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.
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Find the last number of the following series
10 8 16 13 39 35
1)75
2)100
3)130
4)140
The answer is 4) 140.
If we closely examine the pattern of the series, we see that after a number is subtracted by a value, it is multiplied by the same value, and then it moves on to the next natural number.
10 - 2 = 88 × 2 = 1616 - 3 = 1313 × 3 = 3939 - 4 = 35The next step, according to the pattern, would be to multiply 4.
35 × 4140Question 2 Multiple Choice Worth 1 points)
(08.05 MC)
Functions f(x) and g(x) are shown:
f(x)=x²
g(x)=x²-12x+36
In which direction and by how many units should f(x) be shifted to obtain g(x)?
O Left by 18 units
O Right by 18 units
O Left by 6 units
O Right by 6 units
2
Comparing g(x) with f(x), you can see that the function f(x) is translated to the right by 6 units to produce g(x) which is equivalent to (x-6)²
Transformation of functionTransformation is a techniques use to change the position of an object on an xy-plane.
Given the parent function f(x) = x² and the function g(x) = x²-12x +36
Factorize g(x);
g(x) = x²-6x-6x+36
g(x)=x(x-6)-6(x-6)
Group the terms to have;
g(x) = (x-6)²
Comparing g(x) with f(x), you can see that the function f(x) is translated to the right by 6 units to produce g(x) which is equivalent to (x-6)²
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Determine whether or not the lines are parallel based on the
given angle measures. Explain your answer in the case.
Answer:
answer
Step-by-step explanation:
To see whether or not two lines are parallel, we must compare their slopes. Two lines are parallel if and only if their slopes are equal. The line 2x – 3y = 4 is in standard form. In general, a line in the form Ax + By = C has a slope of –A/B; therefore, the slope of line q must be –2/–3 = 2/3.
Relate ratios in right triangles
Consider right triangle ADEF below. Which Expressions are equivalent to cos(E)?
Answer:
B
Step-by-step explanation:
Cos is the adjacent side over the hypotenuse. The adjacent side to <E is side ED. The hypotenuse is side EF. ED/EF. They do not go right out and give you this choice, but you see that B says the same thing.
In a school, all pupils play either Hockey or Football or both. 400 play Football, 150 play Hockey, and
130 play both the games. Find
(i) The number of pupils who play Football only,
(ii) The number of pupils who play Hockey only,
(iii) The total number of pupils in the school
Answer:370 play football and 20 play hockey
Step-by-step explanation: because 400 - 130 equals 370 for football
then hockey 150-130 equals 20
Then the total students are 420
150+400-130 equals 420
need heeeelp please
Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using
a graphing utility, use it to graph the function and verify the real zeros and the given function value.
n=3;
-2 and 7+5 i are zeros;
f(2)=200
f(x) =
(Type an expression using x as the variable. Simplify your answer.)
possible
4
Answer:
f(x) = x³ -12x² +46x +148
Step-by-step explanation:
When p is a root of polynomial function f(x), (x -p) is a factor. When the coefficients are real, any complex roots come in conjugate pairs.
Factored formGiven the two roots of f(x), we know the third root is the conjugate of the given complex root. The factored form will be ...
f(x) = (x -(-2))(x -(7 +5i))(x -(7 -5i))
Rearranging a bit, this is ...
f(x) = (x +2)((x -7) -5i)((x -7) +5i)
The latter two factors are recognizable as the factors of the difference of squares, so this is ...
f(x) = (x +2)((x -7)² -(5i)²) = (x +2)((x -7)² +25)
Standard formMultiplying the factors, we have ...
f(x) = (x +2)(x² -14x +49 +25) = (x +2)(x² -14x +74)
f(x) = x³ -14x² +74x +2x² -28x +148 . . . . . use the distributive property
f(x) = x³ -12x² +46x +148 . . . . . . . . . . collect terms
60% of people who purchase sports cars are men. If
10 sports car owners are randomly selected, find
the probability that exactly 7 are men.
The probability that exactly 7 are men out of 10 sports car owners who are randomly selected is 0.215 given that 60% of people who purchase sports cars are men. This can be obtained by using binomial distribution formula.
Calculate the required probability:This question can be solved using binomial distribution formula.
The formula for binomial distribution is the following,
P(X) = ⁿCₓ pˣ qⁿ⁻ˣ
where,
n = number of trials(or the number being sampled)
x = number of success desired
p = probability of getting a success in one trial
q = 1 - p = probability of getting a failure in one trial
Here in the question it is given that,
⇒ 60% of people who purchase sports cars are men
This statements clearly means that probability of men purchase sports cars is 60%.
⇒ P(men purchasers) = p = 60% = 0.6
From this we can find the probability of women who purchase sports cars,
⇒ P(women purchasers) = q = 1 - p = 1 - 0.6 = 0.4
So we can find the probability that exactly 7 are men out of 10 sports car owners who are randomly selected
It is a binomial case with n = 10
By using the formula for binomial distribution we get,
P(X = 7) = ¹⁰C₇ × 0.6⁷ × 0.4³
P(X = 7) = 120 × 0.0279936 × 0.064
P(X = 7) = 0.21499
P(X = 7) = 0.215
Hence the probability that exactly 7 are men out of 10 sports car owners who are randomly selected is 0.215 given that 60% of people who purchase sports cars are men.
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please anybody solve this problem step by step as soon as possible
Answer:
39 pages
Step-by-step explanation:
If 13 pages are read in 1/3 of an hour, we need to multiply 13 by 3 to get the number of pages read in 1 hour. 13*3 = 39 pages
Can someone please simplify this 9+4t=-3(1-2t)?
Answer:
simplification of the original equation is below/
Step-by-step explanation:
9+4t=-3(1-2t) can be simplified into
9+4t=-3+6t because of distributing the -3 to both the 1 and -2t.
however, this can simplified to
4t-6t=-3-9
and this can simplify to
-2t=-12
which can simplify to
t = 6
give brainliest please!
hope this helps :)
05* Find, for y> 0, the general solution of the differential equation dy/dx=xy.
Inlyl=1/2x^2+c
Inlyl=1/2x^2-c
Inlyl=-1/2x^2-c
Inly|=-1/2x^2+c
The ODE is separable.
[tex]\dfrac{dy}{dx} = xy \iff \dfrac{dy}y = x\,dx[/tex]
Integrate both sides to get
[tex]\displaystyle \int\frac{dy}y = \int x\,dx[/tex]
[tex]\boxed{\ln|y| = \dfrac12 x^2 + C}[/tex]
But notice that replacing the constant [tex]C[/tex] with [tex]-C[/tex] doesn't affect the solution, since its derivative would recover the same ODE as before.
[tex]\ln|y| = \dfrac12 x^2 - C \implies \dfrac1y \dfrac{dy}{dx} = x \implies \dfrac{dy}{dx} = xy[/tex]
so either of the first two answers are technically correct.
In a triangle, the measure of the first angle is twice the measure of the second angle. The measure of the third angle is 76° more than the measure of the second angle. Use the fact that the sum of the measures of the three angles of a triangle is 180° to find the measure of each angle.
Answer:
First angle: 52°
Second angle: 26°
Third angle: 102°
Step-by-step explanation:
Let the measure of the second angle = x.
Measure of the first angle: 2x
Measure of third angle: x + 76
2x + x + x + 76 = 180
4x + 76 = 180
4x = 104
x = 26 second angle
2x = 2 × 26 = 52 first angle
x + 76 = 26 + 76 = 102 third angle
A board, 74 cm long is cut into three pieces such as the second board is twice as long as first board and the third is 4 cm longer than second. Find length of shorter piece
Answer:
The shortest piece is the first piece and it is 14 cm long.
Step-by-step explanation:
We have three unknowns so we need 3 equations.
Let x = the length of the first piece
Let y = the length of the second piece
Let z = the length of the third piece.
x + y + z = 74 y = 2x z = y + 4
There are a number of ways to solve this. I am going to plug in 2x for y into the first and the third equation to get:
x + y + z = 74
x + 2x + z = 74 Combine the x terms
3x + z = 74
Next, I am going to substitute 2x in for y in the third equation above.
z = y + 4
z = 2x + 4 I am going to put both variable on the left side of the equation
z - 2x = 4
I can know take the two bold equations that I have above and solve for the either x or z. I am going to solve for z. I need one of the equation to have a z and the other equation to have -z so that they will cancel one another out. I am going to multiple z - 2x = 4 all the way through by -1 to get:
z - 2x = 4
-1(z - 2x) = 4(-1)
-z +2x = -4
I am going to rearrange 3x + z = 74 so that the z term is first and add it to -z + 2x = -4
z + 3x = 74
-z + 2x = -4
5x = 70 divide both sides by 5
x = 14 This is the length of the first piece.
y = 2x
y = 2(14) = 28
y = 28 This is the length of the second piece.
z = y+4
z = 28 + 4 = 32
or
x + y + z = 74
14 + 28 + z = 74
42 + z = 74 Subtract 42 from both sides.
z = 32
A 22-ft ladder leans against a building so that the angle between the ground and the ladder is 64°. How high does the ladder reach on the building?
The height of the ladder on the building is 19.77 feet
How high does the ladder reach on the building?Represent the height of the ladder on the building with h
So, the given parameters are:
Angle, x = 64 degrees
Length of ladder, l = 22 feet
The height of the ladder on the building is calculated using
sin(x) = h/l
Substitute the known values in the above equation
sin(64) = h/22
Multiply both sides by 22
h = 22 * sin(64)
Evaluate the product
h = 19.77
Hence, the height of the ladder on the building is 19.77 feet
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What is the equation of the line in standard form of the graph below?
Answer:
Step-by-step explanation:
Write the equation y=-3x+3 in function notation using f(x) to denote the function.
Answer:
f(x) = -3x + 3
Step-by-step explanation:
Please solve this now. Everything is attached in the file. You need to provide a full solution. Thanks
Based on the requirements for FICA and Medicare tax, the amount to be withheld in March for FiCA is $685.10 and for Medicare is $160.23.
The amount to be withheld in December of FICA is $523.90 and for Medicare is $160.23.
How much is to be withheld for FICA?In March, the amount to be withheld is:
= 11,050 x 6.2%
= $685.10
To find out the amount withheld in December, find out the earnings up to that point:
= 11,050 x 12
= $132,600
FICA can only be withheld on the first $130,000 so the amount of FICA In December is:
= 6.2% x ( 11,050 - (132,600 - 130,000))
= $523.90
What amount will be withheld for Medicare?The amount will be the same for both March and December as Medicare is for all earnings:
= 11,050 x 1.45%
= $160.23
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The new director of special events at a large university has decided to completely revamp graduation ceremonies. Toward that end, a PERT chart of the major activities has been developed. The chart has five paths with expected completion times and variances as shown in the table. Graduation day is 16 weeks from now. Use Table B and Table B1. Path Expected Duration (weeks) Variance A 10 1.21 B 8 2.00 C 12 1.00 D 15 2.89 E 14 1.44 Click here for the Excel Data File Assuming the project begins now, what is the probability that the project will be completed before: (Round your z-value to 2 decimal places and all intermediate probabilities to 4 decimal places. Round your final answers to 4 decimal places.) a. Graduation time? b. The end of week 15? c. The end of week 13?
The probability that the project will be completed before the graduation time is 0.6873.
What is probability?It should be noted that probability simply means the likelihood of the occurence of an event.
From the table attached, it can be seen that the probability that the project will be completed before the graduation time is 0.6873.
Also, the probability that the project will be completed before the end of week 15 will be 0.3983.
Lastly, the probability that the project will be completed before the end of week 13 will be 0.0203.
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The table below shows the growth of algae cells within the Chesapeake Bay. Which of the following functions models the concentration, C(d), of algae cells per milliliter in d days?
The exponential function that represent the concentration of algae cells per milliliter in d days is [tex]C(d) = 10(2)^d[/tex]
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
The standard form of an exponential funtion is in the form:
y = abˣ
Where a is the initial value and b is the multiplication factor.
Let C(d) represent the concentration of algae cells per milliliter in d days
At point (1, 20)
20 = ab (1)
At point (2, 40)
40 = ab² (2)
From equations 1 and 2:
b = 2, a = 10
The exponential function that represent the concentration of algae cells per milliliter in d days is [tex]C(d) = 10(2)^d[/tex]
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solve x^2 + x - 12 = 0
Answer:
x₁ = -4
x₂ = 3
Step-by-step explanation:
x²+ x + 12 = 0
x = {-1±√((1²)-(4*1*-12))} / (2*1)
x = {-1±√(1+48)} / 2
x = {-1±√49} / 2
x = {-1±7} / 2
x₁ = {-1-7} / 2 = -8/2 = -4
x₂ = {-1+7} / 2 = 6/2 = 3
Check:
x₁
-4² + (-4) - 12 = 0
16 - 4 - 12 = 0
x₂
3² + 3 - 12 = 0
9 + 3 - 12 = 0
Helpppppp What’s the prime factorization of 36 and 22
25)
27)
29)
8-Surface Area of Solids
Find the surface area of each solid. Round to the nearest tenth.
7 yd
9m
5 yd
7 yd
7 yd
8.3 m
9m
7 yd
13.7 yd 26)
4 yd
3.9 ft
28)
3 mi
30)
2 mi
818
2 mi
11.5 yd
2 mi
3 mi
7 yd
7 yd
The surface area of the figure illustrated will be 286 yards²
How to calculate the area?The surface area of a solid object simply implies the measure of the total area which the surface of an object occupies. This is typically done by adding all the areas on the surface of the object.
It should be noted that the surface area of a cuboid will be:
= 2(lw + lh + wh)
w = width = 7
l = length = 9
h = height = 5
Surface area = 2(lw + lh + wh)
= 2(7 × 9) + 2(9 × 5) + 2(7 × 5)
= 126 + 90 + 70
= 286 yards²
Therefore, the surface area of the solid will be 286 yards².
Complete question:
Find the surface area of the solid given that the length is 9 yards, the width is 7 yards, and the height is 5 yards.
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Simply the expression a = -3; b = 9
-7a + 4b
46?
-15?
15?
57?
Answer:
57
Step-by-step explanation:
-7a + 4b
Let a = -3 b = 9
Substitute the values in
-7(-3) + 4(9)
Multiply
21 + 36
Add
57
Function and Reasoning:
There are 60 calories in 5 ounces of a certain brand of soda.
Part A: Represent the relationship between the number of calories and the number of ounces of soda as a line in the coordinate plane below.
Part B: What is the number of calories per ounce of soda?
Part C: How does the unit rate relate to the slope of the line in the graph above? Explain your answer.
The number of calories per ounce of soda is 10
Part A: Represent the relationship between the number of calories and the number of ouncesThe given parameters are:
Calories = 50
Ounces = 5
Let the number of calories be y and the ounces be x.
So, we have:
y = kx
Substitute y = 50 and x = 5
50 = 5k
Divide by 5
k = 10
Substitute k = 10 in y = kx
y = 10x
See attachment for the graph of the relationship between the number of calories and the number of ounces
Part B: What is the number of calories per ounce of soda?In (a), we have:
k = 10
This means that the number of calories per ounce of soda is 10
Part C: How does the unit rate relate to the slope of the line in the graph above?The unit rate and the slope represent the same and they have the same value
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Landon Wallin is an auto mechanic who wishes to start his own business. He will need $4200 to purchase tools and equipment. Landon decides to finance the purchase with a 36-month fixed installment loan with an APR of 5.5% a) Determine Landon's finance charge. b) Determine Landon's monthly payment.
Landon's finance charge is $613.2
Landon's monthly payment is; $80.22
How to find the finance charge?
It is convenient to compute the monthly payment first, then figure the total amount repaid and the finance charge.
The amortization formula is:
A = Pr/(1 - (1 + r)⁻ⁿ)
where;
A is the monthly payment
P is the loan amount
r is the monthly interest rate
n is the number of months
b) Using the above formula, we can get the monthly payment as;
A = $4200(0.055/12)/(1 - (1 +0.055/12)⁻⁶⁰) = $19.708333/0.23995049
A = $80.22
The monthly payment amount is $80.22
a) 60 monthly payments add up to;
$80.22 × 60 = $4813.2
Since $4200 of that amount is principal, the finance charge is;
$4813.2 - $4200.00 = $613.2
Landon's finance charge is $613.2
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(04.01, 04.02 HC)
Eric plays basketball and volleyball for a total of 95 minutes every day. He plays basketball for 25 minutes longer than he plays volleyball.
Part A: Write a pair of linear equations to show the relationship between the number of minutes Eric plays basketball x) and the number of minutes he
plays volleyball (y) every day. (5 points)
Part B: How much time doos Eric spend playing volleyball every day? Show your work. (3 points)
Part C: Is it possible for Eric to have spent 35 minutes playing basketball if he plays for a total of exactly 95 minutes and plays basketball (or 25 minutes
longer than he plays volleyball? Explain your reasoning. (2 points)
Como derivar cos(2x)/tan(2x)
Use the quotient and chain rules. If
[tex]y = \dfrac{\cos(2x)}{\tan(2x)}[/tex]
then the derivative is
[tex]\dfrac{dy}{dx} = \dfrac{\tan(2x) \frac d{dx}\cos(2x) - \cos(2x) \frac d{dx}\tan(2x)}{\tan^2(2x)}[/tex]
[tex]\dfrac{dy}{dx} = \dfrac{\tan(2x) (-\sin(2x)) \frac d{dx}(2x) - \cos(2x)\sec^2(2x) \frac d{dx}(2x)}{\tan^2(2x)}[/tex]
[tex]\dfrac{dy}{dx} = \dfrac{-2\sin(2x)\tan(2x) - 2 \sec(2x) }{\tan^2(2x)}[/tex]
and we can rewrite this by
• multiplying by [tex]\frac{\cos^2(2x)}{\cos^2(2x)}[/tex],
[tex]\dfrac{dy}{dx} = \dfrac{-2\sin^2(2x)\cos(2x) - 2 \cos(2x) }{\sin^2(2x)}[/tex]
• factorizing,
[tex]\dfrac{dy}{dx} = -\dfrac{2\cos(2x) \left(\sin^2(2x) + 1\right)}{\sin^2(2x)}[/tex]
etc
The standard deviation of the following data set is 0.31. 99% of the data would fall in which range? 4.3, 5.1, 3.9, 4.5, 4.4, 4.9, 5.0, 4.7, 4.1, 4.6, 4.4, 4.3, 4.8, 4.4, 4.2, 4.5, 4.4
Answer: Pr(4.19 ≤ X ≤ 4.81)
Step-by-step explanation:
First of all, let's calculate the mean;
x¯ = (4.3 + 5.1 + 3.9 + 4.5 + 4.4 + 4.9 + 5.0 + 4.7 + 4.1 + 4.6 + 4.4 + 4.3 + 4.8 + 4.4 + 4.2 + 4.5 + 4.4)/17
x¯ = 76.5/17
x¯ = 4.5
We are given standard deviation; s = 0.31
Now, z-value for a 68% Confidence interval is 1
Range in which the data falls is;
Range = x¯ ± zs
Range = 4.5 ± (1 × 0.31)
Range is;
Pr[(4.5 - 0.31) ≤ X ≤ (4.5 + 0.31)]
Pr(4.19 ≤ X ≤ 4.81)
Answer:
Pr (3.57 ≤ X ≤ 5.43)
Step-by-step explanation:
Took the quiz.
athletes are running a race. A gold medal is to be given to the winner, a silver medal is to be given to the second-place finisher, and a bronze medal is to be given to the third-place finisher. Assume that there are no ties. In how many possible ways can the medals be distributed?
Using the permutation formula, there are 157,410 ways for the medals to be distributed.
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this problem, 3 athletes are chosen from a set of 55, hence the number of ways is given by:
P(55,3) = 55!/52! = 157,410
157,410 ways for the medals to be distributed.
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Again I need help, If you tell me the answer that would be very nice! ,
Find the surface area of the composite figure :
The surface area of the given two rectangular prism is given as follows:
498 cm².
What is the surface area of a rectangular prism?The surface area of a rectangular prism of length l, width w and height h is given as follows:
S = 2(lw + wh + hl).
For this problem, there are two prisms, with dimensions given as follows:
l = 12 cm, w = 7 cm, h = 7 cm.l = 2 cm, w = 7 cm, h = 2 cm.Hence the surface area of the figure is the combined surface area of each figure, hence:
S = 2(7 x 7 + 12 x 7 + 12 x 7) + 2(2 x 7 + 2 x 2 + 7 x 2) = 498 cm².
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