Answer:
[tex]t = \cfrac{1}{2}[/tex]
Step-by-step explanation:
Given equation:
[tex]4(t+\cfrac{1}{4})=3[/tex]
Divide both sides by 4:
[tex]t+\cfrac{1}{4}=\cfrac{3}{4}[/tex]
Subtract 1/4 from both sides:
[tex]t = \cfrac{3}{4}- \cfrac{1}{4}[/tex]
[tex]t = \cfrac{2}{4}[/tex]
Simplify:
[tex]t = \cfrac{1}{2}[/tex]
Answer:
[tex]t = \frac{1}{2} [/tex]
Step-by-step explanation:
[tex]4(t + \frac{1}{4} ) = 3[/tex]
Divid the whole equation by 4.
[tex] \frac{4(t + \frac{1}{4} )}{4} = \frac{3}{4} [/tex]
[tex](t + \frac{1}{4} ) = \frac{3}{4} [/tex]
[tex]t + \frac{1}{4} = \frac{3}{4} [/tex]
Take 1/4 to right side.
[tex]t = \frac{ 3}{4} - \frac{1}{4} [/tex]
[tex]t= \frac{2}{4} [/tex]
To simplify the answer more divide the numerator and denominator by 2.
[tex]t = \frac{1}{2} [/tex]
cd+(-6c)=150 when d=4
Answer:
c = -75
Step-by-step explanation:
cd + (-6c) = 150
d = 4
c(4) + (-6c) = 150
4c - 6c = 150
-2c = 150
c = -75
Hi,
Could anyone help with this please?
Many thanks,
Length: 2.6 meters
Width: 1.8 meters
Area: 4.68 meters
Since the scale is 1/40, we can multiply the centimeter measurements by 40 thus making it our scale factor.
Length
2.6 x 40 = 260
260 cm = 2.6 m
Width
4.5 x 40 = 180
180 cm= 1.8 m
Area
1.8 x 2.6 = 4.68 m
Length: 2.6 meters
Width: 1.8 meters
Area: 4.68 meters
(-4) (-2) +2 (6+5) if anyone knows pls tell due dates tomm for homework
Thanks,
Unknownaz05
Answer:
21
Step-by-step explanation:
(-4)(-2)+2(6+5)
(8)+2(11)
10+11
21
Hope this helps! :)
Answer:32
Step-by-step explanation: First, we do parentheses. 6+5 = 11. Next, we have to do multiplication (-4)(-2) is positive 8 because there are two negatives. 8+2 is 10 + 2(11) is 10+22 which is 32
Which of the following is equivalent to (5)7/3
Answer:
11 and 2/3
Step-by-step explanation:
The given expression be [tex]$(5)^{7/3[/tex] then the value exists ³√5⁷.
What is exponential form?The base number exists raised to a power of the exponent numerator and estimated to the root of the exponent denominator.
Given: [tex]$(5)^{7/3[/tex]
The given expression contains an exponent of (7/3)
When we exist transforming from exponential form to radical form you always place the numerator as our constant's exponent in the radical ( [tex]$5^{\frac{7}{3} }$[/tex] exists named the radicand because it exists found in the radical) and the denominator in front of the radical, where it would be named the index.
The formula would be: [tex]$(\sqrt[n]{x})^{q}=x^{\frac{p}{q}}$[/tex]
Therefore, the correct answer is ³√5⁷.
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The manger of a company planned to distribute a $50 bouns to each employee from the company fund, but the fund contained $5 less than what was needed. Instead, the manger gave each employee a $45 bouns and kept the remaing $95 in the company fund. How much money was in the company fund before any bonuses were paid?
The total company fund before any bonuses were paid is $995 and there were 20 staffs.
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
Let y represent the total company fund and x represent the number of staffs.
From the first statement:
y - 50x = -5 (1)
Also:
y - 45x = 95 (2)
From equation 1 and 2:
x = 20, y = 995
The total company fund before any bonuses were paid is $995 and there were 20 staffs.
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PLEASE HELP YOU WILL GET ALOT OF POINTS The triangle on the left is rotated to create the triangle on the right as its
image. Which set of congruence statements below is true?
Answer:
The third one
Step-by-step explanation:
It cannot be the first 2 as the corners wouldn't line up. It cannot be the last one as B and R are not the same angles
On a coordinate plane, a circle has center (0, 0) and radius 4. A parabola opens down and goes through (3, 0), has vertex (0, 2) and goes through (negative 3, 0). Everything above the parabola and inside of the circle is shaded. Which system has the solution set shown? x squared + y squared greater-than-or-equal-to 16 and y greater-than-or-equal-to negative one-fourth x squared + 2 x squared + y squared greater-than-or-equal-to 16 and y less-than-or-equal-to negative one-fourth x squared + 2 x squared + y squared less-than-or-equal-to 16 and y greater-than-or-equal-to negative one-fourth x squared + 2 x squared + y squared less-than-or-equal-to 16 and y less-than-or-equal-to negative one-fourth x squared + 2
The inequality system that has the solution set shown will be C. x squared + y squared less-than-or-equal-to 16 and y greater-than-or-equal-to negative one-fourth x squared + 2.
How to illustrate the information?It should be noted that inequalities are simply used to compare two expressions that are unequal.
It can be seen that the solution set that's illustrated is:
x² + y² <= 16
-1/4x² + 2 <= y
Therefore, the inequality system that has the solution set shown will be option C.
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PLEASE HELP!
Let f be the function given by f (x) = (create an original sinusoidal function with an amplitude not equal to 1, a period not equal to 2π, and non-zero phase and vertical shifts).
ex: F of x equals negative one half times sine of quantity 3 times x plus pi over 2 end quantity minus 2
Part A: State the amplitude and vertical shift.
Part B: Determine the period of f (x), showing all necessary calculations.
Part C: Calculate the phase shift of the sinusoidal function with proper mathematical justification.
Part D: Graph the sinusoidal function by hand, using your answers from parts A–C.
Choose an angle θ, in radians, such that 2π < θ < 4π . Let θ = (create an original angle measure).
ex: Theta equals 13 pi over 6
Part E: Determine the exact value of cos θ using the sum formula. Show all necessary mathematical work.
Part F: Determine the exact value of sin θ using the difference formula. Show all necessary mathematical work.
Part G: Calculate the exact value of tan 2θ, using your answers from parts E – F.
The equation of the function f(x) is f(x) = 2 sin(π/2(x + 6)) - 3
How to create the sine function?A sine function is represented as:
f(x) = A sin(B(x + C)) + D
Where
A = Amplitude
Period = 2π/B
C = Phase shift
D = Vertical shift
The requirements in the question are:
Amplitude not equal to 1Period not equal to 2πNon-zero phase and vertical shiftsSo, we can use the following assumptions
A = 2
Period = 4
C = 6
D = -3
So, we have:
f(x) = 2 sin(B(x + 6)) - 3
The value of B is
4 = 2π/B
This gives
B = π/2
So, we have:
f(x) = 2 sin(π/2(x + 6)) - 3
The amplitude, vertical shift, period of f(x)and the phase shiftUsing the representations in (a), we have:
Amplitude = 2Vertical shift = -3Period = 4Phase shift = 6The graph of the functionSee attachment for the graph of f(x)
The value of cos θLet θ = 3π
So, we have:
cos(3π)
This is calculated as:
cos(3π) = cos(2π + π)
Expand
cos(3π) = cos(2π) *cos(π) - sin(2π) *sin(π)
Evaluate
cos(3π) = -1
The value of sin θLet θ = 3π
So, we have:
sin(3π)
This is calculated as:
sin(3π) = sin(2π + π)
Expand
sin(3π) = sin(2π) *cos(π) + cos(2π) *sin(π)
Evaluate
sin(3π) = 0
The value of tan 2θLet θ = 3π
So, we have:
tan(2 * 3π)
tan(6π)
This is calculated as:
tan(6π) = tan(3π + 3π)
Evaluate
tan(3π) = 0
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Show Work Please Thank You
Answer:
[tex]\displaystyle{x = \dfrac{\pi}{12}, \dfrac{\pi}{6}}[/tex]
Step-by-step explanation:
We are given the trigonometric equation of:
[tex]\displaystyle{\sin 4x = \dfrac{\sqrt{3}}{2}}[/tex]
Let u = 4x then:
[tex]\displaystyle{\sin u = \dfrac{\sqrt{3}}{2}}\\\\\displaystyle{\arcsin (\sin u) = \arcsin \left(\dfrac{\sqrt{3}}{2}\right)}\\\\\displaystyle{u= \arcsin \left(\dfrac{\sqrt{3}}{2}\right)}[/tex]
Find a measurement that makes sin(u) = √3/2 true within [0, π) which are u = 60° (π/3) and u = 120° (2π/3).
[tex]\displaystyle{u = \dfrac{\pi}{3}, \dfrac{2\pi}{3}}[/tex]
Convert u-term back to 4x:
[tex]\displaystyle{4x = \dfrac{\pi}{3}, \dfrac{2\pi}{3}}[/tex]
Divide both sides by 4:
[tex]\displaystyle{x = \dfrac{\pi}{12}, \dfrac{\pi}{6}}[/tex]
The interval is given to be 0 ≤ 4x < π therefore the new interval is 0 ≤ x < π/4 and these solutions are valid since they are still in the interval.
Therefore:
[tex]\displaystyle{x = \dfrac{\pi}{12}, \dfrac{\pi}{6}}[/tex]
When a disease is rare in the general population, doctors are not likely to test everyone. Instead, they only test people that have specific risk factors or show symptoms of the disease. Even if resources are available, why do you think doctors would avoid giving a test for a rare disease to everyone in the general population? Explain using ideas from probability that were explored in this project
MY NOTES
lim
n18
ASK YOUR TEACHER
Use the Limit Comparison Test to determine the convergence or divergence of the series.
00
n=1
n3
converges
O diverges
n+ 3
n+ 3
n3-5n+8
- 5n+ 8
Need Help?
-
=L>0
Read It
9,433
PRACTICE ANOTHER
Watch It
AUG
3
tv♫♬
(a
A
Part 1) [tex]\displaystyle \frac{1}{n^2}[/tex] or 1/(n^2) goes in the box.
Part 2) The series converges
======================================================
Work Shown:
[tex]\displaystyle L = \lim_{n\to \infty} \frac{a_n}{b_n}\\\\\\\displaystyle L = \lim_{n\to \infty} \frac{\frac{n+3}{n^3-5n+8}}{\frac{1}{n^2}}\\\\\\\displaystyle L = \lim_{n\to \infty} \frac{n+3}{n^3-5n+8}\times\frac{n^2}{1}\\\\\\\displaystyle L = \lim_{n\to \infty} \frac{n^3+3n^2}{n^3-5n+8}\\\\\\[/tex]
[tex]\displaystyle L = \lim_{n\to \infty} \frac{\frac{n^3}{n^3}+\frac{3n^2}{n^3}}{\frac{n^3}{n^3}-\frac{5n}{n^3}+\frac{8}{n^3}}\\\\\\\displaystyle L = \lim_{n\to \infty} \frac{1+\frac{3}{n}}{1-\frac{5}{n^2}+\frac{8}{n^3}}\\\\\\\displaystyle L = \frac{1+0}{1-0+0}\\\\\\\displaystyle L = 1\\\\\\[/tex]
Because L is finite and positive, i.e. [tex]0 < L < \infty[/tex], this means that the original series given and the series
[tex]\displaystyle \sum_{n=1}^{\infty} \frac{1}{n^2}[/tex]
either converge together or diverge together due to the Limit Comparison Test.
But the simpler series is known to converge (p-series test).
Therefore, the original series converges as well.
The two series likely don't converge to the same value, but they both converge nonetheless.
The accompanying data are the caloric contents and the sugar contents (in grams) of 11 high-fiber breakfast cereals. Find the equation of the regression line. Then construct a
scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. If the x-value is not
meaningful to predict the value of y, explain why not.
(a) x = 160 cal
(b)x= 90 cal
(c)x= 175 cal
(d)x=198 cal
Click the icon to view the table of caloric and sugar contents.
The regression equation based on the information given about the sugar contents will be 0.18x - 20.84.
How to explain the regression?It should be noted that from the information, the accompanying data are the caloric contents and the sugar contents of 11 high-fiber breakfast cereals.
The sugar content will be:
a. 160 calories
= 0.18x - 20.84.
= 0.18(160) - 20.84
= 7.96
b. 90 calories
= 0.18x - 20.84.
= 0.18(90) - 20.84
= -4.64
c. 175 calories
= 0.18x - 20.84.
= 0.18(175) - 20.84
= 10.66
d. 208 calories
= 0.18x - 20.84.
= 0.18(208) - 20.84
= 16.6
Therefore, the sugar contents is illustrated above.
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Mathematics problem..
Answer:
a) x + 10 = 45
b) 3 = 6 - x
c) d = s * t
Step-by-step explanation: This is actually pretty simple. Let's put down one theorem.
SYMMETRIC THEOREM OF PROPERTIES: If a equals b, then b must equal a. Thus, a = b and b = a.
This is all we're really doing.
Take a) for example, 45 = x + 10. Let's label (45) as A, and (x + 10) as B. Thus we have A = B. Now we know by the Symmetric Property, we have B = A. Thus, substituting B and A again, we get x + 10 = 45.
Just keep doing this with all the equations.
Hope this helped!
Using the graph as your guide, complete the following statement.
The discriminant of the function is
Because the parabola intercepts the x-axis only once, we conclude that the discriminant is 0.
What can we say about the discriminant?
For a quadratic equation:
y = a*x^2 + b*x + c
The discriminant is:
D = b^2 - 4ac
If D = 0, there is only one real zero.If D > 0, there are two real zeros.If D < 0, there are two complex zeros.In the graph we can see that the parabola intercepts the x-axis in its vertex, then the parabola has only one real zero, then we conclude that the discriminant is equal to zero.
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A sundae requires 3 ice-cream scoops and 4 strawberries, and a milkshake requires 2 ice-cream scoops and 6 strawberries. Ramses wants to make sundaes and milkshakes with at most 25 ice-cream scoops and 37 strawberries. Let S denote the number of sundaes he makes and M the number of milkshakes he makes. Write an inequality that represents the condition based on the number of ice-cream scoops. Write an inequality that represents the condition based on the number of strawberries.
The system of inequalities be
3x+2y ≤ 25, 4x+6y ≤ 37
1) Maximum number of sundaes possible exists 9.
2) Maximum number of milkshakes possible exists 6.
3) Combination that uses the most of both Ice-cream and Strawberries = 7 scoops of ice cream and 1 scoop of strawberries.
What is system of inequalities?A system of inequalities exists the system where the set of more than one inequalities in more than or equivalent to one variable.
Given: A sundae needs 3 ice-cream scoops and 4 strawberries, and a milkshake requires 2 ice-cream scoops and 6 strawberries.
Ramses have to create sundaes and milkshakes with at most 25 ice-cream scoops and 37 strawberries.
Let x represent the number of sundaes he creates and y the number of milkshakes he creates.
We represent in tabular form,
Sundae(x) Milkshake(y) Total
Ice-cream 3 2 3x+2y
Strawberries 4 6 4x+6y
System of inequalities:
Sundaes and milkshakes with at most 25 ice-cream scoops exist
33x+2y ≤ 25.
Sundaes and milkshakes with at most 37 strawberries exist 4x+6y ≤ 37.
1) Maximum number of sundaes possible:
Maximum number of sundaes possible when y = 0
From the graph y = 0 at x = 9.25
Therefore, the maximum number of sundaes possible exists at 9.
2) Maximum number of milkshakes possible:
Maximum number of milkshakes possible when x = 0
From the graph x = 0 at y = 6.167
Therefore, the maximum number of milkshakes possible exists at 6.
3) Combination that utilizes the most of both Ice-cream and Strawberries:
A combination of both is possible there exists an intersection of both the equation.
From the graph, the intersection point exists x = 7.6 and y = 1.1.
Therefore, the Combination that utilizes the most of both Ice-cream and Strawberries = 7 scoops of ice cream and 1 scoop of strawberries.
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The volume of a rectangular box is 3x(3x + 4)(3x - 1). (Drawing is not to
scale.)
Length 3x + 4
Width 3x
Height 3x - 1
Which statement about the volume of the box is tru?
The volume of the rectangular box is the product of the base area and the height 3x - 1
How to determine the true statement?The given parameters are:
Length = 3x + 4
Width = 3x
Height = 3x - 1
The base area of the rectangular box is calculated as
Base area = Length * Width
Substitute the known values in the above equation
Base area = 3x(3x + 4)
This means that the volume of the rectangular box is the product of the base area and the height 3x - 1
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Grandma is making her grandson french toast. The pan can only fit two pieces of bread at a time. To cook each side of the bread it takes one minute( you have to cook both sides). Grandma made three slices of french toast in three minutes, how was she able to do this
Grandma should be able to make three slices of French toast by slicing one of the original slices into two.
How can grandma make three slices of French toast?Put two slices of bread in the pan and cook them for one minute (first minute)Turn both slices over and cook ( second minute)Remove both slices and slice one of this into two. This will mean the new slices will have one side cooked and another one that is not cooked.Cook these thinner slices (third minute).The result would be three cooked slices, although two of them would be thinner.Learn more about French toast in: https://brainly.com/question/11713135
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The functions fand g are defined as follows. f(x) = 3x-1 g(x)=3x³ +5 Find f(-6) and g (-4). Simplify your answers as much as possible. ƒ(-6) = g (-4) =
Answer:
f(-6)= -19 and g(-4)= -187
Find the slope of the line passing through the points (-4,-4) and (2, 5).
Answer:
the slope of the line passing through the points (-4,-4) and (2, 5) m=3/2.
Step-by-step explanation:
Hello!
To find the slope between two points use the formula
m=(y₂-y₁)/(x₂-x₁)... substitute valuesm=(5-(-4))/(2-(-4))m=9/6m=3/2About 5% of the population has a particular genetic mutation. 300 people are randomly selected.
Find the standard deviation for the number of people with the genetic mutation in such groups of 300. Round your answer to two decimal places.
If the sample size is 300 and about 5% of the population has a particular genetic mutation then the standard deviation for the number of people with the genetic mutation in such groups of 300 is 3.77.
Given sample size be 300 and about 5% of the population has a particular genetic mutation.
We are required to find the standard deviation for the number of people with the genetic mutation in groups of 300.
Sample size=300
The standard deviation for the number of people with the genetic mutation is calculated as:
Standard deviation=[tex]\sqrt{np(1-p)}[/tex]
Use the known values in the above formula.
Standard deviation=[tex]\sqrt{300*0.05(1-0.05)}[/tex]
=[tex]\sqrt{14.25}[/tex]
=3.77
Hence if the sample size is 300 and about 5% of the population has a particular genetic mutation then the standard deviation for the number of people with the genetic mutation in such groups of 300 is 3.77.
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Write your answers as fractions in the format 1/2.
If a learner is picked at random, what is the probability that they are
female and use public transport?
The learner rejoins their class mates and another learner is picked at
random. What is the probability that they are female and walk/cycle to
college?
The probability that they are female and use public transport is [tex]\mathbf{=\dfrac{1}{3}}[/tex]
The probability that they are female and walk/cycle to college is [tex]\mathbf{=\dfrac{1}{9}}[/tex]
What is probability?Probability is an area of mathematics that deals with numerical representations of how probable an event is too probable to occur or how probable a statement is to be true.
Probability is synonymous with possibility. It is a mathematical field that is concerned with the occurrence of a random event. The value ranges from zero to one. The definition of probability is to predict the degree to which something is likely to occur. To determine the likelihood of a particular event occurring, we must first determine the total number of possible outcomes.
Mathematically:
[tex]\mathbf{Probability = \dfrac{number \ of \ required \ outcomes}{total \ number \ of \ possible \ outcomes}}[/tex]
From the table in the image attached below.
The probability that they are female and use public transport is:
[tex]\mathbf{=\dfrac{9}{27}}[/tex]
[tex]\mathbf{=\dfrac{1}{3}}[/tex]
Also, the probability that they are female and walk/cycle to college is:
[tex]\mathbf{=\dfrac{3}{27}}[/tex]
[tex]\mathbf{=\dfrac{1}{9}}[/tex]
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The next model of a sports car will cost 4.4% more than the current model. The current model costs $49,000. How much will the price increase in dollars? What will be the price of the next model?
Answer: $51156
Step-by-step explanation:
a = b x p%
how much will the price increase
a = 49,000 x 4.4%
= 49,000 x 0.044
= $2156
price of next model
49,000 + 2156 = $51156
Solve rs + t = u for the variable s
Answer:
[tex]s=\frac{u}{r} -\frac{t}{r}[/tex]
Step-by-step explanation:
You have to move the variables (r and t) with u to isolate s.
[tex]rs+t=u[/tex]
[tex]-t[/tex] [tex]-t[/tex]
------------------------
[tex]rs=u-t[/tex]
÷ [tex]r[/tex] ÷ [tex]r[/tex]
------------------------
[tex]s=\frac{u}{r} -\frac{t}{r}[/tex]
Solve the system of equations below using a matrix equation.
2x + y = - 7
x − y = 4
Select one:
a.
( 1, 5 )
b.
( - 1, - 5 )
c.
( - 1, -2 )
d.
( 0, - 7 )
Answer is b. ( -1, -5)
Answer is b. (-1, -5)
Step by step
Substitute the x and y values into both equations to find equality
Answer b. Makes both equations equal
2x + y = -7
2(-1) + (-5) = -7
-2 -5 = -7
-7 = -7
it equals now let’s do the 2nd one
x - y = 4
-1 -(-5) = 4
4 = 4
This one equals too. I did the math on the other three answers and they did not equal.
Determine the point (x,y) ( x , y ) on the unit circle associated with the following real number s. Write the exact answer as an ordered pair. Do not round. s=−11π6
The required coordinates of the unit circle for s = -11π/6 is (√3/2, 1/2). Using trigonometric functions, the required answer is calculated.
What are the trigonometric functions?There are six trigonometric functions.
They are sin θ, cos θ, tan θ, sec θ, cosec θ, and cot θ.
Where θ - 0 to 360° or 0 to 2π
Calculation:For a unit circle, the coordinates are given in the form of trigonometric functions as below:
x = cos θ and y = sin θ
Here it is given that s = θ = -11π/6
So, on substituting,
x = cos θ = cos (-11π/6)
⇒ x = √3/2
y = sin θ = sin (-11π/6)
⇒ y = 1/2
Thus, the required coordinate pair is (√3/2, 1/2).
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Find the length indicated
Show work
Answer: 5 units
Step-by-step explanation:
x+2+2x-7=13
solve for x
3x=18
x=6
∴SR: 2x-7
=2(6)-7
=12-7
=5
Answer:
SR = 5
Step-by-step explanation:
[tex]TR=x+2+2x-7=3x-5[/tex]
[tex]3x-5=13[/tex]
[tex]3x=13+5[/tex]
[tex]x=18/3=6[/tex]
[tex]SR=2x-7=2(6)-7=12-7=5[/tex]
Hope this helps
What is the length of the apothem of the regular pentagon shown below? Round to one decimal place
The length of the apothem of the regular pentagon shown is 5.2 meters
How to determine the length of the apothem?Represent the central angle of the regular pentagon using x
The value of the central angle of the regular pentagon is then calculated as:
x = 360/n
Where n represents the number of sides
i.e n = 5
So, we have:
x = 360/5
Evaluate the quotient
x = 72
Represents the apothem with y.
The apothem is then calculated as:
tan(x/2) = (Side length/2)/Apothem
This gives
tan(72/2) = (7.6/2)/y
Evaluate the quotient
tan(36) =3.8/y
Multiply both sides by y
y tan(36) = 3.8
Divide both sides by tan(36)
y = 3.8/tan(36)
Evaluate the quotient
y = 5.2
Hence, the length of the apothem of the regular pentagon shown is 5.2 meters
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The mean of a normally distributed data set is 110, and the standard deviation is 15.
a) Use the Empirical Rule to find the probability that a randomly-selected data value is greater than 95.
b) Use the Empirical Rule to find the probability that a randomly-selected data value is greater than 125.
Step-by-step explanation:
68% of all values are within 1 SD (110 ± 15).
95% of all values are within 2SD (110 ± 2×15 = 30)
99.7% of all values are within 3 SD (110 ± 3×15 = 45)
a)
95 is 110 - 15, so exactly 1 SD apart from the mean value.
68% or 0.68 is the probability of all values between 95 and 125.
so, 34% or 0.34 is the probability of all values between 95 and 110. and 50% or 0.5 is the probability of all values larger than 110.
so, the probability of all values larger than 95 is
0.34 + 0.5 = 0.84
b)
125 is 110 + 15, so exactly 1 SD apart from the mean value.
so, as per a) 34% or 0.34 is the probability of all values between 110 and 125. and 50% or 0.5 is the probability of all values larger than 110.
so, the probability of all values larger than 125 is
0.5 - 0.34 = 0.16
HOW MANY 7 DIGIT TELEPHONE NUMBERS ARE POSSIBLE IF THE FIRST DIGIT CANNOT BE ZERO AND:
A) THE TELEPHONE NUMBER MUST BE A MULTIPLE OF 100?
B) ONLY ODD DIGITS CAN BE USED?
C) THE FIRST 3 DIGITS ARE 277?
Using the Fundamental Counting Theorem, the number of possible telephone numbers is given by:
a) 900,000.
b) 78,125.
c) 10,000.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
For item a, a multiple of 100 means that the last two digits are 00, hence the parameters are:
[tex]n_1 = 9, n_2 = n_3 = n_4 = n_5 = 10, n_6 = n_7 = 1[/tex]
Hence the number is:
N = 9 x 10^5 = 900,000.
For item b, odd digits are 1, 3, 5, 7 and 9, hence the parameters are:
[tex]n_1 = n_2 = n_3 = n_4 = n_5 = n_6 = n_7 = 5[/tex]
Hence the number is:
N = 5^7 = 78,125.
For item c, if the first 3 digits are 277, the parameters are:
[tex]n_1 = n_2 = n_3 = 1, n_4 = n_5 = n_6 = n_7 = 10[/tex]
Hence the number is:
N = 10^4 = 10,000.
More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/24314866
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Please help!!!!!!!!!!!!!!!!
Answer: Option (3)
Step-by-step explanation:
[tex]\frac{1}{6a^2}-\frac{5b}{3a^3}+\frac{b^2}{4a}\\\\=\frac{2a}{12a^3}-\frac{20b}{12a^3}+\frac{3a^2 b^2}{12a^3}\\\\=\frac{3a^2 +b2 +2a-20b}{12a^3}[/tex]