Answer:
B. assumption of conclusions without prior experimentation or observation.
Step-by-step explanation:
In scientific investigation is quite important to demonstrate with facts, with observations, with numbers. All discoveries, new insights, new knowledge found in scientific investigation is based on a very careful finding of facts in a very systematic way of doing that to establish conclusions about the question to be answered and constantly looking for objective evidence.
For instance, one hundred years ago, some physicists found a crucial fact that support one of the predictions that Einstein posted regarding a phenomena described as curved space because of the effect that a massive object exerts around its surrounding space. In fact, that year of 1919, those physicists observed that light traveled around a massive start not in straight line but curving around start's space (a fact), of course, using telescopes, writing observations and quantifying them (a systematic way).
Einstein's theory (in this case, the famous General Relativity Theory) must be supported, at least in part, with the discovery of an important fact, and not because he assumed that it was 'true' without prior experimentation or observation but because some others experimental physicists took a 'secret' from Nature (objective evidence) and gave a crucial fact about what Einstein had predicted some years before.
But it is not a definitive fact, a definitive list, there will be some more facts to look for in order to support that theory (constantly looking) and, why not, some other scientist or scientists could find another one, make a new experiment, test another hypothesis or model that contradicts the whole theory or some part of it.
Explain whether the fractions 3/6 and 7/14 are equivalent. Explain.
**I know it's equivalent but I don't understand how.
3/6 and 7/14 can both be reduced to 1/2
Lets start with 3/6
3 divided by 3 1
-- ----
6 divided by 3 2
now, 7/14
7 divided by 7 1
-- ----
14 divided by 7 2
Whatever you do to the numerator (top number) you have to do to the denominator (bottom number)
Three of four numbers have a sum of 22. If the average of the four numbers is 8, what is the fourth number? a) 4 b) 6 c) 8 d) 10
Answer:
10
Step-by-step explanation:
First you do 8 × 4, this gives the total of the four numbers.
[tex]8 \times 4 = 32[/tex]
Then, subtract the total of 3 of the numbers from the total of 4 of the numbers.
[tex]32 - 22 = 10[/tex]
Jessica has three sports cards, one for football (F), one for baseball (B), and one for soccer (S). She picks one card, replaces it, and then picks another card. The sample space for this compound event is listed.
Answer:
The answer is 9
Answer:
Step-by-step explanation:
9
9x−9y=0 3x−4y=10 solve by elimination
Answer:
(-10,-10)
Step-by-step explanation:
9x-9y=0
3x-4y=10
In elimination, we want both equations to have the same form and like terms to be lined up. We have that. We also need one of the columns with variables to contain opposites or same terms. Neither one of our columns with the variables contain this.
We can do a multiplication to the second equation so that the first terms of each are either opposites or sames. It doesn't matter which. I like opposites because you just add the equations together. So I'm going to multiply the second equation by -3.
I will rewrite the system with that manipulation:
9x-9y=0
-9x+12y=-30
----------------------Add them up!
0+3y=-30
3y=-30
y=-10
So now once you find a variable, plug into either equation to find the other one.
I'm going to use 9x-9y=0 where y=-10.
So we are going to solve for x now.
9x-9y=0 where y=-10.
9x-9(-10)=0 where I plugged in -10 for y.
9x+90=0 where I simplified -9(-10) as +90.
9x =-90 where I subtracted 90 on both sides.
x= -10 where I divided both sides by 9.
The solution is (x,y)=(-10,-10)
Write the standard form of the equation that is parallel to y = -3x + 3 and goes through point (-5, 5).
3x + y = -10. The standard form of the equation that is parallel to y = -3x + 3 and goes through point (-5, 5) is 3x + y = -10.
The equation is written in the slope-intercept form y = mx +b. So:
y = -3x + 3
The slope m = -3
Since the slopes of parallel lines are the same, we are looking for a slope line m = -3 and goes through point (-5, 5).
With the slope-intercept form:
y = mx + b
Introducing the slope m = -3:
y = -3x + b
Introducing the point (-5, 5):
5 = -3(-5) + b
5 = 15 + b
b= 5 - 15
b = -10
then
y = -3x -10
write the equation in standard form ax + by = c:
y = -3x -10
3x + y = -10
To find the standard form of the equation of a line that is parallel to y = -3x + 3 and passes through the point (-5, 5), let's follow these steps:
1. **Identify the slope**: Since parallel lines have the same slope, we can take the slope of the given line y = -3x + 3, which is -3.
2. **Use the point-slope form**: With the slope known and a point provided, we can use the point-slope form of the equation, which is:
\[ y - y_1 = m(x - x_1) \]
where \(m\) is the slope and \((x_1, y_1)\) is the point the line passes through.
3. **Apply the point and slope**: Insert the slope (-3) and the point (-5, 5):
\[ y - 5 = -3(x - (-5)) \]
\[ y - 5 = -3(x + 5) \]
4. **Distribute the slope**: Multiply -3 by both terms inside the parentheses:
\[ y - 5 = -3x - 15 \]
5. **Isolate y:** Add 5 to both sides of the equation to isolate y:
\[ y = -3x - 15 + 5 \]
\[ y = -3x - 10 \]
6. **Convert to standard form**: The standard form of a linear equation is \(Ax + By = C\), where \(A\), \(B\), and \(C\) are integers, and \(A\) should be non-negative. Arrange the terms:
\[ 3x + y = -10 \]
So the standard form of the equation that is parallel to y = -3x + 3 and passes through the point (-5, 5) is \(3x + y = -10\).
help pleaseeeeeeeeeeee
Answer:
Step-by-step explanation:
The temperature at a given altitude is
y = 36 - 3x
The temperature on the surface of the planet is the point (0,t) where t is the temperature for the given height.
y = 36 - 3*0
y = 36
So at the surface of the planet is 36 degrees C.
======================
Effectively it is the slope of the equation which is - 3
So ever km going up will mean a loss of 3 degrees. I think they want you to write -3
A baboon steals an apple and runs to a nearby boulder 10.0 m to its left. The baboon reaches the boulder in 1.0s with a constant acceleration of 20.0m/s^2 leftward. What was the baboon's initial velocity when it started running to the boulder?
Answer:
Initial velocity is zero.
Step-by-step explanation:
According to second equation of motion
[tex]s=ut+\frac{1}{2} at^2[/tex]
where s = distance traveled
t = time taken
a = acceleration
u = initial velocity
here in the question we have
s = 10 m
t = 1 second
a = 20[tex]ms^{-2}[/tex]
plugging the known value in order to find the unknown which is u (initial velocity)
[tex]10=u(1)+\frac{1}{2} (20)(1)^2[/tex
10 = u +10
gives u =0
therefore initial velocity is zero.
a baseball is thrown into the air with an upward velocity of 30 ft/s. its initial height was 6 ft, and its maximum height is 20.06 ft. how long will it take the ball to reach its maximum height? round to the nearest hundredth.
i've been stuck on this question for almost an hour so if anyone can help that would be greatly appreciated
Check the picture below.
where is the -16t² coming from? that's Earth's gravity pull in feet.
[tex]\bf ~~~~~~\textit{initial velocity} \\\\ \begin{array}{llll} ~~~~~~\textit{in feet} \\\\ h(t) = -16t^2+v_ot+h_o \end{array} \quad \begin{cases} v_o=\stackrel{30}{\textit{initial velocity of the object}}\\\\ h_o=\stackrel{6}{\textit{initial height of the object}}\\\\ h=\stackrel{}{\textit{height of the object at "t" seconds}} \end{cases} \\\\\\ h(t)=-16t^2+30t+6 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ h(t)=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+30}t\stackrel{\stackrel{c}{\downarrow }}{+6} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]
[tex]\bf \left(-\cfrac{30}{2(-16)}~~,~~6-\cfrac{30^2}{4(-16)} \right)\implies \left( \cfrac{30}{32}~,~6+\cfrac{225}{16} \right)\implies \left(\cfrac{15}{16}~,~\cfrac{321}{16} \right) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (\stackrel{\stackrel{\textit{how many}}{\textit{seconds it took}}}{0.9375}~~,~~\stackrel{\stackrel{\textit{how many feet}}{\textit{up it went}}}{20.0625})~\hfill[/tex]
Answer:
Step-by-step explanation:
I'm not sure if this question is coming from a physics class or an algebra 2 or higher math class, but either way, the behavior of a parabola is the same in both subjects. If a parabola crosses the x axis, those 2 x values are called zeros of the polynomial. Those zeros translate to the time an object was initially launched and when it landed. The midpoint is dead center of where those x values are located. For example, if an object is launched at 0 seconds and lands on the ground 3 seconds later, it reached its max height at 2 seconds. So what we need to do is find the zeros of this particular quadratic, and the midpoint of those 2 values is where the object was at a max height of 20.06.
I used the physics equation representing parabolic motion for this, since it has an easier explanation. This equation is
[tex]x-x_{0}=v_{0}+\frac{1}{2}at^2[/tex]
where x is the max height, x₀ is the initial height, v₀ is the initial upwards velocity, t is time (our unknown as of right now), and a is the acceleration due to gravity (here, -32 ft/sec^2). Filling in our values gives us this quadratic equation:
[tex]20.06-6=30(t)+\frac{1}{2}(-32)t^2[/tex]
Simplifying that a bit gives us
[tex]14.06=30t-16t^2[/tex]
Rearranging into standard form looks like this:
[tex]0=-16t^2+30t-14.06[/tex]
If we factor that using the quadratic formula we find that the 2 times where the ball was launched and then where it came back down are
t = .925 and .95 (the ball wasn't in the air for very long!)
The midpoint occurs between those 2 t values, so we find the midpoint of those 2 values by adding them and dividing the sum in half:
[tex]\frac{.925+.95}{2}=.9375[/tex]
Therefore, the coordinates of the vertex (the max height) of this parabola are (.94, 20.06). That translates to: at a time of .94 seconds, the ball was at its max height of 20.06 feet
I need help pretty please!
Answer:
cos(z) = .3846153846 and angle z = 67.38°
Step-by-step explanation:
Side UV is corresponding to side YX. Side VW is corresponding to side YZ. Side UW is corresponding to side XZ.
Starting with the first corresponding pair, we are told that side UV is 36, and that side YX is 3/5 of that. So side YX is
[tex]\frac{3}{5}*36=21.6[/tex]
We are next told that side VW is 39, so side YZ is
[tex]\frac{3}{5}*39=23.4[/tex]
In order to find the cos of angle z, we need the adjacent side, which is side XZ. Side XZ is 3/5 of side UW. Right now we don't know the length of side UW, so we find it using Pythagorean's Theorem:
[tex]39^2-36^2=UW^2[/tex] and
[tex]UW^2=225[/tex] so
UW = 15
Now we can say that side XZ is
[tex]\frac{3}{5}*15=9[/tex]
The cos of an angle is the side adjacent to the angle (9) over the hypotenuse of the triangle (23.4) so our ratio is:
[tex]cos(z)=\frac{9}{23.4}[/tex]
which divides to
cos(z) = .3846153846
If you need the value of the angle, use the inverse cosine function on your calculator in degree mode to find that
angle z = 67.38°
Can someone help me please?
A rectangle with a perimeter of 92 inches has a length of 14 inches longer than its width. What is its width in inches.
Please explain step by step thank you.
Answer:
16 inches
Step-by-step explanation:
w = width of the rectangle
l = length of the rectangle
The perimeter of a rectangle is the length around it:
P = 2w + 2l
Given:
P = 92
l = w + 14
Substituting:
92 = 2w + 2(w + 14)
92 = 2w + 2w + 28
64 = 4w
w = 16
The width of the rectangle is 16 inches.
Final answer:
The width of the rectangle is 16 inches, deduced by using the perimeter formula for a rectangle and solving for width with given conditions.
Explanation:
To find the width of the rectangle given its perimeter and the fact that its length is 14 inches longer than its width, we start by listing what we know:
The perimeter of the rectangle is 92 inches.
The length (L) is 14 inches longer than the width (W).
Remember, the perimeter (P) of a rectangle is given by P = 2L + 2W. We can substitute L with W + 14, since the length is 14 inches more than the width. This gives us:
P = 2(W + 14) + 2W
Now we can plug in the value for P:
92 = 2(W + 14) + 2W
Then, distribute:
92 = 2W + 28 + 2W
Combine like terms:
92 = 4W + 28
Now, subtract 28 from both sides:
64 = 4W
Lastly, divide by 4 to solve for W:
16 = W
So, the width of the rectangle is 16 inches.
If f(x) = -2x - 5 and g(x) = x^4 what is (gºf)(-4)
Answer:
81
Step-by-step explanation:
(g∘f)(-4) is another way of writing g(f(-4)).
First, find f(-4):
f(-4) = -2(-4) − 5
f(-4) = 3
Now plug into g(x):
g(f(-4)) = g(3)
g(f(-4)) = 3^4
g(f(-4)) = 81
The vertex form of the equation of a parabola is y=(x-3)^2+35 what is the standard form of the equation
Answer:
x^2 -6x+44
Step-by-step explanation:
Develop form of (x-3)^2 is x^2 - 6x +9
Then y= x^2 -6x +9 + 35
So, y= X^2 -6x +44
Answer:
[tex]y=x^2 -6x+44[/tex]
Step-by-step explanation:
The standard form of a quadratic equation is:
[tex]y = ax ^ 2 + bx + c[/tex].
In this case we have the following quadratic equation in vertex form
[tex]y=(x-3)^2+35[/tex]
Now we must rewrite the equation in the standard form.
[tex]y=(x-3)(x-3)+35[/tex]
Apply the distributive property
[tex]y=x^2 -3x -3x +9+35[/tex]
[tex]y=x^2 -6x+9+35[/tex]
[tex]y=x^2 -6x+44[/tex]
the standard form of the equation is: [tex]y=x^2 -6x+44[/tex]
A right rectangular prism has base dimensions of 3 inches by 12 inches. An oblique rectangular prism has base dimensions of 4 inches by 9 inches.
If the prisms are the same height, how do their volumes compare?
The volumes are equal, because the bases are congruent.
The volumes are equal, because the heights are equal and the horizontal cross-sectional areas at every level are also equal.
The volumes are not equal, because their horizontal cross-sectional areas are not the same at every level.
Answer:
The correct option is 2.
Step-by-step explanation:
Given information: Height of both prism are same.
Right rectangular prism has base dimensions of 3 inches by 12 inches.
Volume of a right rectangular prism:
[tex]V=Bh[/tex]
where, B is base area and h is height of the prism.
The volume of right rectangular prism is
[tex]V=(3\times 12)\times h=36h[/tex]
Therefore the volume of right rectangular prism is 36h cubic inches.
An oblique rectangular prism has base dimensions of 4 inches by 9 inches.
Volume of a oblique rectangular prism:
[tex]V=Bh[/tex]
where, B is base area and h is height of the prism.
The volume of right rectangular prism is
[tex]V=(4\times 9)\times h=36h[/tex]
Therefore the volume of oblique rectangular prism is 36h cubic inches.
The volumes are equal, because the heights are equal and the horizontal cross-sectional areas at every level are also equal.
Option 2 is correct .
The volumes are equal, because the heights are equal and the horizontal cross-sectional areas at every level are also equal.
How to find the volume of the prism?The formula for the Volume of a right rectangular prism is:
V = B * h
where,
B is base area.
h is height of the prism.
Thus:
V = 3 * 12 * h
V = 36h
Similarly, the volume of the oblique rectangle is:
V = Bh
V = 4 * 9 * h
V = 36h
Thus, we can see that the volumes are equal, because the heights are equal and the horizontal cross-sectional areas at every level are also equal.
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Find the value of x, if m arc FN = 5x – 10 and m= arc UN = 3x + 30.
Answer:
x=20
Step-by-step explanation:
we know that
Triangles YNF and YUN are congruent by SSS
Because
YN=YF=YU=r -----> the radius of the circle
FN=NU ----> given problem
therefore
∠FYN=∠NYU
and
arc FN=∠FYN -----> by central angle
arc NU=∠NYU -----> by central angle
so
arc FN=arc NU
substitute the given values
5x-10=3x+30
solve for x
5x-3x=30+10
2x=40
x=20
A growth medium is inoculated with 1,000 bacteria, which grow at a rate of 15% each day. What is the population of the culture 6 days after inoculation? Y = 1,000(1.15)6 2,313 bacteria y = 1,000(1.15)7 y = 1,000(1.5)5 y = 1,000(1.5)6 11,391 bacteria
Answer:
The correct option is Y = 1,000(1.15)6 2,313 bacteria
Step-by-step explanation:
According to the given statement a growth medium is inoculated with 1,000 bacteria.
Bacteria grow at a rate of = 15% = 0.15
Add 1 to make it easier = 0.15+1 = 1.15
We have to find the population of the culture 6 days after inoculation.
= 1000(1.15)^6
=1000(2.313)
= 2313 bacteria
The population of the culture 6 days after inoculation = 2313 bacteria
Therefore the correct option is Y = 1,000(1.15)6 2,313 bacteria....
Answer:AAAAAAAAAAAAAAAAAAAA
URGENT PLEASE HELP ME WITH THIS MATH QUESTION Should
Answer:
A composition of transformations is a combination of two or more transformations.A composition of reflections over parallel lines has the same effect as a translation (twice the distance between the parallel lines.
Step-by-step explanation:
The annual 2-mile fun-run is a traditional fund-raising event to support local arts and sciences activities. It is known that the mean and the standard deviation of finish times for this event are respectively \mu μ = 30 and \sigma σ = 5.5 minutes. Suppose the distribution of finish times is approximately bell-shaped and symmetric. Find the approximate proportion of runners who finish in under 19 minutes.
Answer: 0.0228
Step-by-step explanation:
Given : The mean and the standard deviation of finish times (in minutes) for this event are respectively as :-
[tex]\mu=30\\\\\sigma=5.5[/tex]
If the distribution of finish times is approximately bell-shaped and symmetric, then it must be normally distributed.
Let X be the random variable that represents the finish times for this event.
z score : [tex]z=\dfrac{x-\mu}{\sigma}[/tex]
[tex]z=\dfrac{19-30}{5.5}=-2[/tex]
Now, the probability of runners who finish in under 19 minutes by using standard normal distribution table :-
[tex]P(X<19)=P(z<-2)=0.0227501\approx0.0228[/tex]
Hence, the approximate proportion of runners who finish in under 19 minutes = 0.0228
Final answer:
To find the proportion of runners finishing a 2-mile fun-run in under 19 minutes, we calculate the z-score for a finish time of 19 minutes given the mean of 30 and standard deviation of 5.5. The calculated z-score of -2 corresponds to about 2.28% of runners according to the standard normal distribution.
Explanation:
To find the approximate proportion of runners who finish in under 19 minutes, we will use the properties of the normal distribution because the distribution of finish times is approximately bell-shaped and symmetric. Given that the mean finish time (μ) is 30 minutes and the standard deviation (σ) is 5.5 minutes, we can calculate the z-score for a finish time of 19 minutes.
The z-score is calculated by the formula:
z = (X - μ) / σ
Where X is the finish time of interest (19 minutes), μ is the mean (30 minutes), and σ is the standard deviation (5.5 minutes).
Plugging in our values we get:
z = (19 - 30) / 5.5 = -11 / 5.5 = -2
Using a standard normal distribution table or calculator, we can find the area to the left of z = -2, which corresponds to the proportion of runners finishing in under 19 minutes. This value is approximately 0.0228 or 2.28% of the runners.
HELP ASAP Solve log7 b > 2. Question 18 options: b > 7 b > 49 b > 2–7 b > 14
Answer: Second Option
[tex]b > 49[/tex]
Step-by-step explanation:
We have the following expression:
[tex]log_7(b) > 2[/tex]
We have the following expression:
To solve the expression, apply the inverse of [tex]log_7[/tex] on both sides of the equality.
Remember that:[tex]b ^ {log_b (x)} = x[/tex]
So we have to:
[tex]7^{log_7(b)} > 7^2[/tex]
[tex]b > 7^2[/tex]
[tex]b > 49[/tex]
The answer is the second option
Chester used the regression equation of the weight loss plan to make a prediction within the given data range. Complete his work to calculate the number of weekly hours of aerobic activity needed for a monthly weight loss of 3 pounds. Round to the nearest hundredth.
Interpolated Data
About
hours of weekly aerobic activity will result in 3 pounds of monthly weight loss.
Answer:
The answer is 1.94
You need to have 1.94 hours a week to loose a monthly weight of 3 pounds
If two lines l and m are parallel, then a reflection along the line l followed by a reflection along the line m is the same as a
A. translation.
B. reflection.
C. rotation.
D. composition of rotations.
If two lines l and m are parallel, then a reflection along line l followed by a reflection along line m is the same as a translation. Therefore, the correct answer is: A. translation.
If two lines l and m are parallel, a reflection along l followed by a reflection along m is equivalent to a translation. This can be understood geometrically: when a figure is reflected across parallel lines, it undergoes a displacement without changing its orientation.
The sequence of two reflections results in the figure being shifted along a path parallel to the original lines, akin to a translation. While reflections change orientation and translations shift position, the combination of two reflections across parallel lines maintains the figure's orientation while relocating it.
The value of an antique plate after x years can be modeled by f(x) = 18(1.05)x. Which graph can be used to approximate the number of years it will take for the plate’s value to be $30?
Answer:
The approximate number of years is 10
The graph in the attached figure
Step-by-step explanation:
Let
f(x) the value of an antique plate
x is the number of yeras
we know that
The system of equations that represented the problem is equal to
[tex]f(x)=18(1.05)^{x}[/tex] ----> equation A
[tex]f(x)=30[/tex] ----> equation B
Solve the system by graphing
The solution of the system of equations is the intersection point both graphs
using a graphing tool
The solution is the point (10.47,30)
see the attached figure
therefore
The approximate number of years is 10
Answer:
1st graph
Step-by-step explanation:
just did it in edge
You are riding the bus to school and you realize it is taking longer because of all the stops you are making. The time it takes to get to school, measured in minutes, is modeled using the function g(x) = x4 − 3x2 + 4x − 5, where x is the number of stops the bus makes. If the bus makes 2 stops after you board, how long does it take you to get to school?
Answer:
7 minutes
Step-by-step explanation:
start with formula
g(x) = x^4 - 3x^2 + 4x - 5
substitute x with number of stops (2)g(2) = 2^4 - 3(2^2) + 4(2) - 5
simplify using p.e.m.d.a.s: start with exponents
g(2) = 16 - 3(4) + 4(2) - 5
multiplyg(2) = 16 - 12 + 8 - 5
subtract/add16 - 12 = 4
4 + 8 = 12
12 - 5 = 7
input: 2
output: 7
ordered pair: (2,7)
By modeled function, the time taken to reach the school is 7 minutes.
What is modeled function ?A function which depicts the variation of a given dependent parameter represented by the variable in the function is known as a modeled function. For modeled function, we input the value of the dependent parameter in place of the given variable and the solution of function gives us the result of dependency.
How to calculate the time taken to reach the school ?Given that the time it takes to get to school, measured in minutes, is modeled using the function g(x) = [tex]x^{4} - 3x^{2} + 4x - 5[/tex] , where x is the number of stops the bus makes.
Also said that the bus makes 2 stops after we board.
Thus the dependent parameter is stop which is represented by the variable x in the modeled function g(x) and the solution of g(x) gives us the time period. We will get the time period by putting x = 2 in the modeled function.
Putting x = 2 in g(x), we get -
⇒ g(x) = [tex]2^{4} - 3*2^{2} + 4*2 - 5[/tex]
⇒ g(x) = 16 - 12 + 8 - 5
∴ g(x) = 7
Thus the time period is 7 units.
Therefore, by modeled function, the time taken to reach the school is 7 minutes.
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the radious of each wheel of a car is 16 inches at how many revolutions per minute should a spin balancer be set to balance the tires at a speed of 90 miles per hour is the setting different for a wheel of radious 14 inches
Answer:
revolutions per minute for 16 inches is 946 / minute
revolutions per minute for 14 inches is 1081 / minute
Step-by-step explanation:
Given data
radius = 16 inch
speed = 90 mph = 90/60 = 1.5 miles/minute = 1.5 × 5280 feet /12 inches = 95040 inches /minute
radius 2 = 14 inches
to find out
revolutions per minute
solution
first we calculate the circumference of the wheel i.e. 2×[tex]\pi[/tex]×radius
circumference = 2×[tex]\pi[/tex]×16
circumference = 32[tex]\pi[/tex]
we know that revolution is speed / circumference
revolution = 95040/32[tex]\pi[/tex]
revolution = 945.38 / minute
we have given radius 14 inches than revolution will be i.e.
revolution = speed / circumference
circumference = 2×[tex]\pi[/tex]×14
circumference = 28[tex]\pi[/tex]
revolution = 95040/ 28[tex]\pi[/tex]
revolution = 1080.43 / minute
Can someone please help me with this transformation question
Answer:
x+(-2), y+(-3)
Step-by-step explanation:
Trapezoid ABCD has vertices A(-5,2), B(-3,4), C(-2,4) and D(-1,2).
The reflection across the y-axis has the rule
(x,y)→(-x,y),
so
A(-5,2)→A'(5,2)B(-3,4)→B'(3,4)C(-2,4)→C'(2,4)D(-1,2)→D'(1,2)The translation that maps points A', B', C' and D' to E, H, G, F is
A'(5,2)→E(3,-1)B'(3,4)→H(1,1)C'(2,4)→G(0,1)D'(1,2)→F(-1,-1)and has a rule
(x,y)→(x-2,y-3)
Which of the following has no solution?
Answer:
see below
Step-by-step explanation:
Option 1: the two solution sets overlap at x=1.
Option 2: the two solution sets do not overlap; no solution.
Option 3: together, the two set describe all real numbers.
From a bowl containing five red, three white, and seven blue chips, select four at random and without replacement. Compute the conditional probability of one red, zero white, and three blue chips, given that there are at least three blue chips in this sample of four chips.
Answer:
The probability is [tex]\frac{5}{9}[/tex]
Step-by-step explanation:
Let A be the event of one red, zero white, and three blue chips,
And, B is the event of at least three blue chips,
Since, A ∩ B = A (because If A happens that it is obvious that B will happen )
Thus, the conditional probability of A if B is given,
[tex]P(\frac{A}{B})=\frac{P(A\cap B)}{P(B)}=\frac{P(A)}{P(B)}[/tex]
Now, red chips = 5,
White chips = 3,
Blue chips = 7,
Total chips = 5 + 3 + 7 = 15
Since, the probability of one red, zero white, and three blue chips, when four chips are chosen,
[tex]P(A)=\frac{^5C_1\times ^3C_0\times ^7C_3}{^{15}C_4}[/tex]
[tex]=\frac{5\times 35}{1365}[/tex]
[tex]=\frac{175}{1365}[/tex]
[tex]=\frac{5}{39}[/tex]
While, the probability that of at least three blue chips,
[tex]P(B)=\frac{^8C_1\times ^7C_3+^8C_0\times ^7C_4}{^{15}C_4}[/tex]
[tex]=\frac{8\times 35+35}{1365}[/tex]
[tex]=\frac{315}{1365}[/tex]
[tex]=\frac{3}{13}[/tex]
Hence, the required conditional probability would be,
[tex]P(\frac{A}{B})=\frac{5/39}{3/13}[/tex]
[tex]=\frac{65}{117}[/tex]
[tex]=\frac{5}{9}[/tex]
HELP!
Select the correct answer.
Two equal spheres with the maximum possible radius are carved out of a right cylinder.
Find the ratio of the volume of one sphere to the volume of the right cylinder.
A.
1 : 1
B.
1 : 3
C.
2 : 3
D.
3 : 1
Answer:
The ratio of the volume of one sphere to the volume of the right cylinder is 1 : 3 ⇒ answer B
Step-by-step explanation:
* Lets explain how to solve the problem
- The spheres touch the two bases of the cylinder
∴ The height of the cylinder = the diameters of the two spheres
∵ The diameter of the sphere = twice its radius
∴ The diameter of the sphere = 2r, where r is the radius of the sphere
∵ The height of the cylinder = 2 × diameter of the sphere
∴ The height of the cylinder = 2 × 2r = 4r
- The spheres touch the curved surface of the cylinder, that means
the diameter of the sphere equal the diameter of the cylinder
∴ The maximum possible radius of the sphere is the radius of the
cylinder
∵ The radius of the sphere is r
∴ The radius of the cylinder is r
- The volume of the cylinder is πr²h and the volume of the sphere is
4/3 πr³
∵ The height of the cylinder = 4r ⇒ proved up
∵ The radius of the cylinder = r
∵ The volume of the cylinder = πr²h
∴ The volume of the cylinder = πr²(4r) = 4πr³
∵ The radius of the sphere = r
∵ The volume of the sphere = 4/3 πr³
∴ The ratio of the volume of one sphere to the volume of the right
cylinder = 4/3 πr³ : 4 πr³
- Divide both terms of the ratio by 4 πr³
∴ The ratio = 1/3 : 1
- Multiply both terms of the ratio by 3
∴ The ratio = 1 : 3
∴ The ratio of the volume of one sphere to the volume of the right
cylinder is 1 : 3
Determine if a triangle with side lengths 8, 14, and 15 is acute, right, or obtuse
Answer:
Acute
Step-by-step explanation:
The Converse of the Pythagorean Theorem states that:
If [tex]a^2+b^2 > c^2[/tex] then the triangle is acute.If [tex]a^2+b^2 < c^2[/tex] then the triangle is obtuse.If [tex]a^2+b^2 = c^2[/tex] then the triangle is right.The side lengths 8, 14, and 15 are given. We can assume the hypotenuse (or c) is the longest side length, so it is 15.
c = 15It doesn't matter which order of the numbers are plugged in for a and b, so a and b will be 8 and 14.
a = 8b = 14Now we have to add [tex]a^2[/tex] and [tex]b^2[/tex] to see if the sum is greater than, less than, or equal to 15 (c).
[tex]a^2 + b^2[/tex][tex]8^2 + 14^2[/tex]Calculate the rest of the problem.
[tex]8^2=64 \newline 14^2=196[/tex][tex]64+196=260[/tex]We have to find what [tex]15^2[/tex] is before we can make a decision using the Converse of the Pythagorean Theorem.
[tex]15^2=225[/tex]260 ([tex]a^2+b^2[/tex]) is greater than 225 ([tex]c^2[/tex]). This means that the triangle is acute because [tex]a^2+b^2>c^2[/tex].
In step one do you found the volume (in cubic feet) of the main tank(359,006.67). The maximum density of killer whales per cubic foot is 0.000011142, what is the maximum number of killer whales allowed on the main show tank at any given time? I must explain your answer using words and you must show all working calculations to receive credit
Answer:
4 killer whales
Step-by-step explanation:
The dimensional analysis is ...
(whales/ft³)(ft³/tank) = whales/tank
Putting the numbers with the units, we get ...
(1.1142·10^-5 whales/ft³)(3.5900667·10^5 ft³/tank) = 4.00005... whales/tank
The maximum number of killer whales allowed in the main show tank is 4.
What is the first step in simplifying the expression
For this case we have the following expression:
[tex]\frac {11x-2-3 (1-7x) ^ 2} {(x + 1)}[/tex]
We must indicate the first step that allows to start the simplification of the expression.
It is observed that the first step to follow is to solve the square of the binomial that is in the numerator of the expression.
[tex](1-7x) ^ 2[/tex]
Answer:
Option A
Answer:
0
Step-by-step explanation:
11x-2-3(1-7x)^2/(1x+1)
11x-2-3-21x/1+1
-32x-2-3-1
-32x-1+1
-32=0
/-32 /-32
x=0