Please help me

10 points

Although Alex and Lauren will both step into position 4,6, they will not do it at the same time, so they will not meet.

Lauren:

Alex:

Both will step in the position 4,6, However, Lauren will be in this positon in the second 4, while Alek will do it on the second 3.

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Using the arrangements formula, it is found that 6 different orders of top-three finishers are possible.

The number of possible arrangements of n elements is given by the factorial of n, that is:

[tex]A_n = n![/tex]

In this problem, the possible orders are arrangements of 3 elements, hence, the number of orders is given by:

[tex]A_3 = 3! = 6[/tex]

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Answer:

multiple tasking them right

Answer:

results-driven

Step-by-step explanation:

The two vertices (-5, 8) and (-5, -6) of the rectangle have the same x-coordinates

The distance between the two vertices is 14 units

The vertices are given as:

(-5, 8) and (-5, -6)

The distance between the two vertices is calculated using:

d = √[(x2 - x1)^2 + (y2 - y1)^2]

So, we have:

d = √[(-5 + 5)^2 + (8 + 6)^2]

Evaluate the sum

d = √196

Evaluate the square root

d = 14

Hence, the distance between the two vertices is 14 units

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Answer: 14

Step-by-step explanation:

In order to solve a proportion, you should cross-multiply:-

[tex]\bf{\displaystyle\frac{3x}{10} =\frac{3}{2}}[/tex]

Multiply 3x times 2 and 10 times 3:-

[tex]\bf{6x=30}[/tex]

Divide both sides by 6:-

[tex]\boxed{\bf{x=5}}[/tex]

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I'll comment and/or edit my answer :)

Answer:

option A

Step-by-step explanation:

Answer os option a

Answer:

18.85 years

Step-by-step explanation:

Using the [tex]A=P(1+\frac{r}{n} )^{nt}[/tex] we can manipulate it to give us time.

However, let's identify our variables:

A is our final amount which is given to us, $1400.

P is our principle which is $500.

r is our rate which is 5.5% which can be traducted into 0.055.

n is the # of time our money get compounded per year, in this case quarterly means 4 times a year therefore n = 4.

t is time and is what we are trying to solve for.

Now let's manipulate our equation to find t:

[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

[tex]\frac{A}{P} =(1+\frac{r}{n} )^{nt}[/tex]

[tex]\frac{1400}{500} =(1+\frac{0.055}{4} )^{4t}[/tex]

[tex]2.8=1.01375^{4t}[/tex]

[tex]log_{1.01375}(2.8)=log_{1.01375}1.01375^{4t}[/tex]

[tex]log_{1.01375}(2.8)=4t[/tex]

[tex]\frac{log_{1.01375}(2.8)}{4} =t[/tex]

[tex]18.84876253=t[/tex]

It would take about 18.85 years in order for you to accumulate at least $1400.

The average velocity is the rate of the distance function over time

The average velocity over the interval [1, 3] is 8 kilometers per hour

The distance function is given as:

d(t) = 8(t³ - 6t² + 12t)

The interval is given as: [1,3]

Calculate d(1) and d(3)

d(3) = 8(3³ - 6 * 3² + 12 * 3)

Evaluate

d(3) = 72

d(1) = 8(1³ - 6 * 1² + 12 * 1)

Evaluate

d(1) = 56

The average velocity (v) is the calculated as:

v = (d(3) - d(1))/(3 - 1)

Substitute known values

v = (72 - 56)/(3 - 1)

Evaluate

v = 8

Hence, the average velocity over [1, 3] is 8 kilometers per hour

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Answer:

To find the mean absolute deviation take each number in the data set, subtract the mean, and take the absolute value. Then take the sum of the absolute values. Now compute the mean absolute deviation by dividing the sum above by the total number of values in the data set.

6,6,3,4,4 - Mean Absolute Deviation: 1.12

Answer:

no solution

Step-by-step explanation:

6x + 4x - 1 = 2(5x + 4) ← distribute parenthesis

10x - 1 = 10x + 8 ( add 1 to both sides )

10x = 10x + 9 ( subtract 10x from both sides )

0 = 9 ← not possible

this indicates the equation has no solution

Answer:

Step-by-step explanation:

Given points P and Q have same x-coordinate but different y- coordinates.

The distance between P and Q is the difference of y- coordinates:

The area is 64 cm², it means the adjacent sides are

a)

If the points R and S are to the left, their coordinates are

b)

If the points R and S are to the right, their coordinates are

Answer:

Points R and S are to the left of Points P and Q

R = (-9, 4)

S = (-9, -4)

Points R and S are to the right of Points P and Q

R = (7, 4)

S = (7, -4)

Step-by-step explanation:

Given coordinates:

Points P and Q have the same x-value.

The vertical distance between these two points is:

[tex]\begin{aligned}\implies \sf y_P-y_Q & =\sf 4-(-4)\\ & =\sf 4+4\\ & =\sf 8\:units \\ & =\sf 8\:cm\end{aligned}[/tex]

Area of a rectangle = width × length

If the area of the rectangle PQRS is 64 cm² then:

[tex]\begin{aligned} \implies \sf 64 & = \sf width \times 8\\\implies \sf width & = \sf \dfrac{64}{8}\\\implies \sf width& = \sf 8 \: cm \end{aligned}[/tex]

This means that the y-values of points R and S will be the same as points P and Q, but the x-values will either be 8 less or 8 more.

Points R and S are to the left of Points P and Q

R = (-1 - 8, 4) = (-9, 4)

S = (-1 - 8, -4) = (-9, -4)

Points R and S are to the right of Points P and Q

R = (-1 + 8, 4) = (7, 4)

S = (-1 + 8, -4) = (7, -4)

Answer:

.2 dollars and 17 cents

Step-by-step explanation:

Carlos has 8dollars and 48 cents --->8+0.48=8.48

Alissa has 4dollars and 14 cents--->4+0.14=4.14 let

x--->amount of money that Carlos needs to give Alissa

The linear equation that represents this situation is 8.48-x=4.14+x

2x=8.48-4.14

2x=4.34

x=2.17

the amount of money is 2 dollars and 17 cents.

thank you

by Angel osei

[tex]a~~\pm~~bi\implies r[\cos(\theta ) \pm i\sin(\theta )] \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \sqrt{3}~~ + ~~i\implies \stackrel{x}{\sqrt{3}}~~ + ~~\stackrel{y}{1} i\qquad \qquad \begin{cases} r=\sqrt{x^2+y^2}\\\\ \theta =\tan^{-1}\left( \frac{y}{x} \right) \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]r=\sqrt{(\sqrt{3})^2+(1)^2}\implies r=\sqrt{3+1}\implies r=2 \\\\\\ \theta =\tan^{-1}\left( \cfrac{1}{\sqrt{3}} \right)\implies \theta =\cfrac{\pi }{6} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill 2\left[\cos\left( \frac{\pi }{6} \right)~~ + ~~i\sin\left( \frac{\pi }{6} \right) \right]~\hfill[/tex]

Check the picture below.

Answer:

Cylinder height = 10

Semi-circle height = 3

Cone height = 4

Step-by-step explanation:

The height of the cylinder is always going to be the long side. 6 is the diameter of its circle. Here is a list of variables:

Diameter, D = 6

Radius, r = 3

Slant height of cone, c = 5

To find the height of the cylinder, we will need to find the height's of the cone and semi-circle:

CONE (see image attached)

a² + b² = c²

3² + h² = 5²

h² = 25 - 9

h = √16

h = 4

SEMI-CIRCLE

h = radius

h = 3

CYLINDER

Cylinder height = total h - semi-circle h - cone h

h = 17 - 3 - 4

h = 10

I'm not sure if you're trying to solve for volume, so I'll end it here LOL. Hope this helps and have a great evening!

Answer
[tex]\sqrt29[/tex]

Step-by-step explanation:

1. Write the distance formula:

[tex]\sqrt(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}[/tex]

2. Substitute

Substitue (6, -4) and (1, -6) into

[tex]\sqrt(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}[/tex]

[tex]\sqrt(1 - 6) ^{2} + (-6 + 4)^{2}[/tex]

3. Calculate

[tex]\sqrt(1 - 6) ^{2} + (-6 + 4)^{2}[/tex]

[tex]\sqrt(-5) ^{2} + (-2)^{2}[/tex]

[tex]\sqrt5 ^{2} + 2^{2}[/tex]

[tex]\sqrt25 + 4[/tex]

[tex]\sqrt29[/tex]

Answer:

Step-by-step explanation:

Owing represent a negative balance.

So the inequality for this case is:

The word owing is given which simply denotes to negative transaction

So here the inequality is

Or

Answer:

-5 and 9

Step-by-step explanation:

To find the solutions we will factor the equation.

First we take out a 2:

[tex]2(x^2-4x-45)[/tex]

Then we can factor again:

[tex]2(x+5)(x-9)[/tex]

This provides us with the answer of:

[tex]x+5=0[/tex]

and

[tex]x-9=0[/tex]

Hence the solutions of -5 and 9.

Answer:

not sure if the 4 is seperate but if it is then (30+26)+(6-33)

Step-by-step explanation:

Answer:

Your answers: -5, 0, 1

Step-by-step explanation:

–8 < 3x + 7 ≤ 10 That is the original compount inequality given.

We need to solve it in order to get an easy option.

-15, -5, -3, 0, 1 are the options.

_________________________________________________

Steps to solve:

–8 < 3x + 7 ≤ 10

Subtract 7 from both sides

–8 < 3x ≤ 10 - 7

Now do 10-7

–8 < 3x ≤ 3

Do 3x divided by 3

–8 < x ≤ 1

________________________________________________________

Evaluation and Answer Explanation:

–8 < x ≤ 1

That is your inequality statement.

The inequality statement states that "x" is greater than -8 but less than or equal to 1.

We can automatically choose 0 and 1 because 0 is greater than -8 and less than or equal to 1.

1 is correct because it is greater than -8 and less than or equal to 1

Now, there are two answers remaining: -15; -5.

Let's try -15.

-15 isn't greater than -8 but is less than 1. This is incorrect because it follows one inequality but doesn't follow both.

**Rule: the bigger you go on the negatives like -20 or -99 your numbers get smaller. If you go more towards the 0 like -1, -5, -3 your numbers get bigger.

-5 works because it is greater than -8 and less than or equal to 1.

Your answers: -5, 0, 1

Answer:

81 [ft].

Step-by-step explanation:

1) the basic formula is: h=gt²/2, where g - acceleration due to gravity, t - elapsed time;

2) if the final velocity is 72, g=32, then it is possible to calculate elapsed time:

[tex]t=\frac{V}{g}=\frac{72}{32}=\frac{9}{4} [sec].[/tex]

3) if g=32, t=9/4, then the required height is:

[tex]h=\frac{32*(\frac{9}{4} )^{2} }{2}=\frac{16*81}{16}=81[ft].[/tex]

The height of the building comes to be 81 feet.

Initial velocity u= 0 feet/sec

Final velocity v= 72 feet/sec

The acceleration due to gravity g =32ft /sec²

Height of the building h= suppose h

The equation of a motion is:

[tex]v^{2} =u^{2} +2gh[/tex]

Where u and v are the initial and final velocities.

[tex]72^{2} =0+2*32*h\\144 = 64h\\h=81[/tex]

So, the height of the building = 81 feet.

Therefore, the height of the building comes to be 81 feet.

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Answer:

Exact form would be 1/8

and the decimal form is 0.125

Answer:

2^-3=1/8=0.125

Step-by-step explanation:

We have a negative exponent (-3) in order to make an exponent positive write the reciprocal of the number

We get 2^-3 = 1/(2^3)

and 2^3=8

so we get 2^-3= 1/8 =0.125

Answer:

144 sq cm

Step-by-step explanation:

The base is a triangle. Area of a triangle is:

A = 1/2 b • h

A = 1/2(4)•3

A = 6

There are 2 of these bases.

Area of 2 bases= 12.

There are three rectangular sides. Area of a rectangle is:

A = l × w (or b•h)

A = 5 × 11 = 55

A = 3 × 11 = 33

A = 4 × 11 = 44

Add up three rectangular faces and two bases for Total Surface Area:

12 + 55 + 33 + 44

= 144 sq cm

Answer:

144 cm ²

Step-by-step explanation:

The surface area of a right triangular prism is made up of 2 congruent triangles (these are called the "bases") and 3 rectangles.

Surface area of a right triangular prism formula

Surface area = (S₁ + S₂ + S₃)L + bh

where:

⇒ Surface area = (3 + 4 + 5)11 + 4 × 3

                          = (12)11 + 12

                          = 132 + 12

                          = 144 cm²

The answer is 1/3.

If you're still not sure (and math teachers will appreciate you doing this), you can check. Divide 1 by 3 and you will get 0.333333333333...

I hope this answers your question.

Step-by-step explanation:

to calculate circumference:

[tex]2\pi \: r[/tex]

if the diameter is 16 then the radius would be 8.

[tex]2\pi \:r \\ = 2\pi(8) \\ = 16\pi \\ =Rationalize(50.26548245744) \\circumference = 50.27[/tex]

to calculate the area of a circle:

[tex]\pi {r}^{2} \\ = \pi( {8})^{2} \\ = Rationalize(201.06192982975) \\ area = 201.06 \: ^{2} [/tex]

Applying the Pythagorean theorem, the amount of inches of wood required = Perimeter of triangle = 15 + 13 + 9 = 37 inches.

The Pythagorean theorem is used to find a side of a right triangle, and it states that if c is the hypotenuse and a and b are the other legs, therefore: c² = a² + b².

Find the altitude/height of the triangle using the Pythagorean theorem:

height = √(13² - 5²)

height = 12

Also, use the Pythagorean theorem to find the missing side (part of the longest side of the main triangle):

missing side = √(15² - 12²) = 9

Amount of inches of wood required = Perimeter of triangle = 15 + 13 + 9 = 37 inches.

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Answer:

y = -2/3x + 4

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

like pirates, the stars were their navagation

Answer: Angle 3 and Angle 2

Step-by-step explanation:

The angles form a linear pair, which means they are supplementary.

Answer:

Biased

Step-by-step explanation:

Answer:

Step-by-step explanation:

You are correct that the relationship is inverse, and that the product of x and y is a constant, 25.

__

The equation should be written so that y is a function of x:

  [tex]\boxed{y=\dfrac{25}{x}}[/tex]

The x in the denominator clearly shows that y is proportional to the inverse of x.

Answer:

Linear relationship: increasing or decreasing one variable will cause a corresponding increase or decrease in the other variable.

Inverse relationship:  the value of one variable decreases as the value of the other variable increases.

Exponential relationship: a constant change in the independent variable (x) gives the same proportional change in the dependent variable (y)

Question 5

As the x-value increases (by one unit), the y-value decreases.

Therefore, this is an inverse relationship.

The y-values can be calculated by dividing 25 by the x-value.

[tex]\sf y=\dfrac{25}{x}[/tex]