Answer:
[tex]28 . 26cm[/tex]
Step-by-step explanation:
First find the radius
[tex]d = 2r \\ 9 = 2r \\ \frac{9}{2} = \frac{2r}{2} \\ r = 4.5[/tex]
Now find the CIRCUMFERENCE
[tex]c = 2\pi \: r \\ = 2 \times \pi \times 4.5 \\ = 9 \times \pi \\ = 28.26[/tex]
pls pls help me help me
It is D.
you must multiply the second equation by 3, so that the +3y in the first equation can cancel out the (now) -3y in the second equation.
find the sum of the interior angles of the following polygons.1)Pentagon. 2)hexagon. 3)heptagon. 4)octagon.
Answer:
Sum of interior angles of polygon = (n-2)*180
1) Pentagon:
(5-2)*180= 5402)Hexagon:
(6-2)*180= 7203) Heptagon:
(7-2)*180= 9004) Octagon:
(8-2)*180= 1080One angle of a right triangle measures 33 degrees. what is the other small angle
Answer: 57 degrees
Step-by-step explanation: We can use our knowledge of knowing the sum of the interior angles of a triangle to be 180 degrees, to find the measure of the angle. So we can do 90 degrees plus 33 degrees, and then subtract the sum from 180 to find the measure of the angle. So we get 123 degrees when we add up 90 and 33 and when we subtract 123 degrees from 180 we get, 57 degrees as the answer.
Answer:
57 degrees
Step-by-step explanation:
We can use our knowledge of knowing the sum of the interior angles of a triangle to be 180 degrees, to find the measure of the angle. So we can do 90 degrees plus 33 degrees, and then subtract the sum from 180 to find the measure of the angle. So we get 123 degrees when we add up 90 and 33 and when we subtract 123 degrees from 180 we get, 57 degrees as the answer.
Dominics two daughters both want to take gymnastics this year. It cost 90 per month per child. How much dose dominic need to budget for a year ( 12 months) of gymnastics for both daughters
Answer:
$2,160 is what he need for both daughters for 1 year
Step-by-step explanation:
90 x 2 = 180
180 x 12 = 2,160
Dominic need to budget a total of 2160 for a year of gymnastics for both daughters.
What is Multiplication?Multiplication is one of the basic mathematical operations which includes a number added repeatedly to times of the other number. The final answer is called the product of the numbers.
Multiplication is usually denoted as '×' sign.
a × b indicates that a is added repeatedly upto b times.
Cost for the gymnastics per month per child = 90
In order to find the cost per month for both daughters, we need to multiply 90 with 2.
Cost for the gymnastics per month for 2 daughters = 2 × 90 = 180
To find the total cost for an year, we need to multiply 180 with 12.
Total cost for the year = 180 × 12 = 2160
Hence the total budget for Dominic to send both the daughter in a year is 260.
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If one card is drawn from a deck. find the probability of getting these results. Enter your answers as fractions or as decimals rounded to 3 decimal places.
Part 1
An ace and a heart
P(acc and heart)-
Part 2
An 8 or a diamond
P (8 or diamond)-
Part 3
A red 7
P(red 7)-
Answer: Part 1: 1/52 Part 2: 15/26 Part 3: 1/26
Step-by-step explanation:
A ace of hearts is only 1 card
a 8 or a diamond a 8 is a 4/52 chance and a diamond is a 26 / 52 chance
26 + 4 = 30
30/52 simplifies to 15/26
A red 7 has a 4/52 chance for a 7 and half of that for a red card so 2/52 then 1/26
Red beads cost $1 an ounce and gold beads cost $3
an ounce. Juanita wants to purchase a 12-ounce
mixture of red and gold beads that she can sell for $2
an ounce. The solution of the system shows the
number of beads needed for Juanita to break even.
x + y = 12
x + 3y = 24
How many ounces of red beads will Juanita buy to
break even?
How many ounces of gold beads will she buy?
Answer:
6 ounces of red beads
6 ounces of gold beads
Step-by-step explanation:
x + y = 12
x + 3y = 24
We can solve this with substitution or elimination. In this case, I would suggest elimination. Subtract the first equation from the second:
2y = 12
y = 6
Plug back into either equation to find x.
x = 6
Answer:
How many ounces of red beads will Juanita buy to break even?
6
How many ounces of gold beads will she buy?
6
Step-by-step explanation:
Because I got 100 percent on EDG 2020
Evaluate 9 x 8 = (10 x 8) - ( blank x 8) =80 - blank = blank
Answer:
see below
Step-by-step explanation:
9 x 8 = (10 x 8) - ( blank x 8) =80 - blank = blank
We are replacing 9 with 10 minus something
9 = 10 -1
9 x 8 = (10 x 8) - ( 1 x 8)
80 - 8
72
Want Brainliest? Get this correct Which of the following is the quotient of the rational expressions shown below?
Answer:
B. 3x+15 / 4x+10
Step-by-step explanation:
[tex]\frac{3x+}{2x+5}[/tex] X [tex]\frac{x+5}{2x}[/tex] -> multiply by the reciprocal
[tex]\frac{3x}{2x+5}[/tex] X [tex]\frac{x+5}{2x}[/tex] -> reduce the expression
[tex]\frac{3}{2x+5}[/tex] X [tex]\frac{x+5}{2}[/tex] -> multiply the fractions
[tex]\frac{3(x+5)}{2(2x+5)}[/tex] -> remove parenthesis
and you get:
[tex]\frac{3x+15}{4x+10}[/tex]
-Hope this helps :)
The water was pumped out of a backyard pond. What is the domain of this graph?
Se x .y = 2 e x + y = 9, então x² + y² é :
a) 76
b) 167
c) 77
d) 169
e) 85
Classifique cada sentença em verdadeira ou falsa:
( ) ( a +b )² = a² + 2ab + b²
( ) ( a - b )² = a² - 2ab + b²
( ) ( a + b ) .( a – b) = a² + b²
( ) ( a +b)³ = a³ + 3a²b + 3ab² + b³
( ) ( a -b)³ = a³ - 3a²b + 3ab² - b³
Fatore cada polinômios de acordo com o caso:
a) m² - 14am + 49a² =
b) m2 – 9n² =
c) 30+ 5xy + 12a +2axy =
d) 8a²b + 10ab²
Answer:
1. A resposta é a opção C.
2. ( a +b )² = a² + 2ab + b² Verdade
( a - b )² = a² - 2ab + b² Verdade
( a + b ) .( a – b) = a² + b² Falso
( a +b)³ = a³ + 3a²b + 3ab² + b³ Verdade
( a -b)³ = a³ - 3a²b + 3ab² - b³ Verdade
3. a.) m² - 14am + 49a² = ( m - 7a)²
b) m2 – 9n² = m² - (3n)² = (m + 3n)(m - 3n)
c) 30+ 5xy + 12a +2axy = (6 + xy)(5 + 2a)
d) 8a²b + 10ab² = 2ab( 4a + 5b)
Espero que isso ajude você
Geometry please help. What is the perimeter of XYZ
Answer:
39
Step-by-step explanation:
Angle AQC, AQB and BQC are 120deg. (360/3=120). Therefore, Angle BZC, CXA and AYB are 60deg. Because, angle BZC is half of angle BQC. same for the other three angles. As, all 3 angles are 60deg, it is an equilateral triangle. So, YZ is 13 therefore as all 3 sides are equal its 13*3=39.
The solution is: 39 is the perimeter of XYZ.
What is an angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.
Here, we have,
Angle AQC, AQB and BQC are 120deg.
(360/3=120).
Therefore, Angle BZC, CXA and AYB are 60deg.
Because, angle BZC is half of angle BQC.
same for the other three angles.
As, all 3 angles are 60deg, it is an equilateral triangle.
So, YZ is 13
therefore as all 3 sides are equal
its 13*3=39.
Hence, 39 is the perimeter of XYZ.
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Find dy/dx by implicit differentiation.
x^2/x+y=y^2+7
Answer:
dy/dx = (2x − y² − 7) / (2xy + 3y² + 7)
Step-by-step explanation:
x² / (x + y) = y² + 7
x² = (x + y) (y² + 7)
Take derivative of both sides with respect to x. Use power rule, product rule, and chain rule.
2x = (x + y) (2y dy/dx) + (y² + 7) (1 + dy/dx)
Simplify.
2x = (2xy + 2y²) dy/dx + y² + y² dy/dx + 7 + 7 dy/dx
2x = (2xy + 3y² + 7) dy/dx + y² + 7
2x − y² − 7 = (2xy + 3y² + 7) dy/dx
dy/dx = (2x − y² − 7) / (2xy + 3y² + 7)
A Roper survey reported that 65 out of 500 women ages 18-29 said that they had the most say when purchasing a computer; a sample of 700 men (unrelated to the women) ages 18-29 found that 133 men said that they had the most say when purchasing a computer. Test whether there is a difference between these proportions at α = 0.05. What is the test statistic value? Group of answer choices
Answer:
Step-by-step explanation:
Step(i):-
Given first random sample size n₁ = 500
Given Roper survey reported that 65 out of 500 women ages 18-29 said that they had the most say when purchasing a computer.
First sample proportion
[tex]p^{-} _{1} = \frac{65}{500} = 0.13[/tex]
Given second sample size n₂ = 700
Given a sample of 700 men (unrelated to the women) ages 18-29 found that 133 men said that they had the most say when purchasing a computer.
second sample proportion
[tex]p^{-} _{2} = \frac{133}{700} = 0.19[/tex]
Level of significance = α = 0.05
critical value = 1.96
Step(ii):-
Null hypothesis : H₀: There is no significance difference between these proportions
Alternative Hypothesis :H₁: There is significance difference between these proportions
Test statistic
[tex]Z = \frac{p_{1} ^{-}-p^{-} _{2} }{\sqrt{PQ(\frac{1}{n_{1} } +\frac{1}{n_{2} } )} }[/tex]
where
[tex]P = \frac{n_{1} p^{-} _{1}+n_{2} p^{-} _{2} }{n_{1}+ n_{2} } = \frac{500 X 0.13+700 X0.19 }{500 + 700 } = 0.165[/tex]
Q = 1 - P = 1 - 0.165 = 0.835
[tex]Z = \frac{0.13-0.19 }{\sqrt{0.165 X0.835(\frac{1}{500 } +\frac{1}{700 } )} }[/tex]
Z = -2.76
|Z| = |-2.76| = 2.76 > 1.96 at 0.05 level of significance
Null hypothesis is rejected at 0.05 level of significance
Alternative hypothesis is accepted at 0.05 level of significance
Conclusion:-
There is there is a difference between these proportions at α = 0.05
According to the question,
Women,
[tex]\hat p_1 = \frac{65}{500}[/tex][tex]= 0.13[/tex]
Men,
[tex]\hat p_2=\frac{300}{700}[/tex][tex]= 0.19[/tex]
Now,
The pooled estimate of the proportion will be:
→ [tex]\hat p=\frac{x_1+x_2}{n_1+n_2}[/tex]
By substituting the values,
[tex]= \frac{65+133}{500+700}[/tex]
[tex]= 0.165[/tex]
then,
→ [tex]\hat q = 1- \hat p[/tex]
[tex]= 1- 0.165[/tex]
[tex]= 0.835[/tex]
hence,
The test statistics:
→ [tex]Z = \frac{\hat p_1- \hat p_2}{\sqrt{\hat p\times \hat q\times (\frac{1}{n_1} +\frac{1}{n_2} )} }[/tex]
By putting the values, we get
[tex]= \frac{0.13-0.19}{\sqrt{0.165\times 0.835\times (\frac{1}{500} +\frac{1}{700} )} }[/tex]
[tex]= -2.76[/tex]
Thus the above response is right.
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I NEED HELP PLEASE, THANKS! :)
Answer:
see below
Step-by-step explanation:
It can be useful to remember that the angle θ of rotation between the x-y plane and the x'-y' plane is given by ...
cot(2θ) = (A -C)/B
where the standard form equation is ...
Ax² +Bxy +Cy² +Dx +Ey +F = 0
For a 30° rotation, you want ...
(A -C)/B = cot(2·30°) = 1/√3
Looking at the answer choices, you have ...
A: (A -C)/B = (3 -(-39))/(42√3) = 1/√3 . . . as required
B: (A -C)/B = (3 -(-39))/(-12√3) = 7/(2√3)
C: (A -C)/B = (-39 -3)/(42√3) = -1/√3
D: AC > 0, not a hyperbola
_____
Based on rotation angle only, the appropriate choice is the first choice. Because the term signs in the x'-y' formula are different, the figure is a hyperbola. In general form, the equation describes a hyperbola when AC<0.
Answer:
the first answer choice is correct!
Step-by-step explanation:
took the test amd got it correct:)) hope this helps:)) have a good day:))
Pediatricians prescribe 5ml of cough syrup for every 25lb of a child’s weight. How many milliliters of cough syrup will the doctor prescribe for Jocelyn, who weighs 45lb?
Answer:
x=9
Step-by-step explanation:
for this sort of a problem, I would set up a proportion
5/25=x/45
multiply both sides by 25 and 45
45*5=x*25
225=25x
x=9
There are two consecutive integers such that the larger is nine more than twice the smaller. What is the larger number?
Answer:
[tex]\boxed{Larger \ Number = -7}[/tex]
Step-by-step explanation:
Let the consecutive numbers be x and x+1 (Since they are coming one after another)
So, Given Condition is:
x+1 = 9 + 2(x)
x+1 = 9 +2x
Subtracting -2x to both sides
x+1-2x = 9
-x+1 = 9
Subtracting 1 from both sides
-x = 9-1
-x = 8
=> x = -8
The larger number is:
=> x+1 = -8+1 = -7
Carly owns a T-shirt shop. She pays $2.25 for each shirt.
Carly prints a picture on each shirt. The printing costs
her $1.00 per shirt. She sells the shirts for $10.50 each.
How much is the markup on each shirt?
Answer:
Total number of T-shirts= 200
Cost per T-shirt (without shipping ) = $2.80
Shipping cost per t-shirt ; 5% of a T-shirt = 0.05 *2.80 = $0.14
Total cost of T-shirt (shipping included) = 2.80 +0.14 = $2.94
Markup = 150% of total cost = 1.50 * 2.94 = $4.41
To get the price at which Michelle will sell each T-shirt , add total cost to the markup; 2.94 +4.41 = 7.35.
Therefore, selling price will be $7.35
17. Write the greatest and the smallest 4-digit numbers using four different digits
with the conditions as given:
( Digit 7 is always at units place.
Answer:
Greatest number = 9867
Smallest number = 1027
Step-by-step explanation:
Greatest number:
- - - 7
In order to form the greatest number, we should simply put the greatest available digit at the thousands place, the second greatest at the hundreds place and the third greatest at the tens place (which would be 9, 8, and 6 respectively).
9867
Smallest number:
- - - 7
In order to form the greatest number, we should simply put the lowest available digit at the thousands place (excluding zero since a number can't start with a zero), put zero at the hundreds place and the third lowest at the tens place (which would be 1, 0, and 2 respectively).
1027
This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.
Tutorial Exercise Find the indefinite integral.
a) dx3x 2 + 2
b) x3 + 2x
c) dx6x 5 + 5
d) x6 + 5x
Answer:
a.) dx3x² + 2
Use the properties of integrals
That's
integral 3x² + integral 2
= 3x^2+1/3 + 2x + c
= 3x³/3 + 2x + c
= x³ + 2x + C
where C is the constant of integration
b.) x³ + 2x
Use the properties of integrals
That's
integral x³ + integral 2x
= x^3+1/4 + 2x^1+1/2
= x⁴/4 + 2x²/2 + c
= x⁴/4 + x² + C
c.) dx6x 5 + 5
Use the properties of integrals
That's
integral 6x^5 + integral 5
= 6x^5+1/6 + 5x
= 6x^6/6 + 5x
= x^6 + 5x + C
d.) x^6 + 5x
integral x^6 + integral 5x
= x^6+1/7 + 5x^1+1/2
= x^7/7 + 5/2x² + C
Hope this helps
A new toy hits the local store. Sales (in hundreds) increase at a steady rate for several months, then decrease at about the same rate. This can be modeled by the function S(m)=-0.625\left|\mathrm{m}-8\right|+5S(m)=−0.625∣m−8∣+5 In what month(s) were 400 toys sold? A) 7th and 10th B) 5th C) 5th and 11th D) 4th and 12th
Answer:
Option A.
Step-by-step explanation:
It is given that, sales (in hundreds) for several months can be modeled by the function:
[tex]S(m)=-0.625|m-8|+5[/tex]
We need to find the month in which 400 toys were sold.
Substitute S(m)=4 in the given function.
[tex]4=-0.625|m-8|+5[/tex]
[tex]4-5=-0.625|m-8|[/tex]
[tex]-1=-0.625|m-8|[/tex]
[tex]\dfrac{-1}{-0.625}=|m-8|[/tex]
[tex]1.6=|m-8|[/tex]
Now,
[tex]\pm 1.6=m-8[/tex]
[tex]1.6=m-8[/tex] or [tex]-1.6=m-8[/tex]
[tex]1.6+8=m[/tex] or [tex]-1.6+8=m[/tex]
[tex]9.6=m[/tex] or [tex]6.4=m[/tex]
Approx the value to the next whole number.
[tex]m\approx 10[/tex] or [tex]m\approx 7[/tex]
It means, 400 toys were sold on 7th and 10th month.
Therefore, the correct option is A.
What is the volume of a sphere with a surface area of 9 pi yd2 Options A. 9/2 Pi yd3 B. 9 pi yd3 C. 9/4 pi yd3 D.36 pi yd3
Answer:
=9/2yd³
Step-by-step explanation:
the surface area of a sphere, radius r
S = 4πr²
9 π = 4 π r 2 ⇒ r 2 = 9 π 4 π = 9 4 ∴ r = √ 9 4 = 3 2
The volume of a sphere is
V=43πr3=43×π×(32)3=4×3×3×33×2×2×2π
=9/2yd³
Answer is =9/2yd³ for this question
Please mark brainliest
Hope this helps.
(x+4)/(x^(2)+5x+6)*(x+3)/(x^(2)-16) solve this show all your work
Answer:
1/(x^2-6x+8)
Step-by-step explanation:
1. x^2-16=(x-4)*(x+4)
2. x^2+5x+6=(x+2)*(x+3)
So (x+4)/(x^2+5*x+6) *(x+3)/(x^2-16)=
=(x+4)*(x+3)/((x+4)(x-4)(x+2)(x+3))=1/((x-4)(x-2))=1/(x^2-6x+8)
What is the sum?
StartFraction 3 Over x squared minus 9 EndFraction + StartFraction 5 Over x + 3 EndFraction
StartFraction 8 Over x squared + x minus 6 EndFraction
StartFraction 5 x minus 12 Over x minus 3 EndFraction
StartFraction negative 5 x Over (x + 3) (x minus 3) EndFraction
StartFraction 5 x minus 12 Over (x + 3) (x minus 3)
Answer:
The answer is option D.
Step-by-step explanation:
First we must first find the LCM
the LCM of x² - 9 and x + 3 is x² - 9
So we have
[tex] \frac{3}{ {x}^{2} - 9 } + \frac{5}{x + 3} = \frac{3 + 5(x - 3)}{ {x}^{2} - 9} \\ \\ = \frac{3 + 5x - 15}{(x + 3)(x - 3)} \\ \\ = \frac{5x - 12}{(x + 3)(x - 3)} [/tex]
Hope this helps you
Answer:
D
Step-by-step explanation:
KARUNA OPENED A CANDY SHOP AND SELLS CHOCOLATE AND PEANUT
BUTTER FUDGE BY THE POUND. THE CHOCOLATE FUDGE COSTS $3.20 PER
POUND AND THE PEANUT BUTTER FUDGE COSTS $3.00 PER POUND. ON A
GIVEN DAY KARUNA'S CANDY SHOP SELLS 15.5 POUNDS OF FUDGE FOR A
GROSS PROFIT OF $48.50
A WRITE A SYSTEM OF EQUATIONS TO DESCRIBE THE SCENARIO WHERE C
REPRESENTS THE NUMBER OF POUNDS OF CHOCOLATE FUDGE SOLD,
AND P REPRESENTS THE NUMBER OF POUNDS OF PEANUT BUTTER
FUDGE SOLD
B. HOW MANY POUNDS OF PEANUT BUTTER FUDGE DID KARUNA'S CANDY
SHOP SELL?
Answer:
A. System of equations:
[tex]3.2C+3P=48.5\\C+P=15.5[/tex]
B. 5.5 pounds of peanut butter fudge were sold.
Step-by-step explanation:
Given:
Cost of chocolate fudge = $3.20
Cost of peanut butter fudge = $3.00
Total pounds sold = 15.5
Total gross profit = $48.50
C is the number of pounds of chocolate fudge sold.
P is the number of pounds of peanut butter fudge sold.
To find:
System of equations and number of pounds of peanut butter fudge sold = ?
Solution:
As per given conditions:
1. [tex]C+P=15.5[/tex]
Gross profit from Chocolate fudge: [tex]3.20 \times C[/tex]
Gross profit from Peanut Butter fudge: [tex]3.00 \times P[/tex]
Total gross profit = [tex]3.20C+3.00P = 48.50[/tex]
So, the system of equations is:
[tex]3.2C+3P=48.5\\C+P=15.5[/tex]
2. To find P.
Let us solve the equations.
Multiply 2nd equation with 3 and subtracting from 1st equation:
[tex]0.2C = 48.5- 3 \times 15.5\\\Rightarrow 0.2C = 48.5- 46.5\\\Rightarrow C = 10\ pounds[/tex]
Putting in 2nd equation:
[tex]10+P=15.5\\\Rightarrow P =5.5\ pounds[/tex]
So, the answer is:
5.5 pounds of peanut butter fudge were sold.
Anyone know how to solve 7 and 11
Answer:
7. f⁻⁻¹(x)=x-3 11. f⁻⁻¹(x)= 2x/(1-x)
Step-by-step explanation:
to find the inverse of an expression:
1. change f(x) to y.
2. switch the x and y values.
3. solve to find y.
So....
7.) f(x)=x+3 11.) f(x)= x/(x+2)
y=x+3 y=x/(x+2)
x=y+3 x=y/(y+2)
f⁻⁻¹(x)=x-3 f⁻⁻¹(x)= 2x/(1-x)
ONLY answer is you 100% know this...
Hey there! :)
Answer:
y = 8.
Step-by-step explanation:
Begin by finding the slope of the equation. Use two points from the table and plug them into the formula:
[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{4-16}{1-(-2)}[/tex]
Simplify:
[tex]m = \frac{-12}{3}[/tex]
m = -4. This is the slope.
Create an equation in slope-intercept form (y = mx + b) to solve for the y intercept. Plug in the x and y values from another point.
0 = -4(2) + b
0 = -8 + b
Add 8 to both sides:
8 = b. The 'b' value is the y-intercept.
Therefore, the y-intercept of this table is:
y = 8.
15. In the State of California, there are 25 full-time employees to every 4 part-time employees. If there are 250,000 full-time employees, how many part-time employees are there statewide?
If c(x) = 4x-2 and d(x) = x2 + 5x, what is (c x d) (x)
Answer:
(cd)(x) = 4x³ + 18x² - 10x
Step-by-step explanation:
The question is asking to multiply c(x) and d(x). So we FOIL:
(4x - 2)(x² + 5x)
4x³ + 20x² - 2x² - 10x
4x³ + 18x² - 10x
Stuck on this one, help asap please
Answer:
Tan B = 24/10 = 12/5
Step-by-step explanation:
Tangent is opposite/adjacent. The side opposite of B is 24 and adjacent to that is 10.
4 -letter "words" are formed using the letters A, B, C, D, E, F, G. How many such words are possible for each of the following conditions? (a) No condition is imposed. (b) No letter can be repeated in a word. (c) Each word must begin with the letter A (d) The letter C must be at the end. (e) The second letter must be a vowel.
Answer: a) 2401 b) 840 c)343 d)343 e) 686
Step-by-step explanation:
a) Total are 7 letters
There are 4 possible places in 4-letter word for each of 7 letter.
So total amount of the words is
7*7*7*7= 2401
b) No letter can be repeated mens that in 1st place can stay any of 7 letters,
in 2-nd place- any of 6 letters
in 3-rd place- any of 5 letters
in 4-th place any of 4 letters
Total amount of words is
7*6*5*4=840
c) It is not written if the letters can be repeated. Assume that they can.
1st place occupied by letter A. So at 2-nd, 3-rd and 4th places can stay any of 7 letters
Total amount of words is
1*7*7*7=343
d) Similar case like c). At 1-st ,2-nd, 3-rd can stay any of 7 letters, and at 4th place the letter C (1 letter). Total amount of words is
7*7*7*1=343
e) There are 2 vowels A and E.
So at 1st place can stay any of 7 letters, at 2-nd place -any of 2 letters, at 3-rd place- any of 7 letters and at 4th place any of 7 letters. Total amount of words is
7*2*7*7=686
The total number of 4-letter words possible is 2401
The total number of 4-letter words possible with no letter repeated is 840
The total number of 4-letter words possible with the first letter being A is 343
The total number of 4-letter words possible with the letter C at the end is 294.
The total number of 4-letter words possible with the second letter being a vowel is 1029.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
(a) No condition is imposed:
There are 7 choices for the first letter, 7 choices for the second letter, 7 choices for the third letter, and 7 choices for the fourth letter.
The total number of 4-letter words possible.
7 × 7 × 7 × 7 = 2401
(b) No letter can be repeated in a word:
For the first letter, there are 7 choices.
For the second letter, there are only 6 choices left (since we cannot repeat the first letter). Similarly, for the third letter, there are only 5 choices left, and for the fourth letter, there are only 4 choices left.
The total number of 4-letter words possible with no letter repeated.
7 × 6 × 5 × 4 = 840
(c) Each word must begin with the letter A:
For the first letter, there is only 1 choice (the letter A). For the second letter, there are 7 choices (since any letter can be used).
For the third letter, there are 7 choices, and for the fourth letter, there are 7 choices.
The total number of 4-letter words is possible with the first letter being A.
1 × 7 × 7 × 7 = 343
(d) The letter C must be at the end:
For the fourth letter, there is only 1 choice (the letter C).
For the first letter, there are 7 choices (since any letter can be used).
For the second letter, there are 7 choices, and for the third letter, there are 6 choices (since the letter C cannot be used).
The total number of 4-letter words possible with the letter C at the end.
7 × 7 × 6 × 1 = 294
(e) The second letter must be a vowel:
For the first letter, there are 7 choices (since any letter can be used). For the second letter, there are 3 choices (the vowels A, E, and I).
For the third letter, there are 7 choices, and for the fourth letter, there are 7 choices.
The total number of 4-letter words possible with the second letter being a vowel.
7 × 3 × 7 × 7 = 1029
Thus,
The total number of 4-letter words possible is 2401
The total number of 4-letter words possible with no letter repeated is 840
The total number of 4-letter words possible with the first letter being A is 343
The total number of 4-letter words possible with the letter C at the end is 294.
The total number of 4-letter words possible with the second letter being a vowel is 1029.
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