from 37

4. Add 23 and 2 together

Now, let's compare these steps to the ones given.

There's a mistake in Step 1 because 24 and 3 was divided instead of added; 24 + 3 = 27, not 8.

wait nvm

one candy bar costs 0.60 cents

multiply this number by 2 and get $1.20

Answer:

Step-by-step explanation:

function notation

1) -13

2) -4

3) 7

4) 23

5) 13

6) -4

7) 14

8) -1

9) 15

10) 0

function operations

1) -3x^2 + 11x -4

2) 6x - 12

3) 3x^2 - 2x + 5

4) x^2 - 4x + 5

5) 27x^2 - 32x

6) 2x^5 + 4x^4 - 5x^3 - 10x^2

7) -6x^4 + 8x^3 + 15x^2 - 20x

8) 3x^4 - 2x^3 - 16x^2

Answer:

c

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The perpendicular line bisect the base of isosceles triangle.

Then,

9^2=y^2-x^2

81=324-243

81=81

So the correct answer is D

I Hope this will be helpful for you

A quarterback throws an incomplete pass. The height of the football at time t is modeled by the equation h(t) = –16t² + 40t + 7. Rounded to the nearest tenth, the solutions to the equation when h(t) = 0 feet are –0.2 s and 2.7 s.

the solution to be eliminated is -0.2s this is because time do not have negative values

ax² + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a.

It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be real or complex.

Considering the given function, the answer is both real one is negative the other is positive.

The solution in this case represents time, and time of negative value do not apply in real life

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Answer:

21x - 18y = 30

Step-by-step explanation:

7x - 6y = 10

multiple both sides by 3

3(7x - 6y) = 3(10)

21x - 18y = 30

Answer:

Step-by-step explanation:

Earning last week:

Considering there are 52 weeks in a year, Alexander made in one year:

Given :

To Find :

Solution :

According to the question ,

Profit earned in a year :-

Step-by-step explanation:

X = sin130° + cos130°

= sin50° - cos50°

= sin50° - sin40°.

sin50° is definitely greater than sin40°, therefore X > 0. (3)

The area of the computer monitor display is approximately 0.103 square meters, with three significant figures.

The area of the monitor display in square meters is found by converting the measurements from inches to meters and then calculate the area.

The conversion factor from inches to meters is 0.0254 meters per inch.

Width in meters = 14.60 inches * 0.0254 meters/inch

Height in meters = 10.95 inches * 0.0254 meters/inch

Area = Width in meters * Height in meters

We calculate the area:

Width in meters = 14.60 inches * 0.0254 meters/inch = 0.37084 meters

Height in meters = 10.95 inches * 0.0254 meters/inch = 0.27813 meters

Area = 0.37084 meters * 0.27813 meters = 0.1030881672 square meters

Now, we determine the number of significant figures.

The measurements provided have four significant figures (14.60 and 10.95). However, in the final answer, we should retain the least number of significant figures from the original measurements, which is three (10.95). Therefore, the answer should have three significant figures.

Thus, the area of the monitor display in square meters is approximately 0.103 square meters, with three significant figures.

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The probability of the spinner stopping at a polka-dot section and then stopping at a solid white section is 1/8.

The probability of the spinner stopping at a polka-dot section and then stopping at a solid white section is 1/4.A spinner is a gambling tool used for games and competitions. Spinning games are frequently based on chance, and players frequently wager money or other objects on the result.

When it stops, a pointer will land on one of many different numbered segments of the spinner, each of which corresponds to a particular reward or consequence. Spinning games are frequently based on chance, and players frequently wager money or other objects on the result. Probability is the study of the likelihood of events taking place.

Probability is expressed as a fraction, decimal, or percentage and is always between 0 and 1. The probability of an event can be calculated using the following formula: Probability = number of favorable outcomes / total number of possible outcomes. Given the spinner has a polka-dot section, 2 white sections, and 1 shaded section, it has a total of 4 sections.

Therefore, the probability of the spinner stopping at a polka-dot section is 1/4.Also, after the first spin, the spinner still has 2 white sections. Therefore, the probability of stopping at a solid white section is 2/4 or 1/2 (since there are only 2 possible outcomes after the first spin).

To determine the probability of the spinner stopping at a polka-dot section and then stopping at a solid white section, we must multiply the probability of each event.1/4 × 1/2 = 1/8

Hence, the probability of the spinner stopping at a polka-dot section and then stopping at a solid white section is 1/8.

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To determine the probability that a randomly selected guest is accepted by the host, we need more information about the scenario. For instance, we should know the total number of guests and the number of accepted guests. Let's say there are 'n' guests, and 'a' guests are accepted by the host.
Step 1: Identify the terms.
- n: Total number of guests
- a: Number of accepted guests
Step 2: Calculate the probability.
To find the probability, we'll divide the number of accepted guests (a) by the total number of guests (n). So, the probability is:
P(Accepted) = a / n
Step 3: Identify the type of probability.
In this case, the probability we've calculated is the "marginal probability," as it represents the likelihood of a single event occurring (a guest being accepted) without considering any other factors or events.

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The total area of the room is 37.6376 and the no. of cans required to paint the wall is 3 cans.

The measurement of two of the walls is 2.86 metres and 3.16 metre

Area of the two walls = 2(length x breadth)

Area = 2(2.86 x 3.16) = 18.0752 m²

The measurement of the other two walls is 2.86 metres and 3.42 metres

Area of the two walls = 2(length × breadth)

Area = 2(2.86 × 3.42) = 19.5624 m²

Total area = 18.0752 + 19.5624 = 37.6376 m²

If one can of paint can cover 15 m², the no. of cans required to paint the bedroom will be

No. of cans = Total area/Area covered by one can of paint

No. of cans = 37.6376/15 = 2.5091 = 3 cans (approx.)

Answer:1815 euros left

Step-by-step explanation:

The perimeter of the larger rectangle found using the scale factor of 4/5 is 56.25 cm.

What is meant by the perimeter of a figure?

A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges.

Given,

the scale factor = 4/5

The perimeter of the smaller rectangle = 45 cm

We are asked to find the perimeter of the larger rectangle(x).

Here both the rectangle are similar figures.

So the scale factor is the ratio of their corresponding sides.

But since the perimeter of a rectangle is the sum of the length of its sides.

The scale factor is also the ratio of the perimeter of the smaller rectangle to the larger rectangle.

Perimeter of small rectangle/Perimeter of large rectangle = 4/5

45/x = 4/5

x = 45 * 5 / 4 = 56.25cm

Therefore the perimeter of the larger rectangle found using the scale factor of 4/5 is 56.25 cm.

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Answer:

x = 2 or x = -4

Step-by-step explanation:

-5|x + 1| + 3 = -12

Add -3 to both sides.

-5|x + 1| = -15

Divide 5 into both sides.

|x+1| = 3

Possibility 1:

x + 1=3

x = 2

Possibility 2:

x + 1 = - 3

x = -4

Answer:

Step-by-step explanation:

This is our absolute value equation for which we want the values of x that make it true:

-5 | x + 1 | + 3 = -12. Subtracting 3 from both sides gives us

-5 | x + 1 | = = -15. Divide both sides by -5 to get

| x + 1 | = 3

This says, in words, "how many units from 3 is -1 on a number line?"

We have the following 2 equations:

x + 1 = 3 and x + 1 = -3

Solving the first one for x:

x = 2

Solving the second one for x:

x = -4

Both 2 and -4 are 3 units from -1 on a number line.

Answer:

I need Help on this one too.

Step-by-step explanation:

The equation of line passing through points  (-3,6 ) (-2,9 ) in point slope form is y-6=3(x+3)

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The slope of line passing through  (-3,6 )  and (-2,9 )

m=9-6/-2+3

=3

Point slope form equation is y-y₁=m(x-x₁)

y-6=3(x-(-3))

y-6=3(x+3)

Hence, the equation of line passing through points  (-3,6 ) (-2,9 ) in point slope form is y-6=3(x+3)

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The mode of a dataset is the value that appears most frequently. In this case, we need to find the interval of rainfall that occurs most frequently.

From the given data, we can see that the interval "less than 0.01 inch" has the highest frequency with 165 days. Therefore, the mode of this dataset is "less than 0.01 inch"

Effective communication is crucial in all aspects of life, including personal relationships, business, education, and social interactions. Good communication skills allow individuals to express their thoughts and feelings clearly, listen actively, and respond appropriately. In personal relationships, effective communication fosters mutual understanding, trust, and respect.

In the business world, it is essential for building strong relationships with clients, customers, and colleagues, and for achieving goals and objectives. Good communication also plays a vital role in education, where it facilitates the transfer of knowledge and information from teachers to students.

Moreover, effective communication skills enable individuals to engage in social interactions and build meaningful connections with others. Therefore, it is essential to develop good communication skills to succeed in all aspects of life.

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