Mathematics High School

A relay team ran a race. Each team member ran #1/4# of the distance. The whole race was #8/9# mile. How far did each team member run?

Answers

Answer 1
Each member ran 2/9 miles

Related Questions

ONE LAST QUESTION!!!!!!!!!!WILL GIVE THE BRAIN!!!!!!!!!!

Answers

Reflection across x-axis means multiplying the function value by -1.

Shifting upwards by 3 units means, adding 3 to the function value. So the resulting function after these two transformations will be:

[tex]g(x)=- \sqrt{x}+3 [/tex]

Thus, option C gives the correct answer

Bobby is testing the effectiveness of a new cough medication. There are 100 with a cough in the study. Seventy patients received the cough medication, and 30 other patients did not receive treatment. Thirty-four of the patients who received the medication reported no cough at the end of the study. Twenty of the patients who did not receive medication reported no cough at the end of the study. What is the probability that a patiebt chosen at random from this study took the medication, given that they reported no cough?

A. 63%

B. 53%

C. 38%

D. 43%

Answers

There are a total of 54 who reported no cough after the medication. Out of this 54 patients, 34 took the medication. Therefore, the required probability is 

     [tex]=\frac{34}{54}=63\%[/tex]

The probability that a patient chosen at random from this study took the medication, given that they reported no cough is 63%. 

Answer:

The answer to this question is 63%

In the figure below, lines that appear to be tangent are tangent. Point O is the center of the circle. Which of the following is the value of x?
a. 60 degrees
b. 90 degrees
c. 100 degrees
d. 120 degrees

Answers

Answer:

(D) 120 degrees

Step-by-step explanation:

From the figure drawn, we have

∠ABC=60°

And ∠OAB=∠OCB=90° (angles made by tangent on the circle is 90°)

Thus, ∠AOC+∠OCB∠CBA+∠OAB=360° (Angles sum property of quadrilateral)

[tex]x+90^{\circ}+90^{\circ}+60^{\circ}=360^{\circ}[/tex]

[tex]x+240^{\circ}=360^{\circ}[/tex]

[tex]x=120^{\circ}[/tex]

Therefore, the value of x is [tex]120^{\circ}[/tex]

Hence, option D is correct.

Answer: d. 120 degrees

Step-by-step explanation:

From the given figure drawn, we can see that

∠ABC=60°

Also we know that tangents are radius are perpendicular at the point of tangency

And ∠OAB=∠OCB=90° (∵ tangents are radius are perpendicular at the point of tangency)

Therefore, we have

[tex]\angle{AOC}+\angle{OCB}+\angle{ABC}+\angle{OAB}=360^{\circ}\text{ ( By Angle sum property of quadrilateral)}\\\\\Rightrarrow\ x+90^{\circ}+60^{\circ}+90^{\circ}=360^{\circ}\\\\\Rightarrow\ x=360^{\circ}-240^{\circ}\\\\\Rightarrow\ x=120^{\circ} [/tex]

Verify the equation below with each of the values listed for t to find a solution.
4 = 2t +8

Answers

The solution for t

4 = 2t + 8
4 + (-8) = 2t + 8 + (-8)
-4 = 2t 
-4 / 2 = 2t  / 2
-2 = t
t = -2

Given a possible triangle ABC with a=5,b=11,and a=23, find a possible value for

Answers

The question is as follow:

Given a possible triangle ABC with a=5, b=11, and A=23 degrees, find a possible value for angle B. Round to the nearest tenth.
A. 10.2° B. 11.2° C. 59.3° D. no solution
========================================================

a = 5   ,    b = 11   ,   and    ∠A = 23°

By applying the Law of Sines:
[tex] \frac{sin \ A}{a} = \frac{sin \ B}{b} [/tex]

[tex] \frac{sin \ 23}{5} = \frac{sin \ B}{11} [/tex]

∴ sin B = 11* (sin 23°)/5 ≈ 0.8596

∴ ∠B = [tex] sin^{-1} 0.8596 [/tex] ≈ 59.3°

∴ The correct choice is option (C)
    C. 59.3°



help me please...
Problem: The standard form of a circle is (x-h)2+(y-k)2=r2 and for the parabola, y-k=a(x-h)2. The (h,k) pair will be the center of the circle and the vertex of the parabola. The radius of the circle is ‘r’ and the focal length of the parabola is f=1/(4a). For the following General Conic Equation: x2+y2-4x-6y-12=0 complete the following problems showing all your work:
Complete the square showing all your work to convert to Standard Form:
If this is a circle, state the coordinates of the center and give the radius. If this is a parabola, state the coordinates of the vertex and give the focal length. Show all your work.
Sketch the Conic. Label the values you found in part B. Be sure to draw or show the radius or focal length.

Answers

we have that

x²+y²-4x-6y-12=0
Group terms that contain the same variable, and move the constant to the opposite side of the equation
(x²-4x)+(y²-6y)=12
Complete the square twice. Remember to balance the equation by adding the same constants to each side
(x²-4x+4)+(y²-6y+9)=12+4+9
Rewrite as perfect squares
(x-2)²+(y-3)²=25
the answer part A) is 
(x-2)²+(y-3)²=5²-----> this is the standard form of the equation of a circle

Part B) (x-2)²+(y-3)²=5²
the center is the point (2,3) and the radius is r=5 units


Part C) 
using a graph tool
see the attached figure

A circle has a circumference of 324\pi324π324, pi. what is the radius of the circle?

Answers

Circumference of a Circle is given by :

C = 2πr

=> 324π = 2πR

=> R = ( 324 / 2 ) = 162 units

Suppose a term of a geometric sequence is a4 = 121.5 and the common ratio is 3. write the formula for this sequence in the form an = a1 ⋅ rn−1. explain how you arrived at your answer.

Answers

The rule of the geometric sequence is [tex]a* r^{n-1} [/tex]
a ⇒⇒⇒ the first term
r ⇒⇒⇒ common ratio

Given: the fourth term (a4) = 121.5   and the common ratio = 3  and   n = 4

∴ [tex]121.5 = a* 3^{4-1} [/tex]
∴ a = 121.5/3³ = 121.5/27 = 4.5

So, The formula for this sequence will be    [tex]4.5 * 3^{n-1} [/tex]

Answer:

First I substituted 121.5 for an, 4 for n, and 3 for r in the general form. Then I solved to find a1 = 4.5. Finally, I substituted 4.5 for a1 and 3 for r in the general form to get an = 4.5 ⋅ 3n−1.

Which expression is equivalent to 18x + 45

Answers

maybe 3(6x+15)

not sure what you're looking for
9(2X+5)
9*2X=18X
9*5=45
18X+45=18X+45

Are the two events “choosing a sophomore” and “choosing someone who replied ‘Yes’” independent events?

Answers

Yes, they are independent event such that occurring the first event “choosing a sophomore” does not affect the probability of occurring the second event “choosing someone who replied ‘Yes’”

Dustin is driving his car at speed of 50 kilometres per hour. he going to texas which is located 345 kilometres from his starting point.how long will it take him to reach texas?

Answers

it will take him about 7 hours

Square root of -1 divided by (3+8i)-(2+5i)

Answers

[tex]\sqrt{-1}=i\to i^2=-1\\\\therefore\ we\ have:\\\\\dfrac{i}{(3+8i)-(2+5i)}=\dfrac{i}{3+8i-2-5i}=\dfrac{i}{1+3i}\\\\=\dfrac{i}{1+3i}\cdot\dfrac{1-3i}{1-3i}=\dfrac{i(1-3i)}{1^2-(3i)^2}=\dfrac{i-3i^2}{1-9i^2}=\dfrac{i-3(-1)}{1-9(-1)}\\\\=\dfrac{i+3}{1+9}=\dfrac{3+i}{10}=0.3+0.1i[/tex]

Used:[tex](a+b)(a-b)=a^2-b^2[/tex]

Frank owns 250 acres of land. If he divides the land into 1/3 acre plots, how many plots will he have?

Answers

250 divided by 3 = 83.3 repeating decimal :)
Hope this helps you.
Short answer= 83.3

All you really have to do is 250 divided by 1/3 and you get 83.3333 (repeating) but you can just say 83.3.

What are the lengths?

Answers

In both the figures we have a Right Angled Triangle.

Two sides of the right angled triangles are given and we are to find the Third side. This can be done using the Pythagoras Theorem, which states:

Hypotenuse² = Base² + Perpendicular²

For 1st figure, we have
Base = 21
Perpendicular = 20

So, 

Hypotenuse² = 20² + 21² = 841
⇒
Hypotenuse = 29 (1st option is correct)

For 2nd Image, we have
Base= 6
Hypotenuse = 10

So, we can write:

10² = 6² + Perpendicular²
Perpendicular² = 64
⇒
Perpendicular = 8 (Option Fourth)

An equation of a function y(t) is shown.
y(t)=−t²+14t−40

Which of the following statements are true about the graph of y(t) for
6≤t≤8 and WHY?

a. The value of y(t) increases over the interval 6≤t≤7

b. The value of y(t) increases over the interval 7≤t≤8

c. The average rate of change over the interval 6≤t≤8 is 0

d. The value of y(t) is constant over the interval 6≤t≤8

e. The average rate of changer over the interval 6≤t≤7 is the same as the average rate of change over the interval 7≤t≤8

Answers

From the given function, to explain the correct answer I will plot the graph for :
y(t)=-t^2+14t-40
thus the graph will be as shown in the figure:
From the graph we deduce that the correct statement is:
y'(t)=-2t+14=0
thus
t=7
thus
y(7)=0
thus the correct statement is:
c. The average rate of change over the interval 6≤t≤8 is 0

The graph of y(t) increases over the interval 6≤t≤7 because the derivative is positive. The average rate of change over the interval 6≤t≤8 is 0 due to symmetry about the vertex of the parabola at t=7. The rate of change over the intervals 6≤t≤7 and 7≤t≤8 are equal in magnitude but opposite in direction.

Given the quadratic function y(t)=-t²+14t-40, we need to analyze its behavior over the interval 6≤t≤8. The first derivative y'(t) of the function, which represents the slope of the tangent line to the graph at any point t, is -2t + 14. To determine the intervals of increase and decrease, we can set the first derivative to zero to find the vertex of the parabola, yielding t=7, which means the function increases on the interval 6≤t≤7 and decreases on 7≤t≤8.

The average rate of change over an interval is calculated by taking the difference in the function values at the endpoints of the interval over the difference in t. For the interval 6≤t≤8, since this is a symmetrical interval around the vertex, the average rate of change is 0. Furthermore, it follows from symmetry that the average rate of change over the intervals 6≤t≤7 and 7≤t≤8 should be equal in magnitude but opposite in sign.

Considering the stated properties and analyzing the equation, we can conclude that:

The value of y(t) increases over the interval 6≤t≤7.The value of y(t) decreases over the interval 7≤t≤8, so statement b is false.The average rate of change over the interval 6≤t≤8 is 0, making statement c true.The value of y(t) is not constant over the interval 6≤t≤8.The average rates of change over both intervals 6≤t≤7 and 7≤t≤8 are not equal in value; they are opposite, making e false.

An archway is modeled by the equation y = -2x^2 + 8x. A rod is to be placed across the archway at an angle defined by the equation x − 2.23y + 10.34 = 0. If the rod is attached to the archway at points A and B, such that point B is at a higher level than point A, at what distance from the ground level is point B?
A. 8 units
B. 6 units
C. 5 units
D. 3 units

Answers

To solve this problem you must apply the proccedure shown below: 

1. You have that the the archway is modeled by the equation y=-2x^2+8x and the angle mentioned in the problem is defined by the equation x−2.23y+10.34=0.

 2. Therefore, you must susbtitute y=-2x^2+8x into x−2.23y+10.34=0, as below:

 x−2.23(-2x^2+8x)+10.34=0

 3. When you apply the distributive property, you obtain:

 x−2.23(-2x^2+8x)+10.34=0
 x+4.46x^2-17.84x+10.34=0
 4.46x^2-16.84x+10.34=0

 4. When you solve the quadratic equation, you obtain:

 x=3 units

 Therefore, the answer is the option D: D. 3 units.

Answer

The answer is 6

Step-by-step explanation:

Hugo is 6 feet 4 inches tall, weighs 225 pounds, and very muscular. if you think hugo is more likely to be a professional football player rather than a professional ballroom dancer, you are using:

Answers

I am using an inductive argument. In logical, in this type of argument if the premises are assumed true, it is likely that the conclusion is true (though the conclusion could be false). 

An inductive argument is intended to show that its conclusion is probably or likely true, though not certainly true, if its premises all are true. The author of an inductive argument (if sincere) only aims to establish the intended conclusion with a high degree of probability although not with complete certainty.

Words such as “probably,” “likely,” and “it is reasonable to conclude” suggest that you intend your argument to show that the conclusion is probably, but not certainly, true. The statement above use the words "more likely", then this word tell us that this is, in fact, an inductive argument.


Answer:

I think it is the option "representative heuristic"

Step-by-step explanation:

Heuristics are kind of like "mental shortcuts" that we use to make assumptions quickly. They are based off of our category prototypes and what we believe are typical examples of a certain object or group. The reason why it would be representative heuristic is because when you use this, you are comparing the new situation to an already existing image of the object. In this case, you are comparing Hugo to the "typical" image of a football player.

Hope this helps you :)

The length of a rectangle is twice it’s width.The length is 12cm.Work out the area of the rectangle

Answers

Answer:


Step-by-step explanation:

As with all word problems we first have to convert it to an equation or equations.

L = length of the Rectangle and W = its width

So L = 2 * W

A = area of the rectangle which is 128 cm^2

So    A = L * W = 128 cm^2

substitute 2W for L from the 1st equation to give    A = 2 * W * W = 2 * W^2 = 128 cm^2

Thus    W^2 = 64 cm^2

finally  W = 8 cm  and therefore  L = 2 * W = 16 cm

The perimeter P = 2 * (L+W) = 2* (8cm + 16cm) = 2 * 24cm = 48 cm

You are required to choose two topics from a list of six to write about on your science test. How many different pairings are possible?

10
15
20
12

Answers

2*6=12
The answer is 12 :)

If you want to put a 4x8 piece of plywood through a 3 foot square opening in your ceiling by turning it diagonally is the opening big enough? use a 45-45-90 since its a square

Answers

Here we apply the Pythagorean theorem:
c^2=a^2+b^2
The diagonal of the opening will be:
c^2=3^2+3^2
c^2=9+9
c^2=18
c=3√2 ft

The diagonal of the wood will be:
c^2=4^2+8^2
c^2=16+64
c^2=80
c=4√5 ft

The space will not be enough for the plywood to pass

A shipping box in the shape of a rectangular prism has a volume of 18x^3+5x^2-2x. what are three expressions that can represent possible dimensions of the shipping box?

Answers

Volume of the prism is given by:
Volume=length×width×height
but
V=18x^3+5x^2-2x
V=x(18x^2+5x-2)
V=x(9x-2)(2x+1)
Hence the possible expression for the dimensions of the shipping box is x by (9x-2) by (2x+1)

Answer:

[tex](x), (9x-2), (2x+1)[/tex]

Step-by-step explanation:

[tex]18x^3+5x^2-2x=x(18x^2+5x-2)=x(9x-2)(2x+1)[/tex]

Will mark 5 stars

The variable used to show correlation is r, which is also known as the correlation complement.

A.True

B.False

Answers

r is also known as the correlation coefficient. Hence your statement is ...
   B. False

A number is chosen at random from 1 to 50. find the probability of selecting numbers with 3 in the tens places

Answers

5/50 =.1 or 10% or 1/10

simplify


can u plz help me on this its a math question !!!!!


theres an image below!!!

Answers

The correct answer is:  [A]:  " [tex] \frac{8}{729} [/tex] " .
_________________________________________________________
Explanation:
_________________________________________________________
We are asked to simplify:

                  →    [tex] (\frac{2}{9})^3 [/tex]   

_________________________________________________________
Note the following property of exponents:
_________________________________________________________

[tex]( \frac{a}{b})^n [/tex]  =  [tex] \frac{(a^n)}{(b^n)} [/tex] ;  { b [tex] \neq [/tex]0 } . 

_________________________________________________________
As such:

→  [tex]( \frac{2}{9})^3 [/tex]  ;

                 
 =[tex]\frac{2^3}{9^3}[/tex] = [tex] \frac{(2*2*2)}{(9*9*9)}[/tex] =  [tex] \frac{8}{729} [/tex] .

_____________________________________________________________

The answer is:  " [tex] \frac{8}{729} [/tex] "  ; 

→  which is:  "Answer choice:  [A]:  " [tex] \frac{8}{729} [/tex] " . 
_____________________________________________________________
Hope this answer—and explanation—is of some help to you.
  Please comment below or otherwise respond to me if you have any questions or if I can be of further assistance.
     Best wishes!

Answer:

6

-----------             6 over 729

729

Step-by-step explanation:

2/9 * 2/9 * 2/9

Consider the function graphed below

Answers

For this case we have two study intervals.
 For x <1:
 In this interval we have the following equation:
 f (x) = x ^ 2
 For x> 1:
 In this interval we have the following equation:
 f (x) = (1/3) x + 2/3
 Answer:
 The graph represents the following function:
 f (x) = x ^ 2 (x <1)
 f (x) = (1/3) x + 2/3 (x> 1)

A drawer of loose socks contains 2 red socks, 2 green socks, and 6 white socks. Which best describes how to determine the probability of pulling out a white sock, not replacing it, and pulling out another white sock?

Answers

Well, before you draw out the first sock, you had 60% chance of getting a white sock since six of the ten socks are white! (6/10)

So, if you were to not replace the first drawn white sock, your percentage goes to 55.5556%! This is because you now have 5/9 socks remaining in the drawer being white!

Answer:

The probability that the first sock is white is 6/10 and that the second sock is white is 5/9, so the probability of choosing a pair of white socks is 30/90 = 1/3! Hope that helps.

Step-by-step explanation:

The _____ is a measure of variability that is simply the difference between the highest score and the lowest score. variance standard deviation median range

Answers

The answer to this is range! Because when you are figuring out the range, you subtract the lowest score from the highest score. Good luck on your test!

The range is a measure of variability that is simply the difference between the highest score and the lowest score. which is the correct answer would be option (D).

What is the range of the data?

The range of the data is defined as the difference between the maximum number of data to the minimum number of data.

The range of given data = maximum number - minimum number

The range is the correct answer to this because you subtract the lowest score from the highest score to determine the range.

Therefore, the range is a measure of variability that is simply the difference between the highest score and the lowest score.

Hence, the correct answer would be an option (D).

To learn more about the range of the data click here:

https://brainly.com/question/20607770

#SPJ5

Angles α and β are the two acute angles in a right triangle. Use the relationship between sine and cosine to find the value of β if β < α.


sin(7x − 15) = cos(3x + 5)

Answers

we know that
in a right triangle
if sin A= cos B
then
angle A and angle B are complementary angles
so A+B=90

therefore
(7x-15)+(3x+5)=90-----> 10x-10=90----> 10x=100----> x=10°
so
7x-15------> 7*10-15----> 55°
3x+5------> 3*10+5----> 35°

we know that
β < α
therefore

the answer is
β =35°
α=55°

Answer:

The answer is B). 35

Step-by-step explanation:

I did it on USA Test Prep

Uppose it costs $10 to roll a pair of dice. you get paid the sum of the numbers in dollars that appear on the dice. what is the expected value of this game?

Answers

at most $12, at least $2 a probability chart is best to solve for this

If GP=PH, GA =17, mED = 37, and mAB = 87, find each measure.

Answers

we know that
mAB = 87°
mED = 37°
mEFA=mBCD
360°=mAB+mED+mEFA+mBCD
360=87+37+2mBCD------> mBCD=[360-87-37]/2----> mBCD=118°

therefore
m BCD=118°
m FA=m EFA/2-----> m FA=118/2----> 59°
m FA=59°
m DC=m BCD/2----> m DC=118/2----> 59°
m DC=59°

HB=GA------> HB=17
DB=2*HB----> DB=2*17-----> DB=34

EG=GA------> EG=17

the answers are
DB=34
EG=17
mBCD=118°
mFA=59°
mDC=59°

Other Questions
Why do small fish swim around a large sting ray? Plato explains that we know geometry by _________. Census records for China and India would most likely be used to support which conclusions regarding the two nations?A.Lack of modern sanitation facilities worsens the spread of disease.B.Low food production contributes to malnutrition.C.Overpopulation strains available resources.D.Rapid industrialization increases air, water, and ground pollution. Completa la frase con la forma correcta del verbo apropiado. (Complete the sentence with the correct form of the appropriate verb.) Fernanda _______ a la casa de Manuel y Elena para ayudar con las decoraciones. A pones B dicen C viene D trae Population of victor? who wasEmperor of Ethiopia, 1930-1974 sqrt= Square Root A student is attempting to calculate the square root of 18. His work is shown below. Which statement below best applies to his mathematical reasoning? Givin sqrt 18 I observe that 18 is not a perfect square. I notice the perfect squares closest to 18 are 16 and 25, so I estimate the answer to fall somewhere between those numbers. Since 18 is closer to 16, I estimate that sqrt 18= 17A.18 is a perfect square, and the radical could have been evaluated directly.B.16 and 25 are not perfect squares, and therefore the student should not have chosen those numbers to estimate sqrt 18C.The student did not evaluate sqrt 16 and sqrt 25 before estimating sqrt 18D.The student has made no error. sqrt 18= 17 What are the products obtained in the electrolysis of molten nai? How do you find a missing height in a triangle? Glacier national park has lost _______ glaciers since 1910 when the park was created. PLZ HELP ASAP INSCRIBED QUADRILATERALS Which of the following words is the best descriptive word? A. Vegetable B. Zucchini C. Food D. Plant If Teresa counts 9 leaves on September 1, how will the number of leaves change from may 1 to September 1 People who are polytheistic have many Why did Kearny send most of his soilders back to New Mexico Which historical event does the betrayal by frederick represent? why does the narrator think she should not come to big D's spring break party? in the book the hate u give PLEASE HELP ASAPA 2.9 kg model rocket accelerates at 15.3 m/s2 with a force of 44 N. Before launch, the model rocket was not moving. After the solid rocket engine ignited, hot gases were pushed out from the rocket engine nozzle and propelled the rocket toward the sky. Which of Newtons laws apply in this example? Check all that apply.A the first lawB the second lawC the third lawD the fourth lawE the fifth law each side of rectangular polygon is 2.5cm in length .the perimeter of the polygon is 12.5cm.how many sides does the polygon have A template dna strand contains the sequence 3'-atgctgac-5'. the corresponding sequence in the rna transcript is: