Let u = <-4, 3>. Find the unit vector in the direction of u, and write your answer in component form. (2 points)

Answer:

1) Equation's:

2) Number of guest and the charge:

Part 1

Turn sentences into equation's (Let 'y' be total cost and x per meal) :

(i) charges $500 and $15 per meal

(ii) charges $350 and $18 per meal

Part 2

            y  =  y

500 + 15x = 350 + 18x

18x - 15x = 500 - 350

3x = 150

x = 150/3

x = 50

Charge at guest's 50 meal:

y = 500 + 15(50)

y = $1250

Point : (50, 1250)

Answer:

Perpendicular: [tex]y=-\frac{1}{3}x+\frac{19}{3}[/tex]

Parallel: [tex]y=3x-7[/tex]

Step-by-step explanation:

So when two lines are perpendicular, that means the the slope is the reciprocal with the opposite sign so: [tex]\frac{a}{b} \text{ has a slope perpendicular to } -\frac{b}{a}[/tex]. In this case we have the equation in slope-intercept form, so it's easy to determine the slope, it's 3. So that means the perpendicular line will have a slope of: [tex]-\frac{1}{3}[/tex]. Since you have a slope of 3/1 which becomes 1/3 and also an opposite sign. This gives you the equation: [tex]y=-\frac{1}{3}x+b[/tex]. We can solve for b, by plugging in a coordinate it passes through. This is given in the problem, with it being (4, 5) = (x, y). So plugging these values in as (x, y) gives you the equation: [tex]5=-\frac{1}{3}(4)+b\implies\frac{15}{3}=-\frac{4}{3}+b\implies\frac{19}{3}=b[/tex]. This gives you the complete equation: [tex]y=-\frac{1}{3}x+\frac{19}{3}[/tex]

So when two lines are parallel, that means they have the slope, and a different y-intercept. This is because if they had the same y-intercept, then the two lines would be the same exact line. We already know the slope, it's 3. So we have the general equation: [tex]y=3x+b\text{ where b}\ne-3[/tex]. The restriction on b, was explained on the previous sentence, if b=-3, then we have the same equation, which is not parallel, they would be the same line, meaning they would intersect at infinite points, which is completely different than two lines that never intersect. So now we can plug in the given point (4, 5) to solve for b. Plugging these coordinates in gives you: [tex]5=3(4)+b\implies5=12+b\implies-7=b[/tex]. This gives you the complete equation: [tex]y=3x-7[/tex]

1 atom of C has a mass of 12 amu (atomic mass unit).

1 atom of O has a mass of 16 amu.

1 molecule of CO₂ thus has a mass of 12 + 2×16 = 44 amu.

C thus makes up 12/44 ≈ 0.27 of the total mass of CO₂, while O makes up the remaining 32/44 ≈ 0.73.

Then in a 2 kg = 2000 g block of CO₂, carbon makes up about 12/44 × 2000 ≈ 545 g.

The meter mark at which Ario wil be when Miguel starts the race is; 7.4 meters

A ratio such as the ratio 1:4 shows the proportion of two factors. In this case, it shows the ratio between the completed meters vs the remaining meters.

To find the distance, we will have to determine how much 1:4 represents in the total distance.

Total distance = 25 meters - 3 metes = 22 meters

Thus; 22 * 1/ 5 = 22/5 = 4.4

However, we also know they are three meters behind the start.

Thus, the meter mark at which Ario will be when Miguel starts the race

4.4 + 3 =7.4 meters

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Kelly used a volume of [tex]\frac{3}{4}[/tex] liters of milk at dinner.

Given we have, Initial amount of milk is [tex]2[/tex] liters.

The amount of milk used in the morning is [tex]\frac{1}{2}[/tex] Liters.

Now, Milk left = [tex]2[/tex] liters- [tex]\frac{1}{2}[/tex] liter= [tex]\frac{3}{2}[/tex] liters

[tex]\frac{3}{2}[/tex] liters used in half:

[tex]\frac{1}{2} \frac{3}{2}[/tex] = [tex]\frac{3}{4}[/tex] liters.

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Stacie did the mistake that he put the value of base in place of perpendicular and vice versa.

The triangle is geometric shape which includes 3 sides and sum of interior angle should not grater than 180°

Solution is supposed to be

[tex]tan_ (-1) (28/21) = 53.33[/tex]

Thus,Stacie did the mistake that he put the value of base in place of perpendicular and vice versa.

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Answer: D) 1/5

Step-by-step explanation:

Format for point-slope form:  y-y₁=m(x-x₁)

x1, y1 is a point on the line

m is the slope

So in this equation, m = 1/5

so, the slope is 1/5

hope this helps!

The correct statements are:

There are four ways to choose the committee.

There are three ways to form the committee if person D must be on it.

If persons B and C must be on the committee, there are two ways to form the committee.

It is given that:

A membership committee of three is formed from four eligible members.

1)

There are four ways to choose the committee.

This statement is true.

since we have to choose 3 members out of the 4 members so we can use the method of combination.

2)

There are three ways to form the committee if person D must be on it.

This statement is also true.

since D has to be in the committee, this means we have to choose 2 more people out of the three people to form the committee.

3)

If seven members are eligible next year, then there will be fewer combinations.

This statement is wrong.

Since we have to choose 3 members out of 7 members so the number of possible combinations will be:

i.e. there are 35 combinations possible.

4)

If persons B and C must be on the committee, there are two ways to form the committee.

if B and C have to be in the committee then we have to choose just one person out of the two people left.

Hence, the statement is true.

5)

If persons A and C must be on the committee, then there is only one way to form the committee.

If A and C have to be in the committee then as in last option we have to choose any one of the two person left.

so possible number of ways are 2.

Hence, the statement is false.

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Step-by-step explanation:

Hemisphere Formulas in terms of radius r:

V = (2/3)πr.

Hereof, What is the radius of a hemisphere? As latter is 4πr2 , curved surface area of a hemisphere of radius r is 2πr2 . and hence total surface area of hemisphere is 2πr2+πr2=3πr2 . Hence, radius of hemisphere is 4 cm.

La diferencia entre el denominador y el númerador de la fracción es:

64 - 8 = 56.

Tendremos una fracción de la forma:

[tex]\frac{a}{b}[/tex]

Tal que:

[tex]\frac{a}{b} = \frac{1}{8}[/tex]

[tex]a + b = 72[/tex]

Eso es un sistema de ecuaciones

Primero, podemos reescribir la primer ecuación como:

[tex]8a = b[/tex]

Ahora podemos reemplazar "b" en la segunda ecuación por "8a", así obtenemos:

[tex]a + 8a = 72\\\\9a = 72\\\\a = 72/9 = 8[/tex]

Ahora podemos obtener el valor de b:

[tex]b = 8a = 8*8 = 64[/tex]

La diferencia entre a y b es:

[tex]b - a = 64 - 8 = 56[/tex]

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The correct graph for the given sets of equation is given attached below.
Equation no 2 gives the perfect solution to the graph.

A parabola, is cross section cut out of the cone and represented by an equation [tex]Y=4ax^2[/tex]

Clearly, by property of the parabola, the curve of parabola should symmetric to its axis. From this property set of Equation (2) i.e. downward opening parabola increasing from negative 2 comma negative 3 to a maximum at 0 comma 1 and then decreasing through the point 2 comma negative 3 Holds the property of the parabola

Thus, the required solution for the sets of equation (2) is given in the attachment.

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Answer:

Step-by-step explanation:

C is equal to A. Because angle FCE is on the other side with C, it has to be equal to A

ABCD is a parallelogram (Given)

As opposite angles of a parallelogram are equal

Also

From (1) and (2)

<A is congruent to <FCE

Answer:

[tex]f^{-1}(x)=2^x+3[/tex]

Step-by-step explanation:

Given:

[tex]y=\log_2(x-3)[/tex]

To find the inverse of the given function, make x the subject.

[tex]\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b[/tex]

[tex]\implies 2^y=x-3[/tex]

Add 3 to both sides:

[tex]\implies x=2^y+3[/tex]

Swap x for [tex]f^{-1}(x)[/tex] and y for x:

[tex]\implies f^{-1}(x)=2^x+3[/tex]

If the biologist catches and tags 32 bass and from sample of 55 he found only 5 tagged then there are 352 bas in the lake.

Given Biologist catches and tags 32 bass, when sample of 55 bass is taken  then 5 are found tagged.

Population is basically number of living thing exists in a particular area.

Number of bass which are tagged in lake=32

Sample size=55

Number of bass found tagged=5

means percentage of tagged bas found is 5/32*100=1.6%

We have to calculate number of times 5 is multiplied to get 32 which is 6.4.

Number of bass in the lake=55*6.4

=352 basses.

Hence there are 352 basses in the lake if 5 are found tagged in a sample of 55.

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[tex]f(x)=x(x-3)(x+3)[/tex]

The length of C'B' after dilation using a scale factor of 3 is: D. 15 units.

Dilation is the reduction or enlargement of an image by a scale factor, whereby the original and new images are similar.

Applying the distance formula, we have:

BC = √[(8−12)² + (10−13)²]

BC = √(−4)² + (−3)²]

BC = √(16+9)

BC = √25

BC = 5 units

Applying the scale factor:

Length of C'B' = 3(5) = 15 units.

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The angle of rotation of triangle ABC to A'B'C is 105°

It should be noted that the rotation from ABC to A'B'C is in a clockwise direction.

Point B is also on the x axis and point B' is in the second quadrant.

In this case, the angle that depicts the second quadrant is 105°.

In conclusion, the correct option is D.

The complete question is:

Triangle A’ B’ C’ is the image of A B C under a rotation about the origin, (0,0)

Determine the angle of rotation

A. -105 degrees

B. -75 degrees

C. 75 degrees

D. 105 degrees

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Considering the given equation of the circle, the true statements are given as follows:

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

The equation given is:

x2 + y² - 2x - 8 = 0.

Completing the squares, the equation is given as follows:

(x - 1)² + y² = 8 + 1

(x - 1)² + y² = 9.

Researching the problem on the internet, the true statements are:

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Answer:

2x³+3x²-8x+3

Step-by-step explanation:

So we know x=½,x=1 and x=-3

Then (2x-1)(x-1)(x+3) are the factors

(2x-1)[(x²+3x-x-3)]

(2x-1)[(x²+2x-3)]

2x³+4x²-6x-x²-2x+3

2x³+3x²-8x+3

Answer:

Line or scatter graph.

Step-by-step explanation:

I prefer line, although some of the points deviate a bit.  But the line shows a definite relationship between mass and length.

See attached graph.

Answer:

All of these definitions are correct.

Since it has a variable in the denominator, the function f(x) is a parent function classified as rational.

Rational functions are functions that have the input variable, be it x, t, or any other, in the denominator.

The most simple example is given by:

[tex]f(x) = \frac{1}{x}[/tex].

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Answer: Reciprocal

Step-by-step explanation:

Reciprocal functions are functions that contain a constant numerator and x as its denominator. Its parent function is y = 1/x.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Question reads....}[/tex]

[tex]\textbf{Which set of data does not have a mode?}[/tex]

[tex]\huge\textbf{The choices that you have provided:}[/tex]

[tex]\textbf{(A) 1, 2, 5, 6, 8}[/tex]

[tex]\textbf{(B) 1, 3, 5, 5, 6}[/tex]

[tex]\textbf{(C) 1, 5, 5, 5, 5}[/tex]

[tex]\textbf{(D) 1, 1, 1, 2, 2}[/tex]

[tex]\huge\textbf{Okay, so let's get the understanding}\\\\\huge\textbf{of the word mode is:}[/tex]

[tex]\large\textbf{The best way to understand what \boxed{\bf mode} it is known as}\\\\\large\textbf{the number you see MORE THAN once. }[/tex]

[tex]\huge\textbf{Now that we got that information out of}\\\\\huge\textbf{the way, we can answer your question by}\\\\\huge\textbf{doing process of elimination.}[/tex]

[tex]\huge\textsf{Option A.}[/tex]

[tex]\textbf{1, 2, 5, 6, 8}[/tex]

[tex]\large\textbf{None of the numbers r.e.p.e.a.t so this cann be your}\\\\\large\textbf{answer.}[/tex]

[tex]\huge\textsf{Option B.}[/tex]

[tex]\textbf{ 1, 3, 5, 5, 6}[/tex]

[tex]\large\textbf{1}\rightarrow\large\textbf{ is r.e.p.e.a.t.e.d once}\\\large\textbf{3}\rightarrow\large\textbf{ is r.e.p.e.a.t.e.d once}\\\large\textbf{5}\rightarrow\large\textbf{is r.e.p.e.a.t.e.d twice}\\\large\textbf{6}\rightarrow\large\textbf{is r.e.p.e.a.t.e.d once}[/tex]

[tex]\large\textbf{Just because majority of your numbers r.e.p.e.a.t.e.d}\\\\\large\textbf{once that doesn't mean it does have a mode rarely.}\\\\\\\\\\\large\textbf{So, Option B. isn't your answer because it has a mode.}[/tex]

[tex]\huge\textsf{Option C.}[/tex]

[tex]\textbf{ 1, 5, 5, 5, 5}[/tex]

[tex]\large\textbf{1}\rightarrow\large\textbf{is r.e.p.e.a.t.e.d once}\\\large\textbf{5}\rightarrow\large\textbf{is r.e.p.e.a.t.e.d four times}[/tex]

[tex]\large\textbf{Option C. isn't your answer because it has a mode.}[/tex]

[tex]\huge\textsf{Option D. }[/tex]

[tex]\textbf{1, 1, 1, 2, 2}[/tex]

[tex]\large\textbf{1}\rightarrow\large\textbf{is r.e.p.e.a.t.e.d three times}\\\large\textbf{2}\rightarrow\large\textbf{is r.e.p.e.a.t.e.d twice}[/tex]

[tex]\large\textbf{Just because we have like two modes, it still doesn't mean}\\\large\textbf{you don't have a mode. It 's kind of cool that you have more}\\\large\textbf{than once mode.}[/tex]

[tex]\large\textbf{Option D. isn't your answer because it has a mode though}\\\large\textbf{because it has like 2 sets of modes.}[/tex]

[tex]\huge\textsf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\textsf{Option\ A. 1, 2, 5, 6, 8}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

5*8 = 40

Step-by-step explanation:

2(3) -1 = 5

3 +5 = 8

area = 5*8 = 40

Answer:

formula-Area=l×b

Step-by-step explanation:

Length (l)=2x-1

Breadth(b)=x+5

We know that,

Area(A)=l×b

=(2x-1)×(x+1)

=(2×3-1)×(3+1)

=5×4

=20cm*2*

Answer:

43.2 m square is ur answer .

Answer:

43.2 m^2

Step-by-step explanation:

The area of a rectangle is the width times the length.

Area = (9.6 m)*(4.5 m)

Area = 43.2 m^2

For the linear function in the graph, we have that:

A linear function is modeled by:

y = mx + b

In which:

The line goes through point (0,-4), hence:

The y-intercept is of -4.

The function also goes through point (2,2), hence the slope is:

m = (2 - (-4))/(2 - 0) = 6/2 = 3.

Then, the equation of the line is:

y = 3x - 4.

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Answer: $$y=-2/3x+2$$

Explanation:  Given that we have the slope and a point on the graph we can use the point slope formula to find the equation of the line.

option third "The area of parallelogram ABCD is equal to the area of parallelogram EFGH" is correct.

In two-dimensional geometry, it is a plane shape having four sides, in which two pairs of sides are parallel to each other and equal in length. The sum of all angles in a parallelogram is 360°.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

The area of the parallelogram is:

A = b×h

Here b is the base length and h is the height

In ABCD parallelogram:

A = (3)×(3)

A = 9 square units

EFGH parallelogram:

a = (3)×(3)

A = 9  square units

The area of parallelogram ABCD is equal to the area of parallelogram EFGH.

Thus, option third "The area of parallelogram ABCD is equal to the area of parallelogram EFGH" is correct.

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The ratio of orange juice to apple juice to grape juice is 6: 3 : 2

A ratio says how much of one thing there is compared to another thing.

Therefore, we are comparing the numbers of juice produce by a bottling company.

Hence,

number of orange juice = 24

number of apple juice = 12

number of grape juice = 8

Therefore, the ratio of orange juice to apple juice to grape juice is as follows:

ratio = 24 : 12 : 8

divide through by 4

ratio = 6: 3 : 2

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