Answer:
r=4
Step-by-step explanation:
-6=0.75(r-12)
-6= 0.75r-9
3=0.75r
r=4
Suppose the horses in a large stable have a mean weight of 975lbs, and a standard deviation of 52lbs.What is the probability that the mean weight of the sample of horses would differ from the population mean by less than 15lbsif 31horses are sampled at random from the stable
Answer: The required probability = 0.8926
Step-by-step explanation:
Given: [tex]\mu=975\text{ lbs}[/tex], [tex]\sigma= 52\text{ lbs}[/tex]
Let x = weight of horse stable.
Sample size : n= 31
Then, the probability that the mean weight of the sample of horses would differ from the population mean by less than 15 will be:
[tex]P(-15<P(\overline{x}-\mu)<15)=P(\dfrac{-15}{\dfrac{52}{\sqrt{31}}}<\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}<\dfrac{15}{\dfrac{52}{\sqrt{31}}})\\\\=P(-1.61<z<1.61)\ \ \ [z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=2(z<1.61)-1\ \ \ [P(-z<Z<z)=2(Z<z)-1]\\\\=2( 0.9463)-1\\\\=0.8926[/tex]
Hence, the required probability = 0.8926
The auxiliary equation for the given differential equation has complex roots. Find a general solution. y''-10y' 29y=0
Answer:
[tex]y = Acos5x - Bsin5x[/tex]
Step-by-step explanation:
Given the differential equation y''-10y'+29y=0
First, we need to rewrite it as an auxiliary equation as shown:
Let y'' = m²y and y' = my
Substitute the values into the general equation
m²y-10my+29y = 0
Factor out y:
(m²-10m+29)y = 0 [The auxiliary equation]
Solve the auxiliary equation and find the roots of the equation
m²-10m+29 = 0
m = -b±√(b²-4ac)/2a
a = 1, b = -10, c = 29
m = -10±√(10²-4(1)(29))/2(1)
m = -10±√(100-116)/2
m = -10±√-16/2
m = (-10±4i)/2
m = -10/2 + 4i/2
m = -5+2i
Comparing the complex number with a+bi, a = -5 and b = 2
The general solution for complex solution is expressed as:
[tex]y = Acosax + Bsinax[/tex]
Substitute the value of a in the equation
[tex]y = Acos(-5)x + Bsin(-5)x\\y = Acos5x-Bsin5x[/tex]
Hence the general solution to the differential equation is [tex]y = Acos5x - Bsin5x[/tex]
A projectile is launched straight up from the ground with an initial velocity of 120 ft/s. If acceleration due to gravity is –16 ft/s2, after about how many seconds will the object reach a height of 200 ft?
Answer:
The projectile will reach a height of 200 ft after 1.910 seconds and 13.090 seconds of being launched.
Step-by-step explanation:
This projectile is experimenting a free fall, that is, an uniform accelerated motion of the projectile due to gravity and in which effects of air friction and Earth's rotation are neglected. Given that initial and final heights, initial velocity and gravitational acceleration are known, we need to calculate time by solving the appropriate equation of motion described below:
[tex]y = y_{o} +v_{o}\cdot t +\frac{1}{2}\cdot g \cdot t^{2}[/tex] (Eq. 1)
Where:
[tex]y_{o}[/tex] - Initial height of projectile, measured in feet.
[tex]y[/tex] - Final height of projectile, measured in feet.
[tex]v_{o}[/tex] - Initial velocity of projectile, measured in feet per second.
[tex]g[/tex] - Gravitational acceleration, measured in feet per square second.
As we must remember, quadratic functions have two roots and if we get that [tex]y_{o} = 0\,ft[/tex], [tex]y = 200\,ft[/tex], [tex]v_{o} = 120\,\frac{ft}{s}[/tex] and [tex]g = -16\,\frac{ft}{s^{2}}[/tex], then, the quadratic function is:
[tex]-8\cdot t^{2}+120\cdot t -200 = 0[/tex]
Roots are found by the Quadratic Formula:
[tex]t_{1,2} = \frac{-120\pm \sqrt{120^{2}-4\cdot (-8)\cdot (-200)}}{2\cdot (-8)}[/tex]
Whose solutions are:
[tex]t_{1} \approx 13.090\,s[/tex] and [tex]t_{2} \approx 1.910\,s[/tex].
Both roots are physically reasonable, first root represents the instant when the projectile reaches 200 feet when it is moving downwards, whereas second root represents the projectile moving upwards. Therefore, the projectile will reach a height of 200 ft after 1.910 seconds and 13.090 seconds of being launched.
Answer:
It will take 2.5 s to reach a height of 200ft.
Step-by-step explanation:
Una partícula se mueve sobre el eje x de acuerdo con la ecuación del movimiento
s=f(t) donde s es la distancia dirigida al origen en pies a los t segundos.
a) La velocidad v(t) y la aceleración a(t) en el instante t.
b) El instante t en el que la velocidad es cero.
s= 6t-t²
s=t²-6t
s= t²-9t+24
Answer:
a)
s= 6t-t² --> v = 6 -2t --> a = -2
s=t²-6t --> v = 2t-6 --> a = 2
s= t²-9t+24 --> v = 2t -9 --> a = 2
b)
v = 6 -2t = 0 --> t = 3
v = 2t-6 = 0 --> t = 3
v = 2t -9 = 0 --> t = 9/2
Step-by-step explanation:
si s(t) es la distancia, la velocidad es la primera derivada v(t) = s'(t)
y la acceleracion es la segunda derivada : a(t)= v'(t) = s''(t)
s= 6t-t² --> v = 6 -2t --> a = -2
s=t²-6t --> v = 2t-6 --> a = 2
s= t²-9t+24 --> v = 2t -9 --> a = 2
how can you plot,compare,and order rational numbers using a number line?
5 of 10
Which of the following are one-dimensional figures?
Check all that apply.
O A. Segment
B. Ray
O C. Angle
O D. Line
D E. Plane
F. Cube
Its (Ray , Segment, line, )
Segment, ray and line are one-dimensional figures.
We need to check from the given options which are one-dimensional figures.
What are one-dimensional figures?One-dimensional: Only a single measurement is possible for a one-dimensional figure. A line segment drawn on a surface is a one-dimensional object, as it has only length and no width.
Here, the segment is a one-dimensional figure.
Ray is a one-dimensional figure.
Angle is a two-dimensional figure.
A line is a one-dimensional figure.
The plane is a two-dimensional figure.
A cube is a three-dimensional figure.
Therefore, segment, ray and line are one-dimensional figures.
To learn more about one-dimensional figures visit:
https://brainly.com/question/17967616.
#SPJ2
What is
f(x) = x3 – 4x2 – 7x + 10 in factored form given that 5 is a zero of the function?
Answer:
(x-2)(x+1)(x-5)
Step-by-step explanation:
The equation x + y = z relates the whole numbers x, y, and z. How does z compare to x? If it helps, consider an example where you substitute 3 for x, 5 for y, and 8 for z
Answer:
The equation x + y = z relates the whole numbers.
Hopefully, this helps! :D
Ask your question below!
5,049 +48=105
MD Model with Mathematics A comic store sells two rare
comic books for $1,824. The price of one comic book is
11 times as much as the price of the other.
• 'Write an equation to model the price of the less expensive
comic book. Then find the price.
• Write an equation to model the price of the more expensive
comic book. Then find the price.
Let the cost of the less expensive comic book be x .
Then :-
[tex]1284 - 11x = x[/tex]
Using this equation , we can find the cost of the less expensive comic book .
Price of the less expensive book :-
[tex]1284 - 11x = x[/tex]
[tex]11x + x = 1284[/tex]
[tex]12x = 1284[/tex]
[tex]x = \frac{1284}{12} [/tex]
[tex]x = 107[/tex]
Cost of the less expensive book is 107 .
Therefore , the epice of the less expensive book = $ 107 .
Solution (b) :-Cost of the more expensive book = 11x
Which means :-
[tex]1284 - x = 11x[/tex]
[tex]11x + x = 1284[/tex]
[tex]12x = 1284[/tex]
[tex]x = 107[/tex]
[tex]11x = 11 \times 107[/tex]
[tex] = 1177[/tex]
Therefore , the price of the more expensive book = $ 1177 .
A random sample drawn from a population with mean μ= 66 and standard deviation σ= 6.
Required:
a. Comment on the sampling distribution of the sample mean with n = 16 and n = 36.
b. Can you use standard normal distribution to calculate the probability that the sample mean falls between 66 and 68 for both sample sizes?
c. Report the probability if you answered yes to the previous question for either sample size.
Answer:
In step by step explanation
Step-by-step explanation:
a) Normal distribution N( 0, 1 )
If the sample size is equal n = 16 we have to use t-student distribution since n < 30.
In the case n = 36 we should use normal distribution (z tables)
b) We can´t use the standard normal distribution to calculate the probability that the sample mean falls between 66 and 68 in the first case n < 30 .
We can calculate that probability in the case of the second sample
-2/3 - (-1 1/3)
A. -1 2/3
B. -2/3
C. -1/3
D. 2/3
Answer is 2/3
Hope this helps
Pls helpppppp this stuff makes no sense
Answer:
x = 5
Step-by-step explanation:
a || b and a line intersecting them is their transversal.
[tex] \therefore m\angle 1=m\angle 5\\(corresponding \:\angle 's) \\\\
\therefore 60 - 2x = 70 - 4x\\\\
\therefore 4x - 2x = 70 - 60\\\\
\therefore 2x = 10\\\\
\therefore x =\frac{10}{2} \\\\
\huge \orange {\boxed {\therefore x = 5}}[/tex]
The state of Tennessee is shaped like a parallelogram. Its approximate dimensions are a base of 440 miles and a height of 120 miles. The state of Colorado is shaped like a rectangle, with approximate dimensions of 385 miles long and 275 miles wide. Ted works for a geographical company that is working on finding the areas of each state in the Union. Ted asked an assistant to double‐check his answers. Approximate area of Tennessee: 63,000 mi2 Approximate area of Colorado: 106, 000 mi2 11. If you were Ted’s assistant, would you agree with his answers? Explain why you answered yes or no by showing your work and explaining how it helped you come to your answer.
Answer:
Tennessee area we don´t know there is something wrong
Colorado area is ok close to 106000 mi²
Step-by-step explanation:
Tennessee is shaped like a parallelogram base is equal to 440 miles and the height is 120 miles. Therefore
Ap = b*h = 440 * 120 = 52800 mi²
But the area of Tennessee is 63000 mi²
Then there is something wrong because difference in mi² is
10400 mi²
10400/ 63000 = 0,165 % faraway of the real number
In the case of Colorado
Ac = 385 * 275
Ac = 105875 mi² pretty close to 106000 mi²
Then from double check in the areas, we conclude in a high difference in the figures for the state of Tennessee ( one or both of the figures are incorrect ). The state of Colorado area is oK
Which of the following is equal to −|−43|
-43
0
43
-(-43)
Answer:
i think ur answer is -43.i hope u get it
Answer:
the answer is i guess -43
Step-by-step explanation:
|-43| = 43
so -|-43| = -43
Pendiente 6 y puntos (5, -2)
Step-by-step explanation:
In the diagram, the origin is at the center of a cube that has edges 6 units long. The x-, y-, and z-axes are perpendicular to the faces of the cube. Give the coordinates of the corner at point E.
(3, 3, –3)
(3, –3, –3)
(–3, 3, 3)
(–3, –3, 3)
Answer:
I really think that (3 , -3 , -3) is the answer but I could be wrong.
Step-by-step explanation:
I'm taking the quiz right now and from the graph it looks like point E is in the position (3 , -3 , -3).
Once again, sorry if I'm wrong.
Please help me solve What is m
Answer:
a=60
b=85
c=35
Step-by-step explanation:
a is shown to be 60 in the text along with c being 85 with its angle so just add 60 and 85 to get 145 and fill in the remaining to get 180 which gives you c as 35
light travels 3 x 10^5 kilometers in one second. how far does it travel in 7.6 seconds?
Answer:
1800000 kilometers
Step-by-step explanation:
i think im not 100% sure
A small town has two local high schools. High School A currently has 750 students
and is projected to grow by 75 students each year. High School B currently has 900
students and is projected to grow by 25 students each year. Let A represent the
number of students in High School A in t years, and let B represent the number of
students in High School B after t years. Write an equation for each situation, in terms
of t, and determine how many students would be in each high school in the year they
are projected to have the same number of students.
Ok
Answer:
A=750 +75*t
B=900 +25*t
There would be 975 students in each high school in year 3 when they are expected to have the same number of students.
Step-by-step explanation:
You know that High School A currently has 750 students and is projected to grow by 75 students each year. With A being the number of students in High School A in t years, this number will be the number of students it has initially added to the number of students who have joined after t years. This is represented by:
A=750 +75*t
You know that High School B currently has 900 students and is projected to grow by 25 students each year. With B being the number of students in High School B in t years, this number will be the number of students it has initially added to the number of students who have joined after t years. This is represented by:
B=900 +25*t
You want to determine how many students there would be in each high school in the year that they are projected to have the same number of students. That is, in year t the number of students is the same, so
A = B
750 +75*t=900 + 25*t
Solving:
75*t -25*t= 900 - 750
50*t= 150
[tex]t=\frac{150}{50}[/tex]
t=3
This indicates that in year 3 both High Schools are projected to have the same number of students. To get that amount, you simply replace this value in the expressions:
A=750 +75*t= 750 +75*3= 975
B=900 + 25*t=900 + 25*3= 975
There would be 975 students in each high school in year 3 when they are expected to have the same number of students.
Answer: REAL ANSWER
A= 75t +750
B=25t +900
Answer: 975 students
Please help!!
Square ABCD has vertices A(-2,-3), B(4, -1), C(2,5), and D(-4,3). Find the length of a side
of the square. Round your answer to the nearest tenth if necessary.
Answer:
The length of a side of the square is 6.3 units.
Step-by-step explanation:
When given vertices for a given shape, the length of the side is calculated using the formula:
√(x2 - x1)² + (y2 - y1)²
When given vertices (x1 , y1) and (x2 , y2)
Square ABCD has vertices A(-2,-3), B(4, -1), C(2,5), and D(-4,3). Find the length of a side
Side AB : A(-2,-3), B(4, -1)
√(x2 - x1)² + (y2 - y1)²
= √(4 -(-2))² + (-1 -(-3))²
= √ 6² + 2²
= √36 + 4
= √40
= 6.3245553203
≈ 6.3 units
B(4, -1), C(2,5),
√(x2 - x1)² + (y2 - y1)²
= √ (2- 4)² + (5- (-1))²
= √-2² + 6²
= √4 + 36
= √40
= 6.3245553203
≈ 6.3 units
C(2,5), D(-4,3).
√(x2 - x1)² + (y2 - y1)²
= √(-4 - 2)² + (3 - 5)²
= √-6² + -2²
= √36 + 4
= √40
= 6.3245553203
≈ 6.3 units
A(-2,-3), D(-4,3).
√(x2 - x1)² + (y2 - y1)²
= √(-4 -(-2))² + (3 - (-3))²
= √-2² + 6²
= √4 + 36
= √40
= 6.3245553203
≈ 6.3 units
your job requires that you work at least 40 hours a week you have already worked 15 and there are 4 more days left in the week how many hours do you have to work each day to get at least 40 hours: inequality and solution
Answer:
6.25 hours
Step-by-step explanation:
this is rather simple really,
first, you have to work 40 hours a week
you have already worked 15 so now you can subtract that
40-15= 25hrs
if you have 4 more days of the week you divide the remaining hours by the days left
25/4= 6.25hrs
that would be the bare minimum of hours for you to work a 40 hour week.
Given m|n, find the value of x.
t
xo
>m
53°
Answer:
32 degrees goto the x vaule
On day 3 of a canned food drive, the students had collected 80 cans and were 40% of the way to their goal. What was their goal for the total number of cans they hoped to collect?
Answer:
200 cans
Step-by-step explanation:
use rate method
80 40
x 100
40x=8000
x=8000/40
x=200
Ellie the elephant has some peanuts. She eats up 49 peanuts. Now Ellie the elephant has 31 peanuts. How many peanuts did she have before?
Answer:
80
Step-by-step explanation:
do: 49+31=Your answer
Ellie had 80 peanuts before she ate 49 of them.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let x be the number of peanuts Ellie had before she ate 49 of them.
After eating 49 peanuts, Ellie has 31 peanuts left, so we can write an equation:
x - 49 = 31
To solve for x, we add 49 to both sides of the equation:
x - 49 + 49 = 31 + 49
Simplifying, we get:
x = 80
Therefore, Ellie had 80 peanuts before she ate 49 of them.
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ2
4. Tell whether the equation is a linear equation.
4x-3y = 2
Answer:
What Is X and Y
Step-by-step explanation:
Answer:
It is a linear equation.
Step-by-step explanation:
It has no squares in the equation, meaning the line is straight, therefore meaning the equation is linear.
juan feeds his dog 2 scoops of dry dog food every day. each scoop weighs 1/3 pound. he bought a new 12 pound of dog food. how many days will it last
Multiply. Express your answer in simplest form. 9 1/6 × 1 1/11. A. 10 B. 9 1/66 C. 10 1/17 D. 10 5/6
Answer:
9 1/66
Step-by-step explanation:
9 x 1 is 9 so its that but to add more proof the problem is 9 1/6, 1 1/11 multiply 6 and 11 it is 66 so the answer is 9 1/66
What is the slope of the line passing through the points (0,-5) and (4,2)?
Enter your answer in the box
Answer:
[tex] \huge{ \boxed{ \tt{ \frac{ 7}{4} }}}[/tex]
Step-by-step explanation:
[tex] \text{Let \: the \: points \: be \: A \: and \: B}[/tex]
[tex] \sf{A \:( \: 0 \:, - 5 \: ) \longrightarrow{ \: (x1 \:, y1)}}[/tex]
[tex] \sf{B(4 \:, 2) \: \longrightarrow{ \:( x2 \:, y2)}}[/tex]
[tex] \underline{ \text{Finding \: the \: slope} }: [/tex]
[tex] \boxed{ \sf{Slope = \frac{y2 - y1}{x2 - x1}}} [/tex]
[tex] \sf{➳ \: Slope = \frac{2 - ( - 5)}{4 - 0}} [/tex]
[tex] \sf{➳ \: Slope = \frac{ 2 + 5}{4} }[/tex]
[tex] \sf{➳ \: Slope = \frac{7}{4} }[/tex]
[tex] \text{Hope \: I \: helped!}[/tex]
[tex] \text{Best \: regards!}[/tex]
~[tex] \text{TheAnimeGirl}[/tex]
a baseball field is being constructed. the builders noticed that the batters would have the sun in their eyes when batting from point a. the builders decided to rotate the model 90 counterclockwise about the origin where is the new location of the batter?
A) E
B)F
C)G
D)H
Answer:
b
Step-by-step explanation:
Answer:
G
Step-by-step explanation:
Andy was at Level –1 and took the elevator to Level 21. How many levels did the elevator move upward?
Answer: 22 Levels
Step-by-step explanation: He would need to go one level higher just to get to level one, and another 21 to get to the level that he wants to, so the total would be 22 levels.
Answer:
The elevator moved up 21 levels
