[tex]\dfrac{_nP_3}{_nC_2}=6\\\\\dfrac{\dfrac{n!}{(n-3)!}}{\dfrac{n!}{2!(n-2)!}}=6\\\\\dfrac{n!}{(n-3)!}\cdot \dfrac{2(n-2)!}{n!}=6\\\\2(n-2)=6\\\\2n-4=6\\\\2n=10\\\\n=5[/tex]
The value of n is 5
The formula to calculate permulation and combination are:
[tex]_nP_r = \frac{n!}{(n-r)!}\\\\\\_nC_r = \frac{n!}{r!(n-r)!}[/tex]
Putting in values we get:
[tex]_nP_3 = \frac{n!}{(n-3)!}\\\\\\_nC_2 = \frac{n!}{2!(n-2)!}[/tex]
Now we know that
[tex]\frac{_nP_3}{_nC_2} = 6[/tex]
So, putting in values we get:
[tex]\frac{\frac{n!}{(n-3)!}}{\frac{n!}{2!(n-2)!}} =6\\\\ \frac{n!}{(n-3)!} \times \frac{(n-2)! \times 2!}{ n!} = 6\\\\ \frac{1}{(n-3)!} \times (n-2)! \times 2! = 6\\\\ 2(n-2) = 6\\\\ n = 5[/tex]
Thus the value of n is 5.
The surface temperature averages at 15 degrees Celsius and increases 25 degrees Celsius with each kilometer of depth. Let one variable be the distance away from the surface and the other variable be the temperature. Now write an equation that models the relationship between the variables. I choose the variable, d for distance and t for temperature.
Answer:
15+25d=t
Step-by-step explanation:
the initial value is 15 it increases(+) by 25 to each kilometer(distance=d) of depth.
The equation that models the relationship between distance d in kilometers and temperature t in degrees Celsius is t = 25d + 15. This means that for each kilometer increase in depth, the temperature increases by 25 degrees Celsius in addition to the initial 15 degrees Celsius surface temperature.
Explanation:
The relationship between the variables, distance (d) and temperature (t), is described as a linear function. Given that the surface temperature is 15 degrees Celsius and it increases by 25 degrees Celsius with every kilometer, the mathematical model is expressed as:
t = 25d + 15
In this equation, t represents the temperature and d is the distance from the surface in kilometers. This implies that for every kilometer increase in depth, the temperature increases by 25 degrees Celsius on top of the initial 15 degrees Celsius surface temperature.
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Why is causation so much more difficult to prove than correlation?
What is the value of f(4)in the function below? F(x)=1/4•2^x
Answer:
f(4) = 4
Step-by-step explanation:
F(x)=1/4•2^x
Let x = 4
F(4)=1/4•2^4
= 1/4 * 2^4
= 1/4 *16
= 4
Answer: f(4) = 4
Step-by-step explanation:
f(x) = 1/4 . 2^x
To find f(4) we simply replace x by 4 in the above equation;
f(4) =1/4 . 2^4
f(4) = 1/4 . 16
f(4) = 16/4
f(4) = 4
Therefore f(4) is equal to 4
Plzzz HELP (3 QUESTIONS!!)
6) Which of the following numbers is written in standard notation for 1.31x10^-5?
a) 11,310
b) -11,310
c) .01131
d) .00001131
7) Select the expression written in scientific notation that is equivalent to 4.8 x 10^5-9.7 x 10^4.
a) -4.83x10^9
b) 480,000-97,000
c) 3.83x10^5
d) 0.000048 – 0.00097
8) Select the expression that is equivalent to (4 x 10^3)(5x10^7).
a) 4.5 x 10^3+7
b) (4+5) (10^3+10^7)
c) 4.5 x 10^3x7
d) ( 4 x 5) (10^3+10^7)
Answer:
6: d, 7: b and c, 8: a
Step-by-step explanation:
6) The answer is (d).
We have,
0.00001131 =1.131×0.00001
= 1.131/100000
= 1.131×10^-5.
So, this is correct answer.
7) This question have two answers (b) and (c), both are correct.
(b) 480000-97000
= 4.8x100000-9.7x10000
=4.8x10^5-9.7x10^4
(c) 4.8x10^5-9.7x10^4
= 4.8x10^5-0.97x10^5
= (4.8-0.97) x10^5
=3.83x10^5
8)(a)
(4 x 10^3)(5x10^7).
= 4x5x10³x10^7
= 4x5x10^(3+7).
Evaluate sin(arccos(-4/
[tex]evaluate \: sin(arccos( - \frac{4}{ \sqrt{25))[/tex]
Answer:
sin(arccos(-4/√25)) = 0.6
Step-by-step explanation:
The expression you want to evaluate is
sin(arccos(-4/√25))
= sin(arccos(-4/5))
We place this expression into a calculator and get the result
arccos(-4/5) = 2.498 rads = 143.1°
then
sin(143.1°) = 3/5
sin(143.1°) = 0.6
sin(arccos(-4/√25)) = 0.6
Write the following phrase as an expression.
half of n
Translating the half to symbols would be 1/2. Therefore, your answer is 1/2(n)
Hope this helps!
Answer:
1/2n
Step-by-step explanation:
half of n
of means multiply
1/2 * n
n/2
there are only blue cubes, yellow cubes and green cubes in a bag there are
three times as many blue cubes as yellow cubes
and five times as many green cubes as blue cubes
sarah takes a random cube from the bag
what is the probability sarah takes out a yellow cube?
give your answer in its simplest form
Answer: [tex]\bold{\dfrac{1}{19}}[/tex]
Step-by-step explanation:
Let x represent the quantity of yellow cubes
Yellow: x
Blue: three times yellow --> 3x
Green: five times blue --> 5(3x) = 15x
Yellow + Blue + Green = Total cubes
x + 3x + 15x = 19x
[tex]Probability=\dfrac{yellow}{total}=\dfrac{x}{19x}=\large\boxed{\dfrac{1}{19}}[/tex]
The probability of Sarah taking out a yellow cube from the bag is 0.7 or 5/7.
What is probability?The fraction of favorable outcomes of an event to the total number of outcomes of the event is said to be the probability. The fraction can also be written in the simplest form.
P(E)= n(E)/n(S) where E -event, n(E) - favorable outcomes and n(S) is the total outcomes.
Calculation:It is given that a bag contains blue cubes, yellow cubes, and green cubes.
Consider the number of blue cubes = n
So, the number of yellow cubes = 3 times as many as blue cubes
= 3n
Then, 5 times as many as green cubes = blue cubes
⇒ number of green cubes = n/5
Then the total number of cubes in the bag
= n + 3n + n/5
⇒ [5n + 15n + n]/5
⇒ 21n/5
Then the probability of taking out a yellow cube = (possible outcomes of a yellow cube)/(total number of cubes)
⇒ [tex]\frac{(3n)}{(21n/5)}[/tex]
⇒ 15n/21n
⇒ 5/7
∴ The probability of taking out a yellow cube = 5/7 = 0.7.
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I need to know this answer please!
Answer:
3*5=15
15 is your answer
ANSWER
15 square units.
EXPLANATION
Each box is 1 square units.
When we count the number of boxes we obtain 15 boxes.
This implies that the area of the rectangle is 15 square units.
Alternatively, we can observe that:
The rectangle is a 3 by 5 rectangle.
So the area is
[tex]3 \times 5 = 15 \: units \: square[/tex]
The rectangle is 15 units square.
Find the greatest common factor: 24y8 + 6y6
For this case we must find the GCF of the following expression:
[tex]24y ^ 8 + 6y ^ 6[/tex]
By definition, the largest common factor (GCF) of two numbers is the largest number that is a factor of both numbers. We find the factors of each number:
24: 1,2,3,4,6,8,12,24
6: 1,2,3,6
Thus, the GCF of both numbers is 6
The GCF of the expression is: [tex]6y ^ 6[/tex]
Answer:
[tex]6y ^ 6[/tex]
Which system of equations below has no solution?
y = 4x + 5 and y = 4x-5
y = 4x + 5 and 2y = 8x + 10
y = 4x + 5 and y =
x+5
y = 4x + 5 and y = 8x + 10
Answer:
y = 4x + 5 and y = 4x - 5Step-by-step explanation:
(1) y = 4x + 5 and (2) y = 4x - 5
substitute (1) to (2):
4x + 5 = 4x - 5 subtract 4x from both sides
5 = -5 FALSE (no solution)
(1) y = 4x + 5 and (2) 2y = 8x + 10
substitute (1) to (2):
2(4x + 5) = 8x + 10 divide both sides by 2
4x + 5 = 4x + 5 subtract 4x from both sides
5 = 5 TRUE (infinitely many solutions)
(1) y = 4x + 5 and (2) y = x + 5
substitute (1) to (2):
4x + 5 = x + 5 subtract 5 from both sides
4x = x subtract x from both sides
3x = 0 divide both sides by 3
x = 0
Put it to (2):
y = 0 + 5 = 5
One solution (0, 5)
(1) y = 4x + 5 and (2) y = 8x + 10
substitute (1) to (2):
4x + 5 = 8x + 10 subtract 5 from both sides
4x = 8x + 5 subtract 8x from both sides
-4x = 5 divide both sides by (-4)
x = -1.25
Put it to (1):
y = 4(-1.25) + 5 = -5 + 5 = 0
One solution (-1.25, 0)
A window is in the shape of a kite. Caleb wants to apply a layer of plastic film on the top half of the window so that the glass appears crackled. What are the dimensions of the layer of film he will apply?
9 inches in width and 7 inches in height
9 inches in width and 14 inches in height
18 inches in width and 7 inches in height
18 inches in width and 14 inches in height
Answer:
18 inches in width and 7 inches in height
Using kite, the dimensions of the layer of film the Caleb will apply is 18 inches in width and and 7 inches in height.
What is Kite?
A Kite is "quadrilateral with two distinct pairs of congruent consecutive sides".
What is relationship between kite and quadrilateral?If a kite is quadrilateral, then "its diagonal are perpendicular and exactly one diagonal each other".
According to the question,
A window is in the shape kite has an height of 14 inches and a width of 18 inches. Caleb wants to apply a layer of plastic film on the top half of the kite shape window. The window has dimensions of width 18 inches and 14 inches of height.
In order to the find new dimensions to apply a layer of plastic film on the top half of the kite shape window only if we divide the height by two then we get new dimensions on the top half of the kite shape window.
= [tex]\frac{14}{2}[/tex]
=7 inches
Hence, new dimensions to apply a layer of plastic film on the top half of the kite shape window is 18 inches in width and and 7 inches in height.
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e shown below.
(93)10 - 930
Answer:
0
Step-by-step explanation:
(93)10 - 930=
930 - 930=
0
How do you know if something is divisible by four
Answer:
To test whether or not a number is divisible by 4 is to check to see if the number that’s made from the final two digits of the original number is itself divisible by 4. If it is, then the entire number is divisible by 4 too.
What is the value of a in the equation a = 2 + 3a + 10?
Answer:
a= -6
Step-by-step explanation:
Given
a=2+3a+10
In order to find the value of a, we have to isolate a on a single side of the equation
So,
subtracting 3a from both sides
a-3a = 2+10+3a-3a
=>a-3a=12
=> -2a = 12
Dividing both sides by -2
=> -2a/-2 = 12/-2
=> a = -6
The value of a in the given equation is -6 ..
Which of the following is the equation of a circle whose center is at the origin and whose radius is 4?
Answer:
x²+y²=16
Step-by-step explanation:
the general equation for a circle is given as :
(x−h)²+(y−k)²=r²
where (h, k) is the coordinate of the center of the circle and r is the radius
in this case h=0, k=0 and r = 4
equation becomes
x²+y²=4²
or
x²+y²=16
Answer: Last option.
Step-by-step explanation:
The equation of a circle in Center-radius form is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Where the center is at the point (h,k) and "r" is the radius.
If the center of this circle is at the origin, means that:
[tex]h=0\\k=0[/tex]
Since the radius is 4, then:
[tex]r=4[/tex]
Now we need to substitute these values into the equation of the circle.
[tex](x-0)^2+(y-0)^2=(4)^2[/tex]
Simplifying the equation, we get:
[tex]x^2+y^2=16[/tex]
This matches with the last option.
Which of the following vectors are orthogonal to (2,1)? Check all that apply.
A. (1,-2)
B. (-3,6)
C. (1,2)
D. (-2,-3)
Answer:
A. (1,-2)
B. (-3,6)
Step-by-step explanation:
we know that
If two vectors are orthogonal, then the dot product ( or scalar product) of the vectors is equal to zero
so
Let
a (x1,y1) and b(x2,y2)
The dot product is equal to
a.b=(x1*x2+y1*y2)
Verify each case
case A) (2,1) with (1,-2)
(2,1).(1,-2)=(2)*(1)+(1)(-2)=2-2=0
therefore
(1,-2) is orthogonal to the given vector
case B) (2,1) with (-3,6)
(2,1).(-3,6)=(2)*(-3)+(1)(6)=-6+6=0
therefore
(-3,6) is orthogonal to the given vector
case C) (2,1) with (1,2)
(2,1).(1,2)=(2)*(1)+(1)(2)=2+2=4
therefore
(1,2) is not orthogonal to the given vector
case D) (2,1) with (-2,3)
(2,1).(-2,3)=(2)*(-2)+(1)(3)=-4+3=-1
therefore
(-2,3) is not orthogonal to the given vector
Answer: B, D, E
On EDGE
Step-by-step explanation:
Celia simplified the expression - 4x{1-3)-(2x+2). She checked her work by letting X-5 in both expressions. Her work for the
original expression is shown below.
Answer: I think it is the last one
Step-by-step explanation: if you work it out, it equally 6x-2
Answer:
6x-2
Step-by-step explanation:
[tex]- 4x(1-3)-(2x+2)[/tex]
When x=5 the value of the expression is 28
Now we check with each expression given in the options
Plug in 5 for x in each option
[tex]-6x-1=-6(5)-1=-30-1= -31[/tex]
[tex]-6x+2=-6(5)+2=-30+2= -28[/tex]
[tex]6x+1=6(5)+1=30+1= 31[/tex]
[tex]6x-2=6(5)-2=30-2=28[/tex]
So 6x-2 gives us 28 when x=5
Find the coordinates of the focus and equation of the directrix for the parabola given by
y2 = −4x.
The general formula for this parabola is y2 = 4px.
Therefore, the value of p is _____
The coordinates of the focus are ______
The equation of the directrix is ______
Answer:
The answers to your three problem question are shown
1) the value of p is
p = -1
2) The coordinates of the focus are
Focus = (-1,0)
3) The equation of the directrix is
Directrix
x = 1
Step-by-step explanation:
The general equation for this parabola is
y^2 = 4px
Problem 1
Find the value of p.
We are told that the equation of the problem is
y^2 = -4x
And the general formula is
y^2 = 4px
From there, we can deduce that
p = -1, because
y^2 = 4(-1)x = -4x
This means that p = -1
Problem 2
Find the focus
To find the focus we can see the equations attached below for the focus, vertex and directrix.
In these case, the equations still apply, even though the variable is inverted, we just need to adjust it
y^2 = -4x =>
x = (-1/4)*y^2
x = a*y^2 + b*y +c
Focus
((4ac -b^2 + 1)/4a, -b/2a)
But, b = 0 and c = 0
=>
(1/4a,0) = (1/4(-1/4),0) = (-1,0)
Focus = (-1,0)
Problem 3
Find the directrix
The equation is
x = c - (b^2 + 1).4a
But, b = 0 and c = 0
x = -4*a
x = -4* (-1/4) = 1
x = 1
Directrix
x = 1
Answer: P is -1
Focus is (-1,0)
Directrix is X= 1
9(x-2) + 3(5-2x) = 2
First you must distribute the numbers outside the parentheses to the numbers inside the parentheses
Let's start with the first one:
9(x-2) + 3(5-2x) = 2
9(x - 2)
9*x + 9*-2
9x + (-18)
9x - 18
so...
9x - 18 + 3(5-2x) = 2
Now on to the second set of parentheses:
9x - 18 + 3(5-2x) = 2
3(5 - 2x)
3*5 + 3*-2x
15 + (-6x)
15 - 6x
so...
9x - 18 + 15 - 6x = 2
Now you must combine like terms. This means the numbers with the same variables must be combined...
First set of like terms:
9x - 18 + 15 - 6x = 2
9x + (-6x)
3x
so...
3x - 18 + 15 = 2
Second set of like terms:
3x - 18 + 15 = 2
-18 + 15
-3
so...
3x - 3 = 2
Now bring -3 to the right side by adding 3 to both sides (what you do on one side you must do to the other). Since -3 is being negative on the left side, addition (the opposite of negative/subtraction) will cancel it out (make it zero) from the left side and bring it over to the right side.
3x + (- 3 + 3) = 2 + 3
3x + 0 =5
3x = 5
Next divide 3 to both sides to finish isolating x. Since 3 is being multiplied by x, division (the opposite of multiplication) will cancel 3 out (in this case it will make 3 one) from the left side and bring it over to the right side.
3x/3 = 5/3
x = [tex]\frac{5}{3}[/tex]
Hope this helped!
~Just a girl in love with Shawn Mendes
what is measure of cgf?
Answer:
[tex]<CGF = 130[/tex]
Step-by-step explanation:
A triangle adds up to 180.
180 - 50 = 130
Since both of the missing angles are congruent each of the missing angles is 65 degrees.
130/2 = 65
As per the exterior angle theorem, the measure of the exterior angle is determined by the sum of the opposite interior angles.
65 + 65 = 130
So, the measure of [tex]<CGF = 130[/tex]
One leg of an isosceles right triangle measures 5 inches. Rounded to the nearest tenth, what is the approximate length of the hypotenuse?
Answer:
7.1 inches
Step-by-step explanation:
An Isosceles right triangle is one with two sides equal and the angles equal too.The angles in this case are 45°
For this question, to get the hypotenuse, you apply the Pythagorean relationship where the legs will be represented by a and b where as the hypotenuse will be represented by c.
[tex]a^2+b^2=c^2\\[/tex]
Given;
One leg = 5 inches, but you know that in this triangle, the two sides are equal, hence the other side/leg is 5 inches.
Lets take one side of the triangle as a=5 inches
The other side as b=5 inches
The hypotenuse as c=?
Apply the expression;
[tex]a^2+b^2=c^2\\\\5^2+5^2=c^2\\\\25+25=c^2\\\\50=c^2\\\\c=\sqrt{50} =7.071[/tex]
To the nearest tenth 7.071 = 7.1 inches
Vhat is the equation, in slope-intercept form, of the line
That is perpendicular to the given line and passes through
che point (2, -1)?
y=-23-
y=-2x-
y = 3x - 3
10 y = 3x - 7
Answer:
Step-by-step explanation:
There is no given equation, so it is impossible to figure this out. I apologize.
Find the distance between the given points.
R(0, 0) and S(6, 8)
Distance =
2√7
√(22)
10
Answer:
The correct answer is last option
10
Step-by-step explanation:
Points to remember
Distance formula
Length of a line segment with end points (x1, y1) and (x2, y2) is given by,
Distance = √[(x2 - x1)² + (y2 - y1)²]
To find the distance between given points
Here (x1, y1) = R(0, 0) and (x2, y2) = S(6, 8)
Distance, RS = √[(x2 - x1)² + (y2 - y1)²]
= √[(6 - 0)² + (8 - 0)²]
= √[6² + 8²]
= √[36 + 64]
= √100
= 10
Therefore the correct answer is last option 10
the speed of a new microprocessor is 800mhz but a new test of its speed gives a measurement of 820mhz. what is the abolute error? what is the relative error?
The answers are:
[tex]AbsoluteError=20mhz[/tex]
[tex]RelativeError=2.5(Percent)[/tex]
Why?To solve the problem we need to remember that the absolute error is the difference between the expected value and the measured value, also, to calculate the relative error we first need to calculate the absolute error, and then, divide it by the expected measure.
So, calculating we have:
[tex]AbsoluteError=Expected-MeasuredValue\\\\AbsoluteError=800mhz-820mhz=-20mhz[/tex]
We can see that we obtained a negative value, however, when we are working with "absolute" values, the negative symbol is discarded, so, we have that:
[tex]AbsoluteError=20mhz[/tex]
Now, to calculate the relative error, we need to use the following formula:
[tex]RelativeError=\frac{AbsoluteError}{ExpectedValue}*100\\\\RelativeError=\frac{20}{800}*100=0.025*100=2.5(Percent)[/tex]
So, we have that the relative error is equal to 2.5%.
Hence, we have that:
[tex]AbsoluteError=20mhz[/tex]
[tex]RelativeError=2.5(Percent)[/tex]
Have a nice day!
Absolute error is 20 MHz and relative error is 2.5%.
Absolute error: Absolute error is the difference between the measured value and the actual value. In this case, the absolute error is 820 MHz - 800 MHz = 20 MHz.
Relative error: Relative error is the ratio of the absolute error to the actual value. The relative error can be calculated as (820 MHz - 800 MHz) / 800 MHz = 0.025 or 2.5%.
(a) Find an angle between 0° and 360° that is coterminal with – 120°.
(b) Find an angle between 0 and 2π that is coterminal with 15π/4
Give exact values for your answers.
Answer:
a) [tex]240\degree[/tex]
b) [tex]\frac{15\pi}{4}[/tex]
Step-by-step explanation:
Coterminal angles have the same terminal sides in standard position.
a) To find an angle between [tex]0\degree[/tex] and [tex]360\degree[/tex], that is coterminal with [tex]-120\degree[/tex], we keep adding multiples of [tex]360\degree[/tex] until we get an angle within the specified range.
[tex]-120\degree \implies -120\degree +360\degree=240\degree[/tex].
In some cases you would have to subtract in order to get the specified angle. That is when the angle given is positive.
b) This time we want to find an that coterminal with [tex]\frac{15\pi}{4}[/tex] radians.
We keep subtracting multiples of [tex]2\pi[/tex] until we get an angle measure within the specified range.
[tex]\frac{15\pi}{4}=\frac{15\pi}{4}-2\pi=\frac{7\pi}{4}[/tex]
What expression is equivalent to (3x^2-7)
Answer:
C.(10x^2-4) - (7x^2+3)
In option C,
(10x^2-4) - (7x^2+3) = 10x^2 - 4 - 7x^2 - 3 = 3x^2 - 7
⇒ Option C is correct
Is g(x)= 5x-1 an odd function
Answer:
No
Step-by-step explanation:
g(x)= 5x-1 is the same as g(x)= 5x^1 - 1x^0, which contains one odd power (x^1) and one even power (x^0). Therefore, g(x)= 5x-1 is neither even nor odd.
Answer:
This is not an odd function.Step-by-step explanation:
[tex]\text{If}\ f(-x)=f(x)\ \text{then}\ f(x)\ \text{is an even function.}\\\\\text{If}\ f(-x)=-f(x)\ \text{then}\ f(x)\ \text{is an odd function.}[/tex]
======================================================
[tex]g(x)=5x-1\\\\g(-x)=5(-x)-1=-5x-1=-(5x+1)\\\\g(-x)\neq-g(x)\ \wedge\ g(-x)\neq g(x)[/tex]
In your lab, a substance's temperature has been observed to follow the function T(x) = (x − 2)3 + 8. The turning point of the graph is where the substance changes from a solid to a liquid. Using complete sentences in your written answer, explain to your fellow scientists how to find the turning point of this function. Hint: The turning point of the graph is similar to the vertex of a quadratic function. (10 points). Please help
Answer:
The turning point is (2,8)
Step-by-step explanation:
we know that
The general equation of the substance's temperature is equal to
[tex]T(x)=(x-h)^{3}+k[/tex]
where
(h,k) is the vertex (turning point)
In this problem we have
[tex]T(x)=(x-2)^{3}+8[/tex]
so
(h,k)=(2,8)
therefore
The turning point is (2,8)
Can someone please help me out here ?
Answer:
D
Step-by-step explanation:
Since its less then the circle is open and the arrow goes to the left. The circle must be on -1. The answer is D.
Which geometric object is defined as the set of all points in a plane that are equidistant from the two sides of a given angle ?
A.Parabola
B. Bisector of an angle
C. Circle
D. Hyperbola
Answer:
B) Bisector of an angle ~apex
Step-by-step explanation:
Option B is correct, bisector of an angle is defined as the set of all points in a plane that are equidistant from the two sides of a given angle.
What is Coordinate Geometry?A system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.
The bisector of an angle is a straight line or a line segment that divides an angle into two equal angles.
In other words, the bisector of an angle is the set of all points in a plane that are equidistant from the two sides of a given angle.
The geometric object defined as the set of all points in a plane that are equidistant from the two sides of a given angle is the Bisector of an angle.
Hence, bisector of an angle is defined as the set of all points in a plane that are equidistant from the two sides of a given angle.
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