3. Students at Polk Middle School are given a fitness test. The results of their tests are shown in the table. Use the table to answer questions a-c. a. Find the time it takes each student to run . Evian:_ Toby:_ Jillian:_ b. Which student is running at the fastest rate? Expl c. Jillian is trying out for the cross country team. To make the team, she must run in less than . Will Jillian make the team? Explain.

Answer:

a_n = 5 × 3^(n - 1)

Step-by-step explanation:

The first term is 5. Each subsequent term is the previous term multiplied by 3.

a_1 = 5 × 3^0

a_2 = 15 = 5 × 3^1

a_3 = 45 = 5 × 3²

Notice that the exponent of the 3 is 1 less then the term number.

a_n = 5 × 3^(n - 1)

The numbers of the atoms of each element are;

6 atoms of carbon, 12 atoms of oxygen

12 atoms of hydrogen, 6 atoms of oxygen

6 atoms of carbon, 12 atoms of hydrogen, 6 atoms of oxygen

12 atoms of oxygen

In a chemical reaction, there is the combination of the atoms of the reactants and a consequent recombination as the products are formed. In accordance with the law of the conservation of mass, we know that the number of atoms before reaction must be equal to the number of atoms after reaction.

Now we have to look at the atoms and count up the number of atoms of each element in each of the compounds and this is how we are able to obtain the number of each atom as shown above.

Learn more about reaction:https://brainly.com/question/28984750

#SPJ1

Answer:

5

Step-by-step explanation:

2 +3 = 5    

Answer:

15.1

Step-by-step explanation:

tan(angle) = opposite/adjacent

tan 37 = AB/20

AB = 20 x tan 37 = 20 x 0.754 = 15.08 or 15.1

Answer:

24 Inches

Step-by-step explanation:

The length of a piece of wood that uses 8 nails as required in the task content is; 24 inches.

What is the length of a piece of wood that uses 8 nails?

It follows from the task content that the length of a piece of wood that uses 8 nails is to be determined from the task content.

If the snails moves at a constant rate, it will take 25 minutes to travel 55 feet.

We know that the snail travels at a rate of 2.2 feet per minute, so after x minutes, the distance traveled by the snail is:

D = 2.2ft*x

To see how many minutes it takes the snail to travel 55 feet, we need to solve the equation:

55 ft = 2.2ft*x

If we divide both sides by 2.2ft, we will get:

55ft/2.2ft = x

25 = x

So the snail takes 25 minutes to travel the 55 feet.

Learn more about distances:

https://brainly.com/question/7243416

#SPJ1

Fátima tiene un total de $ 160, Gabriel tiene un total de $ 690 y José tiene un total de $ 230.

En este problema tenemos a tres personas, Fátima, Gabriel y José, que reúnen un total de $ 1.080. A continuación, traducimos las variables y ecuaciones asociadas a la situación:

x - Cantidad de dinero de Fátima.

y - Cantidad de dinero de Gabriel.

z - Cantidad de dinero de José.

Ecuaciones: Fátima, Gabriel y José tienen un total de $ 1080.

x + y + z = 1080

Gabriel tiene 3 veces lo que José tiene.

y = 3 · z

Fátima tiene $ 70 menos que José.

x = z - 70

A continuación, resolvemos el sistema de ecuaciones lineales:

x + y + z = 1080

(z - 70) + 3 · z + z = 1080

5 · z - 70 = 1080

5 · z = 1150

z = 1150 / 5

z = 230

x = z - 70

x = 230 - 70

x = 160

y = 3 · z

y = 3 · 230

y = 690

Para aprender más de sistemas de ecuaciones lineales: https://brainly.com/question/29142634

#SPJ1

Answer:

Step-by-step explanation:

so you don't understand at all

Answer:

a.+1,-1

b.+√13,-√13

c.no real solutions

d.no real solutions

Step-by-step explanation:

question no c&d has no real solutions but they have complex solutions

if you are not taught about complex numbers then the Answers to c&d are no real solutions but for complex solutions

c.+3i,-3i

d.+√5i,-√5i

Answer:

Step-by-step explanation:

the answer is 11/12

The four letter code from the transformations is given as follows:

FB H.

The four letter code is obtained applying the transformations to the given points.

The coordinates of point 1 are given as follows:

(-4,2).

The transformation is a reflection over the x-axis, which has the rule given as follows:

(x,y) ->(x,-y).

Hence the coordinates of the image of point 1 are given as follows:

1'(-4,-2).

Meaning that the first letter is of F.

The coordinates of point 2 are given as follows:

(-2,3).

The transformation is a reflection over the y-axis, which has the rule given as follows:

(x,y) ->(-x,y).

Hence the coordinates of the image of point 2 are given as follows:

2'(2,3)

Meaning that the second letter is of B.

The coordinates of point 4 are given as follows:

(-1,2)

The transformation is a reflection over the line y = x, which has the rule given as follows:

(x,y) ->(y,x).

Hence the coordinates of the image of point 4 are given as follows:

4'(2,-1)

Meaning that the fourth letter is of H.

The third transformation is missing.

More can be learned about transformations at https://brainly.com/question/29209050

#SPJ1

Using the formula for the distance between two points and using the provided points, The error is missing a square root. The actual length is [tex]\sqrt{61}[/tex] units.

A line or line segment's length between two points along the line or line segment.

The required formula is:

[tex]d = \sqrt{(x2-x1)^{2}+(y2-y1)^{2}}[/tex]

(x1,y1)= (6,2)

(x2,y2)=(1,-4)

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

[tex]d=\sqrt{25+36}[/tex]

[tex]d=\sqrt{61}[/tex] units.

To learn more about distance visit:

https://brainly.com/question/29130992

#SPJ1

Using the formula for the distance between two points and using the provided points, The error is missing a square root. The actual length is  units.

What do you mean by distance?
Distance refers to the amount of space between two or more points, or the measure of how far apart two or more points are. It can be measured in various ways, including miles, kilometers, inches, centimeters, and more. Distance is often used to measure the length of a journey or the amount of space between two physical objects. It can also refer to the amount of time between two events, such as the distance between two birthdays. Distance can also be used to describe the relative or emotional separation between two people, such as the distance between a parent and a child.

What is the formula to calculate distance between two points?

The required formula is:

[tex]d =\sqrt{(x2-x1)^2 +(y2-y1)^3}[/tex]

(x1,y1)= (6,2)
(x2,y2)=(1,-4)

[tex]d = \sqrt{(1-6)^2 + (-4 -2)^2}[/tex]
[tex]d = \sqrt{25+36}[/tex]
[tex]d = \sqrt{61} units[/tex]

To learn more about distance visit:
brainly.com/question/29130992
#SPJ1

From the given options, option 2. x= -8 is the correct option. Here, the x is change in height in inches so the, change in height is -8 inches.

A linear equation is simply an equation with the highest degree always being 1. The standard form of a linear equation in one variable is Ax + B = 0. x is a variable in this equation, and A and B are constants. A two-variable linear equation has the standard form Ax + By = C. The variables x and y are variables, their coefficients A and B are variables, and C is a constant.

Given, linear equation is

[tex]4(2x+1)=6x-12\\\\8x+4=6x-12\\\\8x-6x=-4-12\\\\2x=-16\\\\x=-8[/tex]

Hence, the x equals to -8.

To learn more about linear equation refer here

https://brainly.com/question/29739212

#SPJ4

a) The value of P(Y∩P) =0.23

b) The value of (Y|P) = 0.34

c)  The value of (P|Y) = 0.27

d) The value of P(Y/P') = 0.68

What is Venn diagram?

A Venn diagram can also be referred to as a set diagram or a logic diagram that illustrates various set operations including the intersection, union, and difference of sets. Subsets of a set are also represented using it. A subset of whole numbers, which is a subset of integers, is a collection of natural numbers, as an example.

Given that there are two events Y and P.

P(Y) = 0.57

P(P) = 0.5

P(Y∪P) = 0.84

The formula of intersection is  P(Y∩P)  = P(P) + P(Y) - P(Y∪P)

Putting P(Y) = 0.57, P(P) = 0.5, P(Y∪P) = 0.84

P(Y∩P)  = 0.5 + 0.57 - 0.84

P(Y∩P) = 0.23.

b)

P(Y|P) = P(Y) - P(Y∩P)

P(Y|P) = 0.57 - 0.23

P(Y|P) = 0.34

c)

P(P|Y) = P(P) - P(Y∩P)

P(P|Y) = 0.5 - 0.23

P(P|Y) = 0.27

d) P(Y/P') = P(Y∩P') / P(P')

P(Y/P') = P(Y|P)/[1 - P(P)]

P(Y/P') = 0.34/(1- 0.5)

P(Y/P') = 0.68

To learn more about conditional probability, click on below link:

https://brainly.com/question/17888647

#SPJ1

Net profit is a company's profit after all expenses have been deducted. What remains after deducting fixed costs from gross profit is the net profit.

Subtracting the cost function from the revenue function yields the profit function. Assume that the profit is denoted by P(x), the revenue is denoted by R(x), the cost is denoted by C(x), and x is the quantity of goods sold. Consequently, the profit function is denoted by P(x) = R(x0 - C) (x).

Total Revenue - Total Expenses = Net Profit

A company that sells online has a $350,000 revenue and a $50,000 cost of products sold.The net income formula is defined as the difference between the total revenue earned and the total costs.Total revenue minus all costs equals net income.

The money a corporation makes after deducting interest, operational costs, and taxes over a specific time period is known as net profit.Profit After Tax is another name for Net Profit (PAT).

To learn more about net profit refer to :

https://brainly.com/question/13788133

#SPJ1

we conclude at the 1% level of significance that the claim is true by accepting H₀

What is Hypothesis?

A hypothesis outlines your expectations for the results of your investigation. It is a speculative, untested response to your research question.

Given,

n = 81

x bar = 7

s= 2

Here, a doctor claims that people are atmost 6 pound over weight

H₀ : μ ≤ 6 versus

H₀ : μ > 6 versus

Now,

The Test Stastistic is

t = x bar - μ / s√n

t = 7-6/2√81

t = 4.5

let ∝ = 0.10, then p value = 0.000

p value >∝

yes, conclude the claim is true by accepting H₀

To learn more about Hypothesis visit:

brainly.com/question/11560606

#SPJ4

Answer: [tex]2^4 \times 5[/tex]

Step-by-step explanation:

[tex]80=2 \times 40\\\\80=2 \times 2 \times 20\\\\80=2 \times 2 \times 2 \times 10\\\\80=2 \times 2 \times 2 \times 2 \times 5\\\\80=2^4 \times 5[/tex]

By solving a linear equation, it can be calculated that

Each club can order 21.1 cupcakes if they both have the same amount of

money to spend

What is a linear equation?

Equation shows the comparison between two algebraic expressions by connecting the two algebraic expressions by an equal to sign

A one degree equation is called linear equation

Let the number of cupcakes ordered by each club be c

The band would like to order cupcakes from Walmart at a cost of $3.35 per cupcake and a $13.00 order fee

Total amount spent = $(13 + 3.35c)

The orchestra would like to order cupcakes from Publix at $2.90 each

and a $22.50 order fee

Total amount spent = $(22.5 + 2.90c)

By the problem,

The linear equation is

13 + 3.35c = 22.5 + 2.90c

3.35c - 2.90c = 22.5 - 13

0.45c = 9.5

c = 21.1

This solution is not viable as the number of cupcakes must be an integer not a decimal.

To learn more about linear equation , refer to the link-

https://brainly.com/question/2030026

#SPJ1

The odds ratio for the association between exposure to emf's and breast cancer would be (11/5) / (108/436) = 2.2.

1. Calculate the odds of exposure for cases: 11/5 = 2.2

2. Calculate the odds of exposure for controls: 108/436 = 0.25

3. Divide the odds of exposure for cases by the odds of exposure for controls: 2.2/0.25 = 8.8

4. Finally, the odds ratio for the association between exposure to EMF's and breast cancer is 2.2.

The odds ratio for the association between exposure to EMF's and breast cancer can be calculated by dividing the odds of exposure for cases by the odds of exposure for controls. To calculate this, first take the number of cases exposed (11) and divide it by the number of cases not exposed (5). This will give the odds of exposure for cases (2.2). Second, take the number of controls exposed (108) and divide it by the number of controls not exposed (436). This will give the odds of exposure for controls (0.25). Finally, divide the odds of exposure for cases (2.2) by the odds of exposure for controls (0.25). This will give the odds ratio for the association between exposure to EMF's and breast cancer (2.2).

Odds ratio = (11/5) / (108/436) = 2.2

Learn more about ratio here

https://brainly.com/question/13419413

#SPJ4

Answer:

should be angle 7, 1, and 3

hope i could helpppp

Answer: 1 , 7 , 3

Step-by-step explanation:

The angles that habe the same measurement of angle 5 are;

1 , 7 , 3

Because the lines are parallel, these angles correspond to angle 5.

When Ms. Hall is buying Ms. Ward some gifts for Christmas as described in the problem,

the Constant: $90 and $7

the Coefficient: $7

the Equation:  $90 + $7x

Information form the problem shows that

one big gift that will cost $90

some small gifts that cost $7 each

the constant in this case is the price of the gifts

$90 and $7

the coefficient is $7

the equation is

$90 + $7x

where x is the number of the small gifts

Learn more about equations at

https://brainly.com/question/22688504
#SPJ1

The Slope of the line is -3/2

By Substituting x=26

=1/9/8*26+8/3

=-3/2

To learn more about Slope of the Line refer  to:

https://brainly.com/question/27212023

#SPJ1

The value of the shaded area from the rectangle ACDE is approximately 52.124 square centimeters.

In this problem we must calculate the shaded area of the section within the rectangle ACDE, this can be found by the subtracting the area of the region ABDE, which is the combination of the areas of the right triangle ABE and the arc BDE, whose formulas are shown below:

Triangle ABE

S = (1 / 2) · AB · AE

Arc BDE

S = (1 / 2) · α · ED²

Where α is the central angle, in radians.

Rectangle ACDE

S = ED · AE

If we know that AE = 20 cm, ED = 28 cm, α = π / 4 and AB = 20 cm, then the area of the shaded area is:

S = (28 cm) · (20 cm) - (1 / 2) · (π / 4) · (28 cm)² - (1 / 2) · (20 cm) · (20 cm)

S ≈ 52.124 cm²

To learn more on areas: https://brainly.com/question/27683633

#SPJ1

Answer: 68600

hope it helps!

Answer: $16 = 4s + 3g

Step-by-step explanation:

s = shoes

g = games

Answer:

Answers below

Step-by-step explanation:

1. The value 550 represents the initial balance in the account, which means the account started with $550.

2. 528.28

425.00 x  2.7% x 9 = 103.275

Then we add 103.275 to the initial deposit of $425.00

425.00 + 103.275 = 528.275

Therefore the answer is $528.28

3. The answer for this one is  f(n) = 56 + 3(n − 1)

So, as we can see the first value is 56 and the common difference is 3 and the rule for the nth term is [tex]a_{n} =a_{1} +d(n-1)[/tex]

Therefore, its 56 + 3(n − 1)

4. For this one we solve for r and using a calculator its r = 0.04

The value of r from the given equation is 0.04. Therefore, option A is the correct answer.

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

1) The given equation is 687.5=550(1+0.05t)

Here, amount=$687.5, principal (initial balance)=$550 and rate of interest =0.05×100 =5%

So, the value 550 represents the initial balance in the account, which means the account started with $550.

2) Given that, principal=$425.00, time period=9 years and rate of interest=2.7%

We know that, S.I=(P×T×R)/100

= (425×9×2.7)/100

= 103.275

Amount=103.275+425

= 528.275

≈ $528.28

3) The given arithmetic sequence is 56, 59, 62, 65, 68,.…

Here, first term (a)=56 and common difference=59-56=3

We know that, general form of arithmetic sequence is aₙ=a+(n-1)d

Now, f(n)=56+(n-1)3

4) The given equation is 816=600(1+9r)

1+9r =816/600

1+9r =1.36

9r=0.36

r=0.04

The value of r from the given equation is 0.04. Therefore, option A is the correct answer.

To learn more about the simple interest visit:

https://brainly.com/question/25845758.

#SPJ2

TRUE: The given contrapositive statement are correct,

If m ≤ 3, then, m < 5.

For the stated conditional statement -

If m ≤ 3, then, m < 5.

Then, contrapositive statement for the given statement will be

(m < 5)' ⇒ (m ≤ 3)'

That is;

(m > 5) ⇒ (m > 3)

That is, if m> 5 then, m > 3, which is true.

Thus, the contrapositive statement for the given conditional statement is true.

To know more about the contrapositive statement, here

https://brainly.com/question/1713053

#SPJ1

The sequences of transformations that could be applied to the parent function are Reflected over the y-axis, vertically stretch by a factor of 2, and then shift up 6 units i.e. Option (4).

What is transformation?

An operation that manipulates a polygon or other two-dimensional object on a plane or coordinate system is known as a transformation. Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

The two-dimensional shape without any transformations is known as a preimage or inverse image. The transformed figure is shown in the image.

Given, the parent function, f(x) = x

From the given graph, the equation will be

y = -2x + 6

Then, the transformation will be

Shifted up 6 units

Vertical stretch by a factor of 2

Reflected over the y-axis

Hence, the required answer is Option 4.

To learn more about transformation

https://brainly.com/question/2458900

#SPJ1

Answer: The answer is y=7x+4

M is the slope and the y-intercept is b