Jenna believes that she doesn't have an aptitude for statistics, so doesn't put much effort into her statistics class. She performs poorly in the class, supporting her initial belief. This is an example of a(n):

Let , a, b and c be the length of three sides of triangle, represented in terms of vectors as [tex]\vec{a},\vec{b},\vec{c}[/tex].

Now, vector of same Magnitude acts as normal vector to each side.

So, equation of any vector p having normal q is given by

      [tex]\vec{p} \times\vec{q}[/tex]

Now sum of three vector and it's normal is given as

    [tex]=\vec{a} \times\vec{a}+\vec{b} \times\vec{b}+\vec{c} \times\vec{c}\\\\=0+0+0\\\\=0[/tex]

Cross product of two identical vectors is Zero.

[tex]\rightarrow \vec{i} \times\vec{i}=0[/tex]

The sum of the outward normal vectors of a triangle's sides is always 0 due to vector closure around the triangle.

Let us denote the vertices of the triangle as A, B, and C. The sides of the triangle are AB, BC, and CA. We need to show that the sum of the outward normal vectors of these sides is zero.

Let u be the outward normal vector of side AB.

Let v be the outward normal vector of side BC.

Let w be the outward normal vector of side CA.

These normal vectors are each associated with a side of the triangle and have the same length as the corresponding side.

For any triangle, the vector from one vertex to another can be expressed as the difference of position vectors:

AB = B - A

BC = C - B

CA = A - C

The normal vector u to side AB can be aligned such that u is perpendicular to AB and has magnitude equal to the length of AB.

Similarly, v is perpendicular to BC and has magnitude equal to the length of BC.

Similarly, w is perpendicular to CA and has magnitude equal to the length of CA.

To show that the sum of these vectors is zero, consider that the sum of vectors around a closed polygon (in this case, the triangle) is zero. The outward normal vectors form a closed system since each side’s normal vector effectively cancels out with the adjacent ones due to their perpendicularity and length.

Thus:

u + v + w = 0.

Answer:

Part A) In the scale drawing the length of the swimming pool is 10 cm and the width is 5 cm

Part B) The actual length of the bus is 45 ft

Step-by-step explanation:

Part A) Make a scale drawing of the swimming pool where 1 centimeter represents 5 meters

we know that

The scale is [tex]\frac{1}{5} \frac{cm}{m}[/tex]

To find out the dimensions of the pool in the scale drawing, multiply the actual dimensions by the scale factor

Find the length in the scale drawing

[tex]\frac{1}{5} \frac{cm}{m}(50\ m)=10\ cm[/tex]

Find the width in the scale drawing

[tex]\frac{1}{5} \frac{cm}{m}(25\ m)=5\ cm[/tex]

Part B) What is the actual length of the bus?

we know that

The scale is [tex]\frac{0.5}{5} \frac{in}{ft}=0.1\frac{in}{ft}[/tex]

The length of the school bus is 4 1/2 inches on the scale drawing

To find out the actual length of the bus, divide the length in the scale drawing by the scale

Convert mixed number to an improper fraction

[tex]4\frac{1}{2}\ in=\frac{4*2+1}{2}=\frac{9}{2}\ in[/tex]

Find the actual length of the bus

[tex]\frac{\frac{9}{2}\ in}{0.1\frac{in}{ft}}=45\ ft[/tex]

Answer:

Slope and y-intercept

Step-by-step explanation:

The complete question is shown in the image attached with.

For each trip an initial fee of $ 25 is charged and $ 0.10 is charged for each vertical meter descended.

Since, for each vertical meter the charge is $ 0.10, for x meters the charges will be $ 0.10x. So,

Total charges of the trip would be:

Total charges/fee = Initial Fee + Fee for x meters

y = 25 + 0.10x

y = 0.10x + 25

The general slope intercept form of the equation of the line is:

y = mx + c

Where,

m = slope of the line

c = y-intercept

Compairing both the equations given above we, get:

Slope of line = m = 0.10

y-intercept = c = 25

So, the given statements gives us the slope and the y-intercept of the graph.

Answer:

Slope and y-intercept

Step-by-step explanation:

Final answer:

The maximum length of the playground is 38 meters, given that the perimeter cannot exceed 120 meters and the width cannot exceed 22 meters. The possible lengths are therefore from 0 to 38 meters.

Explanation:

Possible Lengths of the Playground

Given that the maximum width (w) is 22 meters and the maximum perimeter is 120 meters, we can substitute these values to find the maximum length:

The maximum length of the playground is 38 meters. However, the length can be any value less than or equal to 38 meters, so the possible lengths of the playground are from 0 meters to 38 meters.

Answer:

Step-by-step explanation:

Let x represent the amount invested at 9%. Then Roberto's interest was ...

  x(9%) +(10000-x)(6%) = 810

  0.03x + 600 = 810 . . . . . . . . . simplify

  0.03x = 210 . . . . . . . . . . . . . . . subtract 600

  x = 210/0.03 = 7000 . . . . . . . divide by the coefficient of x

Roberto invested $7000 at the higher interest rate.

To solve the problem, set up a system of equations using x and y for the amount invested at 6% and 9% respectively. Solve the system of equations to find the values of x and y, which represent the amounts invested at each interest rate. Roberto invested $3000 at 6% and $7000 at 9%

To solve this problem, we can set up a system of equations. Let x represent the amount invested at 6% and y represent the amount invested at 9%. The equation for the total amount invested is x + y = $10000. The equation for the total interest earned is 0.06x + 0.09y = $810. We can solve this system of equations to find the values of x and y.

Therefore, Roberto invested $3000 at 6% and $7000 at 9%.

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Answer: so in the first 7 games, eh scored between 3 and 18 touchdowns.

if you assume there is a even distribution, you will get a media of (18 -3) /2 + 3 = 10.5

so yes, in theory he will score 10.5 more or less.

the first error is assuming that he will score at least 10.5 on watching this result, 10.5 is the most probable number, not the minimum.

the second problem here, is that you are doing statistics with just 7 samples, that is not enough samples to do proper statistics.

Answer:

The answer to your question is: length = 14 ft; width = 3 ft

Step-by-step explanation:

Data

Area = 42 ft²

length = 8 + 2w

w = width = ?

length = ?

Formula

Area = length x width = l x w

Substitution

                     42 = (2w + 8)w

                     42 = 2w² + 8w

                     2w² + 8w - 42 = 0

                                                                  Dividing by 2

                      w² + 4w - 21 = 0                 Factorize

                     (w + 7) (w - 3) = 0

                     w1 = -7                      w2 = 3

     It's not possible to have negative widths

So the answer is w = 3 ft

      length = 2(3) + 8

      length = 6 + 8

      length = 14 ft

The length and width of the rectangle barn are 14 feet and 3 feet, respectively.

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

Let the width of the rectangle be represented by x. Therefore, the dimension of the barn is,

Width = x

Length = 2x + 8

The area of a rectangular wall of a barn is 42 square feet.

Area = Width × Length

Area = x × (2x+8)

42 square feet = x(2x + 8)

42 = 2x² + 8x

2x² + 8x - 42 = 0

x² + 4x - 21 = 0

x² + 7x - 3x - 21 = 0

x(x + 7) - 3(x + 7) = 0

(x + 7)(x - 3) = 0

x = -7, 3

Since width can not be negative, therefore, the length and the width of the wall of the barn are,

Width = x = 3

Length = 2x+8 = 2(3)+8 = 14

Hence, the length and width of the rectangle barn are 14 feet and 3 feet, respectively.

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Answer:8,400. I think that is the answer. Hope you get it right.

Answer:

1) 6840

2) 4845

3) 1050

Step-by-step explanation:

1) How many different ways are there to choose a chairman, assistant chairman, and a treasurer department of 20 people?

As it ordered:

C   AC   TD  

20    19      18   = 20.19.18 = 6840

2) How many ways are there to choose a committee of 4 people from this same committee?

Not ordered:

C₂₀,₄ = 20!   = 20.19.18.17.16! = 20.19.18.17 = 4845

         16! 4!        16! 4.3.2.1             4.3.2.1

3) If the committee is required to be comprised of 2 women and 2 men, and there are 5 women in the department, how many different committees are possible?

5 women and 15 men

committee: 2 w and 2 m

C₁₅,₂*C₅,₂ = 105*10=1050

C₁₅,₂ = 15!   = 15.14.13! = 15.14 = 105

         13! 2!     13! 2.1           2

C₅,₂ = 5!   = 5.4.3! = 5.4 = 10

         3! 2!   3! 2.1      2

Answer:

  6.44×10⁷ g

Step-by-step explanation:

The scenario seems unlikely, as a brachiosaurus weighs about 6.9 times as much as a tyrannosaur. The sum of the two weights is ...

  8.16×10³ kg + 1.24×10⁵ lb

  = 8.16×10³ kg + (1.24×10⁵ lb)/(2.2046 lb/kg)

  = 8.16×10³ kg + 5.62×10⁴ kg

  = 6.44×10⁴ kg . . . . . rounded to 3 significant figures

  = 6.44×10⁷ g . . . . . . weight of not-so-hungry tyrannosaur

_____

1 kg = 10³ g

Answer: Hi!

Let's start, you have 3 boxes and 3 types off eggs inside of each. The fact that they each box is labelled incorrectly means that inside the box labelled Large, only can be the set of small or mixed eggs.

So, let's suppose we open this Box labelled LARGE and inside of it we find the small eggs.

now we have two remaining boxes, the labeled SMALL and the labelled MIXED.

the MIXED can only contain the set of large eggs or the set of small, because you know that is wrong labelled, and also you know that the small eggs are in the first box that you oppened, so here are the large eggs, and now in the last box is the last set of eggs, the mixed one.

So you only will need to open one box to know which eggs are in what box.

Answer:

We can form a triangle if none of the resulting pieces is at least 1/2, i.e. if no ... It is not hard to show that if you choose a point randomly in this triangle, the distances to the three ... of lengths that you obtain by breaking a stick at two random points. ..... we get line segments joining the midpoints of the edges of the triangle.

Step-by-step explanation:

The probability that three pieces from breaking a unit length stick can form a triangle, based on the triangle inequality theorem and geometric probability principles, is 1/4.

The question belongs to the area of Mathematics called geometric probability. Here, we are asked to find the probability that three stick pieces formed from a unit length stick can form a triangle.

The rule which applies to this situation is the triangle inequality theorem. This theorem states that for any triangle, the length of any side (say c) must be less than the sum of the lengths of the other two sides (say a and b). In mathematical terms, a + b > c.

Considering the above theorem, since we break the stick into three pieces simultaneously, the break points must be such that each piece is less than 0.5 units to be able to form a triangle. In this case, the length of the longest piece (c) will be less than the sum of the lengths of the other two pieces.

So, to form a triangle, each piece must be less than 0.5 in length. The region where this condition is satisfied forms a triangle in a unit square, thus giving a geometric probability of 1/4. Hence, the probability that the three pieces can form a triangle is 1/4.

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When trying to find a root of a number ( the little number included with the square root symbol) this is the same as raising the number to that fraction.

Example : ∛5 would be the same as 5^1/3

So in the given problem the 5th root can be written as x^1/5

Now the number is 13^3, so to simplify the 5th root, the value could be written as 13^3/5

Answer:

When trying to find a root of a number ( the little number included with the square root symbol) this is the same as raising the number to that fraction.

Example : ∛5 would be the same as 5^1/3

So in the given problem the 5th root can be written as x^1/5

Now the number is 13^3, so to simplify the 5th root, the value could be written as 13^3/5

Step-by-step explanation:

Answer:

24 minutes.

Step-by-step explanation:

Let D represent the distance from school to home and T represent time.

We have been given that your brother takes 40 minutes to get to school.

[tex]\text{Speed}=\frac{\text{Distance}}{\text{Time}}[/tex]

[tex]\text{Your brother's speed}=\frac{D}{40}[/tex]

You take 30 minutes to get to school.

[tex]\text{Your speed}=\frac{D}{30}[/tex]

Your brother left 4 minutes before you did, so distance traveled by him would be:

[tex]\frac{D}{40}\times (T+8)[/tex]

You speed: [tex]\frac{D}{30}\times T[/tex]

You will catch your brother, when both distances would be same:

[tex]\frac{D}{40}\times (T+8)=\frac{D}{30}\times T[/tex]

Cross multiply:

[tex]30D(T+8)=40DT[/tex]

Use distributive property:

[tex]30DT+240D=40DT[/tex]

[tex]30DT-30DT+240D=40DT-30DT[/tex]

[tex]240D=10DT[/tex]

Switch sides:

[tex]10DT=240D[/tex]

[tex]\frac{10DT}{10D}=\frac{240D}{10D}[/tex]

[tex]T=24[/tex]

Therefore, it will take you 24 minutes to catch up your brother.

To catch up to your brother who has a 4-minute head start, it will take you 12 minutes.

To determine how long it will take for you to catch up with your brother on the way to school, we need to consider the different walking speeds and the time advantage your brother has.

First, let's determine your walking speeds. If your brother takes 40 minutes to reach school and you take 30 minutes for the same route, then assuming you both walk at a constant speed, we can say that your walking speed is 4/3 times faster than your brother's speed because 40 minutes divided by 30 minutes equals 4/3.

Now, given that your brother has a 4-minute head start, let's calculate the time it takes for you to catch up to him:

Therefore, it will take you 12 minutes to catch up with your brother.

Answer:

[tex] -4 = m[/tex]

Step-by-step explanation:

According to the Point-Slope Formula, y - y₁ = m(x - x₁), m represents the rate of change [slope], so in this case, -4 is our slope.

I am joyous to assist you anytime.

Answer:

a.0011100000

b.1010010001

c.0111001110

Step-by-step explanation:

We are given that a universal set

U={1,2,3,4,5,...10}

We  have to express each given set with bit strings , where the ith bit in the string is 1 if i is in the set and 0 otherwise

a.{3,4,5}

For 1=0  because 1 is not in the given set

For 3=1, For 4=2 , For 5=1 because 3,4 and 5 are in the set

For 2=0

For 6=0

For 7=0

For 8=0

For 9=0

For 10=0

Therefore, bit string=0011100000

b.{1,3,6,10}

For 1,3,6 and 10 write 1 because these elements are present in the set and for 2,4,5,7,8,9 write 0 because these elements are not present in the set

Bit string =1010010001

c.{2,3,4,7,8,9}

Similarly

Those elements which are present in the set then for those elements write 1 otherwise 0.

Bit string =0111001110

Answer:

  3

Step-by-step explanation:

Let "a" represent Alondra's number. Then the math she performs on it is ...

  2a-6 . . . .double my number and subtract 6

  | 2a-6 | < 2 . . . . . the result is less than 2 units from zero

This absolute value expression can be "unfolded" to two of them ...

  -2 < 2a -6 < 2

Dividing by 2 gives ...

  -1 < a -3 < 1

Adding 3, we get ...

  2 < a < 4

The only whole number in this range is ...

  a = 3

Alondra is thinking of the number 3.

Answer:

$4083.21

Step-by-step explanation:

Compound interest is an interest rate that stacks on top of each other

So basically I did 3600 × 1.065 for the first year

=3834

then i did 3834 × 1.065 again to calculate the second year

=4083.21

Hope this helps! If you have any questions ask! :)

Answer:

D. $4083.21

Step-by-step explanation:

Answer:

the answer is 5

Step-by-step explanation:

if you have any questions or a more detailed explanation feel free to ask in the comments.

Answer:

[tex]u+v =8.323717394km[/tex]

Ф=[tex]64.86489406[/tex]°

Step-by-step explanation:

[tex]u=4km[/tex]

[tex]v=5km[/tex]

For easy calculations let's decompose the vector in its rectangular components:

[tex]u_x=u*cos(\alpha )=4000*cos(90)=4000*0=0[/tex]

[tex]u_y=u*sin(\alpha )=5000*sin(90)=4000*1=4000[/tex]

[tex]v_x=v*cos(\beta )=5000*cos(45)=3535.533906[/tex]

[tex]v_y=v*sin(\beta )=5000*sin(45)=3535.533906[/tex]

Now lets calculate the resultant vector:

[tex]u+v=R[/tex]

[tex]R=R_x+R_y[/tex]

[tex]R_x=u_x+v_x=0+3535.533906=3535.533906[/tex]

[tex]R_x=u_y+v_y=4000+3535.533906=7535.533906[/tex]

Finally let´s calculate the magnitude and direction of R:

║[tex]R[/tex]║=[tex]\sqrt{(R_x)^{2}+(R_y)^{2}  }=\sqrt{(3535.533906)^{2}+(7535.533906)^{2}  }  =8.323717394km[/tex]

Ф=[tex]arctan(\frac{R_y}{R_x})=arctan(\frac{7535.533906}{3535.533906})=64.86489406[/tex]°

Answer:

A. The selection is a combination.

Step-by-step explanation:

A combination is a selection of all or part of a set of objects, without regard to the order in which they were selected.  

Then, a permutation is an arrangement of all or part of a set of objects, with regard to the order of the arrangement.

For example, the student scans the novels to be checked out in no particular order hence it is a combinations problem. Scanning novels with titles A, B, C, D and E in the order B, C, D, E and then A produces the same result. When it comes to library books, the order in which we scan the novels for check out is of no importance since in the end the same novels are carried out the door by the library patron.

Explanation:

The cost for retaining the services when no time is spent is $18. That $18 is the minimum cost of the service call.

The added cost each hour is $48, so the per-hour charge is $48.

Answer:

  $32.67

Step-by-step explanation:

Her purchase total was ...

  (1.4 lb)($12.00/lb) +(4.5 lb)($0.35/lb) = $17.33

Her change from $50 will be ...

  $50 - 17.33 = $32.67

Answer:

662.64

Step-by-step explanation:

i got it wrong on apex and it told me the right answer. you're welcome.

Answer:

$662.63

Step-by-step explanation:

Cost of mortgage = $120,000

Interest rate of first period = 5.25%

The loan was amortized over 30 years.

The interest rate at the end of the initial loan period = 6.75%

Margin = 1.5%

The loan was amortized for over (30*12) months

= 360 months

The interest rate of the first period per month = 5.25% / 12

= 0.0525/12

= 0.004375

Payment for monthly mortgage =

(120000(0.004375)) / 1 - (1 + 0.004375)^-360

= 525 / 1 - (1.004375)^-360

= 525 / (1 - 0.2077)

= 525 /0.7923

= 662.63

= $662.63

Answer:

Step-by-step explanation:

y = -2x^5 - 1

Desired reflection would be f'(x) = -2x⁵ -1

The reflection over the x-axis equation's basic guidelines The reflection equation of the new reflected graph will be y=f(x) y = f (x) given an equation, y=f(x) y = f (x). Simply multiplying the function by 1 will result in a curve that is mirrored across the x-axis.

Given the equation f(x) = x⁵, From reflection rile, the reflection of this graph would be f'(x) = - x⁵.

asked to stretch the graph by 2 and shift down 1 unit.

Therefore, the function results after applying the sequence of transformation are f'(x) = -2x⁵ -1. for better understanding a graph is attached below.

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Answer:

time period is 260.57 years

Step-by-step explanation:

given data

growth rate = 3.4 % = 0.034

population = 4118000

area  P = 29000000000 square yard

to find out

time period that one person for every square yard of​ land need

solution

we will apply here population growth formula that is

total population P  = initial population × [tex]e^{rt}[/tex]    ..............1

here r is rate of growth and t is time period and

we consider here initial population is current population

so put value in equation 1 to get t

29000000000 = 4118000 × [tex]e^{0.034t}[/tex]

take ln both side

ln 7042.25 = ln [tex]e^{0.034t}[/tex]

8.8596 = 0.034 t

t = 260.57

so time period is 260.57 years

Answer:

kn

Step-by-step explanation:

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Answer:

A. 160 balls

Step-by-step explanation:

First we find the volume of each sphere.

diameter = d = 0.75 in.

radius = r = d/2 = 0.75/2 in. = 0.375 in.

V = (4/3)π(r^3) = (4/3)(3.14159)(0.375 in.)^3 = 0.221 in.^3

Because of the assumption about the space occupied by a sphere in random packing, we now calculate 190% of the volume of the sphere.

190%V = 1.9 * 0.221 in.^3 = 0.420 in.^3

Now we calculate the volume of the box.

V = LWH = 3 in. * 3 in. * 7.5 in. = 67.5 in.^3

To find out the number of balls that fit in the box, we divide the volume of the box by the randomly packed ball volume.

number of balls = (67.5 in.^3)/(0.420 in.^3) = 160.8

Answer: 160 balls

Answer:

Part 1) The converse is "If one of the two angles is acute then two angles are supplementary"

Part 2) The inverse is " If two angles are not supplementary, then one of the two angles is not acute"

Part 3) The contrapositive is "If one of the two angles is not acute then two angles are not supplementary"

Step-by-step explanation:

we  have

The following conditional statement " If two angles are supplementary, then one of the two angles is acute"

The hypothesis is "If two angles are supplementary"

The conclusion is " one of the two angles is acute"

Part 1) Rewrite the conditional statement as a converse

we know that

To form the converse of the conditional statement, interchange the hypothesis and the conclusion

therefore

The converse of " If two angles are supplementary, then one of the two angles is acute"  is "If one of the two angles is acute then two angles are supplementary"

Part 2) Rewrite the conditional statement as a inverse

we know that

To form the inverse of the conditional statement, negating both the hypothesis and conclusion of a conditional statement.

therefore

The inverse of " If two angles are supplementary, then one of the two angles is acute"  is " If two angles are not supplementary, then one of the two angles is not acute"

Part 3) Rewrite the conditional statement as contrapositive

we know that

To form the contrapositive, switching the hypothesis and conclusion of a conditional statement and negating both

therefore

The contrapositive of "If two angles are supplementary, then one of the two angles is acute" is "If one of the two angles is not acute then two angles are not supplementary"

Concetta initially had 2kg of flour. After using 180g to make biscotti, she was left with 1820g of flour. This equates to 1.82kg when converted back from grams to kilograms.

At the beginning, Concetta had a bag of flour weighing 2kg. We need to convert kilograms to grams first to make the units the same, and we know that 1kg is equal to 1000g. Therefore, she initially had 2000g of flour.

After making biscotti, she used 180g of flour. So, to find out how much she has left, we subtract the amount used (180g) from the total amount (2000g), which results in 1820g of flour remaining.

Finally, we need to convert this back to kilograms. Because there are 1000g in 1kg, we divide 1820 by 1000, which gives us that Concetta has 1.82kg of leftover flour.

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