Nicolas is setting up water stations for a 10-mile run. He already has the first one set up 8 miles from the starting line. He needs to set up two more that are 1.5 miles on either side of the first water station. Where will he put the two additional water stations?

A number line divided into increments of 1 and labeled 0 through 10. The number 8 is labeled with Nicolas.

The absolute value equation that models this situation is |x –
|=

.

The two additional water stations will be
and

miles from the starting line.

Answer:

41.41°

Step-by-step explanation:

do shift cos 6/8 = 41.41°

as it's a right angle triangle and cos angle = adjacent ÷ hypo.

The x- and y-coordinates of the center of mass are; (20, 0)

The center of mass is the location where the sum of the relative position of the masses in a mass distribution is zero. It is the point where force can be applied on the distributed mass without causing a rotation of the system.

The mas of the steel plate = 800 g = 0.8 kg

The base length of the isosceles triangular plate = 20 cm = 0.2 m

The height of the isosceles triangular plate = 30 cm = 0.3 m

Considering a small strip of height, dx and width, I, we get

Area of small strip, dA = I·dx

Density of the plate for a unit thickness, ρ = M/A

Density of the small strip of mass dm = dm/dA

Considering the density of the plate as uniform, we get;

\(\displaystyle {\frac{dm}{dA} =\frac{M}{A}\)

Therefore;

\(\displaystyle {dm=\frac{M}{A}\times dA}\)

The area of the triangular plate, A = (1/2) × 0.2 m × 0.3 m = 0.03 m²

Mass of the plate, M = 0.8 kg

Therefore;

\(\displaystyle {dm=\frac{0.8}{0.03}\times I\cdot dx}\)

The width of the small strip, I, located at a distance x from the vertex of the triangular plate, using similar triangles, indicates;

\(\dfrac{I}{20} = \dfrac{x}{30}\)

\(I=20\times \dfrac{x}{30} = \dfrac{2}{3} \cdot x\)

Therefore;

\(\displaystyle {dm=\frac{0.8}{0.03}\times I\cdot dx} = \frac{0.8}{0.03}\times \dfrac{2}{3} \cdot x\cdot dx}\)

The center of mass, \(x_{cm}\), can be obtained with the formula; \(\displaystyle {x_{cm} = \dfrac{1}{M} \cdot \int\limits {x} \, dm }\)

Therefore; \(\displaystyle {x_{cm} = \dfrac{1}{0.8} \cdot \int\limits {x} \cdot \frac{0.8}{0.03} \cdot \frac{2}{3}\cdot x\, dx }\)

\(\displaystyle {x_{cm} = \dfrac{1}{0.8} \cdot \int\limits {x} \cdot \frac{0.8}{0.03} \cdot \frac{2}{3}\cdot x\, dx } = \dfrac{1}{0.8} \times \frac{0.8}{0.03} \times \frac{2}{3}\cdot \int\limits^3_0 {x^2} \, dx\)

\(\displaystyle {x_{cm} = \dfrac{1}{0.8} \times \frac{0.8}{0.03} \times \frac{2}{3}\cdot \int\limits^3_0 {x^2} \, dx = \frac{200}{9} \cdot \left[\frac{x^3}{3} \right]^{0.3}_0\)

\(\displaystyle {x_{cm} = \frac{200}{9} \cdot \left[\frac{x^3}{3} \right]^{0.3}_0=\frac{200}{9} \times \frac{0.027}{3} =0.2\)

The location of the x-coordinate center of mass, \(x_{cm}\) = 0.2 m = 20 cm from the vertex, which is the same location as the x-coordinate of the centroid of the plate of uniform density.

The plate is symmetrical about the x-axis, therefore, the y-coordinate of the center of mass is along the x-axis, which is \(y_{cm}\) = 0

The coordinate of the center of mass = (0.2, 0)

Part of the question requires the location of the coordinate of the center of mass of the triangular plate

Learn more about the center of mass of regular shapes here:

https://brainly.com/question/28021242

#SPJ1

So, Vanessa's score = v. Let's work from there.

We know that 59 is decreased by Vanessa's score, which is subtraction, and thus: 59 - v

Then, we're told that that quantity is 7. "Is" can be used in place of an equals sign: = 7

Therefore, our equation is as follows: 59 - v = 7

Hope this helps!! :)

If circle has diameter lm and chord pq, lm = 20 cm, and pq = 16 cm, the length of RM is 10√2 centimeters.

In a circle, a diameter is a chord that passes through the center of the circle. Therefore, the point where the diameter and the chord intersect, in this case, point R, bisects the chord.

Since LM is a diameter, its length is twice the radius of the circle, which means LM = 2r. Thus, we can find the radius of the circle by dividing the diameter by 2: r = LM/2 = 20/2 = 10 cm.

Since point R bisects the chord PQ, RP = RQ = 8 cm (half of PQ). Thus, we need to find the length of RM. To do that, we need to use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, we have a right triangle RLM with RM as the hypotenuse, so we can use the Pythagorean theorem as follows:

RM² = RL² + LM²

RM² = (10)² + (10)²

RM² = 200

RM = √200 = 10√2 cm

To learn more about circle click on,

https://brainly.com/question/25070177

#SPJ4

Complete question is:

Consider circle o with diameter lm and chord pq.

if lm = 20 cm, and pq = 16 cm, what is the length of rm, in centimeters?

Using the probability, if you choose two cards out of a deck of cards, then the chances one is a red face card and the other is a black non-face card is 1/2.

In the given question,

If you choose two cards out of a deck of cards, then we have to find the chances one is a red face card and the other is a black non-face card.

As we know that in a deck having 52 cards. In which 26 are red and 26 are black.

We have to choose a red face card.

As we know that in a deck have 12 face cards. In which 6 red face cards and 6 black face cards.

So the chance of getting red face card is

P(R)=Total number of red face cards/Total number of cards

P(R)=6/52

We have to choose a black non-face card.

We know that in a deck have 6 black face cards and total black cards are 26. So the non face cards are 20.

So the chance of getting black non-face card is

P(B)=Total number of black non-face cards/Total number of cards

P(B)=20/52

Now the chances of getting one is a red face card and the other is a black non-face card is

P(R or B)=P(R)+P(B)

P(R or B)=6/52+20/52

P(R or B)=(6+20)/52

P(R or B)=26/52

P(R or B)=1/2

Hence, if you choose two cards out of a deck of cards, then the chances one is a red face card and the other is a black non-face card is 1/2.

To learn more about probability link is here

brainly.com/question/11034287

#SPJ4

Answer:

N+1

Step-by-step explanation:

It begins with = 2

then n+1=3

then n+2=4 and so on it is n+1

Answer:

c

Step-by-step explanation:

False. Null and alternative hypothesis are not statements about descriptive statistics.

Null and alternative hypothesis are fundamental concepts in hypothesis testing, a statistical method used to make inferences about population parameters based on sample data. These hypothesis are not directly related to descriptive statistics, which involve summarizing and describing data using measures such as mean, median, standard deviation, etc.

The null hypothesis (H0) represents the default or no-difference assumption in hypothesis testing. It states that there is no significant difference or relationship between variables or groups in the population. On the other hand, the alternative hypothesis (H1 or Ha) proposes that there is a significant difference or relationship.

Both null and alternative hypotheses are formulated based on the research question or objective of the study. They are typically stated in terms of population parameters or characteristics, such as means, proportions, correlations, etc. The aim of hypothesis testing is to gather evidence from the sample data to either reject the null hypothesis in favor of the alternative hypothesis or fail to reject the null hypothesis due to insufficient evidence.

Finally, null and alternative hypotheses are not statements about descriptive statistics. Rather, they are statements about population parameters and reflect the purpose of hypothesis testing in making statistical inferences.

Learn more about Null hypothesis here:

https://brainly.com/question/29387900

#SPJ11

Answer:

QR = 15

Step-by-step explanation:

The product of the length of the secant segment and its external part equals the square of the length of the tangent segment.

(QR+5) *5 = 10^2

(QR+5) *5 = 100

Divide each side by 5.

(QR+5) *5/5 = 100/5

(QR+5)  = 20

Subtract 5 from each side.

QR = 20-5

QR = 15

Answer:

See explanation

Step-by-step explanation:

Let the number of adults = a and the number of children = c.

Since the number of people using the pool is 288, we know that a + c = 288

Based on the price information, we know that 1.75c + 2.5a = 528

Combining these two equations allows us to solve for the values of a and c, the process for which follows

a = 288 - c

1.75c + 2.5(288 - c) = 528

c = 256

a = 288 - c = 288 - 256 = 32

a = 32

c = 256

For more math help and free-online tutoring visit Growth In Youth's online forum, which can be found on our website growthinyouth org.

The side length of the equilateral triangle is 4 cm.

The area of an equilateral triangle can be calculated using the formula:

\(A = \frac{\sqrt{3} }{4} a^{2}\)

where a is the side length of the triangle

We have:

A = 4√3 cm²

Substitute into the formula and solve for a:

\(4\sqrt{3} = \frac{\sqrt{3} }{4} a^{2}\)

Divide both sides by √3:

\(4 = \frac{1}{4} a^{2}\)

a² = 4 * 4

a² = 16

a = √16

a = 4 cm

Learn more about equilateral triangle on:

https://brainly.com/question/17264112

#SPJ1

Answer:

32 degrees

Step-by-step explanation:

An inscribed angle is an angle with its vertex on the circle, formed by two intersecting chords. Angle N perfectly fits this description. An inscribed angle is equal to 1/2 of its intercepted arc (the arc opposite the angle). The arc opposite angle N is equal to 64 degrees, so angle N is equal to 1/2 of that, or 32 degrees

Answer:

the third option

Step-by-step explanation:

it is simple :

for the sum of 2 functions we need to sum the functional expressions.

for the product of 2 functions we need to multiply the functional expressions.

...

so,

(f.p)(x) = (3x - 2)(x + 3)

remember, when we multiply 2 expressions, then we have to multiply every term of one expression with every term of the other expression and sum up all the individual results (while considering the right signs, of course).

(3x - 2)(x + 3) = 3x² + 9x - 2x - 6 = 3x² + 7x - 6

In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and divide by two (2).

Since S is the midpoint of line segment RT, it simply means that line segment RT is divided into two (2) sections RS and RT and they are equal in length. By applying the midpoint rule, we have:

RT = RS + ST

60 = 2x - 1 + 4x + 7

60 = 6x - 6

6x = 60 + 6

6x = 66

x = 66/6

x = 11.

By applying the midpoint rule, we have:

PR = PQ + QR

10x - 11 = 2x - 3 + 5x + 7

10x - 11 = 7x + 4

10x - 7x = 11 + 4

3x = 15

x = 15/3

x = 5.

For the measure of segment PR, we have:

PR = 10x - 11

PR = 10(5) - 11

PR = 50 - 11

PR = 39 units.

By applying the midpoint rule, we have:

CE = DE + D

CE = 2DE

28 = 2DE

DE = 28/2

DE = 14 units.

Read more on midpoint here: https://brainly.com/question/28262767

#SPJ1

Answer:

the slope should represent the fee of each class

.

the vertical intercept is the membership fee

Answer:

the y-inyetcept means the starting fee to join

and the slope means fee per class paid by the customers.

Step-by-step explanation:

Answer:

A = $ 9,257.50

A = P + I where

P (principal) = $ 7,000.00

I (interest) = $ 2,257.50

Step-by-step explanation:

Answer:1/6

Step-by-step explanation:

Answer:

Given :principle =Rs. 1200

rate of interest =9%

time =3yrs

we know that simple interest =PTR /100

=1200*9*3/100

=Rs. 324

Amount of the farmer will receive at the end of the 3 yrs =principle + interest

=1200+324=1524/-

The Answer is 25.12 I know this because I used a calculator. Hope this helped! :)

Answer: 25.12

Step-by-step explanation:

The Answer is 25.12 I did a test and got it right. I hope this helps!

Driving from North Carolina to Florida at an average speed of 70 mph takes about 7 hours and 12 minutes.

Velocity is a term used to describe how fast an object is moving in a particular direction. It is measured as distance traveled in a period of time and is usually expressed in units of meters per second (m/s). Velocity is an important concept in physics and is used to calculate how fast an object moves in a given environment. Velocity is related to speed, which is the rate of change of distance in a particular direction. Speed ​​is an important factor in many sports and activities such as running, cycling and driving. It is also used in different ways in our daily life. For example, it is used to determine how fast a car can go from A to B, or how long it will take to walk to a destination.

Speed = Distance/Time

55 = Distance/9

Distance = 495 miles

When speed is 70 mph:

70 = 495/Time

Time = 495/70

Time = 7 hours and 12 minutes

To know more about speed click-

https://brainly.com/question/13943409

#SPJ1

As stated in the text, the central pole forms a right angle with the floor. The side of the tent corresponds to the hypotenuse of the right triangle formed with the pole and the floor.

The cosine of an angle is the ratio between the side adjacent to it and the hypotenuse of the triangle. In this case, the cosine of the missing angle is equal to 20ft divided by 26ft, which is approximately 0.77.

Applying the arccos function, we can find the angle whose cosine is equal to 20/26:

Then, the angle that the tent pole makes with the sides of the tent is approximately 39.7º.

The size of the marked angle is determined as 38°.

The value of the marked angle is calculated as follows;

∠BOD + ∠AOD = 180° [AOB is a straight line]

⇒ ∠BOD + 140° = 180°

⇒ ∠BOD = 40°

OB = OD

∴ ∠OBD = ∠ODB

In triangle AOD,

∠BOD + ∠OBD + ∠ODB = 180° [Sum of angles of triangle]

⇒ 40°+ 2 ∠OBD = 180°

⇒ 2∠OBD = 140°

⇒ ∠OBD = 70°

∴ ∠OBD = ∠ODB = 70°

ABDC is a cyclic quadrilateral.

∴ ∠CAB + ∠BDC = 180°

⇒ ∠CAB + ∠ODB + ∠ODC = 180°

⇒ 38° + 70°+ ∠ODC = 180°

⇒ ∠ODC = 72°

Now,

∠EDB = 180° – ∠BDC [Because CDE is a straight line]

⇒ ∠EDB = 180° – (∠ODB + ∠ODC)

⇒ ∠EDB = 180° – (70°+ 72°)

⇒ ∠EDB = 180° – 142°

⇒ ∠EDB = 38°

Learn more about angles in a triangle here: https://brainly.com/question/25215131

#SPJ1

The solution of the equation is x=3 or x=-5.

Given that the equation is (x+2)²-2(x-+2)-15=0 and use u substitution method to solve.

Let's assume that the (x+2)=u.

The given equation is rewritten as u²-2u-15=0.

Factorize the quadratic equation by adding or subtracting two number that gives the sum of -2u and product 15u² as

u²-5u+3u-15=0

u(u-5)+3(u-5)=0

Taking out (u-5) as common and get

(u-5)(u+3)=0

Compare each equation with 0 and get

u-5=0 or u+3=0

u=5 or u=-3

Performing back substitution by substituting the values of u in x+2

when u=5 then x is

x+2=5

x=3

And when u=-3 then x is

x+2=-3

x=-5

Hence, the solutions of the (x+2)²-2(x-+2)-15=0 is x=3 and x=-5.

Learn about the substitution here brainly.com/question/12802700

#SPJ4

Answer:X=-5 and X=3

Step-by-step explanation: