The number of ways to draw the socks in each case is given as follows:
a) 90 ways.
b) 48 ways.
c) 42 ways.
What is the Fundamental Counting Theorem?The Fundamental Counting Theorem states that if there are m ways for one trial and n ways for another trial, then there are m x n ways in which the two trials can happen simultaneously.
This can be extended to more than two trials, where the number of ways in which all the trials can happen simultaneously is the product of the number of outcomes of each individual trial, according to the equation presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
For item a, we have that there are no restrictions, hence there are 10 options for the first sock and 9 for the second, hence:
10 x 9 = 90.
For item b, we need one of each, hence the possible combinations are:
One of six(blue) and then one of four(white).One of four(white) and then one of six(blue).Hence:
6 x 4 + 4 x 6 = 48.
For item c, we can take 6 then five(two blue) or 4 then 3(two white), hence:
6 x 5 + 4 x 3 = 42.
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You are considering a 5/1 ARM. What does the 1 represent?
A. The total number of years in the loan
B. The number of years that a fixed interest rate will be applied to the
loan
OC. The number of years between adjustments in the interest rate
D. The interest rate of the initial, fixed-rate loan period
SUBMIT
As far as a 5/1 ARM is concerned, note that the "1" refers to how often the rate can be adjusted after the initial fixed-rate period ends.
What is 5/1 ARM?A 5/1 ARM is an adjustable rate mortgage loan (ARM) that has a fixed interest rate for the first five years. Following that, the 5/1 ARM transitions to an adjustable interest rate for the remainder of its term. The terms "variable" and "adjustable" are frequently used synonymously.
If you want a low monthly payment and don't expect to stay in your house for long, a 5/1 adjustable-rate mortgage (ARM) loan may be worth considering. For the first five years, rates on 5/1 ARMs are typically lower than rates on 30-year fixed-rate mortgages.
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Find the y intercept for a line with a slope or 2 that goes through (5, 4)
Answer:
y- intercept = - 6
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here slope m = 2 , then
y = 2x + c ← is the partial equation
to find c substitute (5, 4 ) into the partial equation
4 = 2(5) + c = 10 + c ( subtract 10 from both sides )
- 6 = c
that is the y- intercept c = - 6
johnny can build in 3 1/2 lego planes in 60 minutes. how many can he build in 40 minutes?
The number of lego planes that can be build in 40 minutes is A = 2.33
Given data ,
Johnny can build in 3 1/2 lego planes in 60 minutes
On dividing the number of planes he can build in 60 minutes (3 1/2) by 60:
From the proportion , we get
To find out how many planes he can build in 40 minutes, we can multiply the amount he can build in one minute by 40:
3.5 / 60 = A / 40
Multiply by 40 on both sides , we get
A = 2.33
Hence , Johnny can build approximately 2.33 lego planes in 40 minutes
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A chambered nautilus is a marine animal that lives in the outermost chamber of its shell
The chambered nautilus is a fascinating marine animal that belongs to the family of cephalopods.
It is notable for its unique, spiral-shaped shell that is divided into a series of chambers.
The nautilus lives in the outermost chamber of its shell, which it can control by adjusting the amount of gas and fluid inside it. This allows the nautilus to regulate its buoyancy and move up or down in the water column.
The nautilus has been around for millions of years and is sometimes called a "living fossil" because of its ancient lineage.
Unfortunately, due to overfishing and habitat destruction, many species of nautilus are now endangered.
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The given question is incomplete, the complete question is:
A chambered nautilus is a marine animal form which family?
What is the measure of this angle?
60
80
120
125
Answer:
60
Step-by-step explanation:
180 - 120 = 60
209 g = ___ kg
0.0209
0.209
20,900
209,000
Following is a table for the present value of an annuity of $1 at compound interest
please help with geometric series
Answer:
[tex]C. -5.15\cdot10^{13}[/tex]
Step-by-step explanation:
[tex]Common\ ratio\ (r)=\frac{a_{n+1}}{a_n}=(-3)\\\\Sum\ (S_n)=\frac{a(r^n-1)}{r-1}\ \ (r\neq1)\\\\\implies S_n=\frac{1\ (\ (-3)^{30}-1\ )}{-4}\\\\\implies S_n=\frac{205891132094649-1}{-4}\\\\\approx\frac{206\cdot10^{12}}{-4}\\\\\approx-5.15\cdot10^{13}[/tex]
Which equation can be used to solve for � xx in the following diagram?
Equation which can be used to solve for the value of x is
3x° + 2x° + 80 °= 180° .
Straight angle pair is the sum of two or more angles that are in pair of angles that form a straight line is always equal to 180°.
As shown in the diagram angle on the lines are -
3x ° , 80° , 2x° respectively
Sum of all these angle will be equal to 180°.
3x° + 2x° + 80° = 180
The correct equation to find the value of x is 3x° + 2x° + 80° = 180° .
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every year 5 rows and 5columns are increased . derive the formula for the number of students in each row
The number of students in each row after any number of years, as long as the increase in rows and columns is uniform every year.
Assuming that the increase in rows and columns is uniform every year, we can derive the formula for the number of students in each row as follows:
Let's start with the initial number of rows and columns, which we'll call R0 and C0, respectively, and the number of students in each row, which we'll call S.
After one year, the number of rows and columns will increase by 5, so we'll have R1 = R0 + 5 and C1 = C0 + 5. The total number of students will be R1 x S. We can also express this in terms of the initial number of rows and columns as:
R1 x S = (R0 + 5) x S
Expanding the brackets, we get:
R1 x S = R0 x S + 5 x S
Subtracting R0 x S from both sides, we get:
(R1 - R0) x S = 5 x S
Dividing both sides by 5 x (R1 - R0), we get:
S = 5 / (R1 - R0)
We can use this formula to calculate the number of students in each row after any number of years, as long as the increase in rows and columns is uniform every year.
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An Inverse Variation Includes The Points(3, 3)and(1, n).Find
n .
The inverse variation is y = 9/x, using that equation we can see that n = 9.
How to find the value of n?An inverse variation between two variables x and y can be written as:
y = k/x
Where k is a constant.
We know that this inverse variation contains the point (3, 3), replacing these values we have:
3 = k/3
3*3 = k
9 = k
Then the inverse variation is:
y = 9/x
Now we want to find n such that (1, n) is on the relation above, then we will get:
n = 9/1
n = 9
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Can someone please help me with this? Explaining would really help thank you
The solution of the equation is x=1/2 and y=1/3
The given equations are
18x+12y=13...(1)
30x+24y=23...(2)
Let us form the matrix form to solve the equation
[tex]\left[\begin{array}{ccc}18&12\\30&24\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] =\left[\begin{array}{ccc}13\\23\end{array}\right][/tex]
Multiply equation (1) with 2
36x+24y=26..(3)
Subtract equation 3 from equation 2
30x+24y-36x-24y=23-26
-6x=-3
x=1/2
Now plug in the value of x in equation 1
18(1/2)+12y=13
9+12y=13
12y=4
y=4/12
y=1/3
Hence, the solution of the equation is x=1/2 and y=1/3
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Can someone help me with this? Thank you
The area of the triangle is 6 sq units.
What is the area of the triangle?The area of the triangle is calculated by applying the following formula;
A = ¹/₂ x b x h
where;
b is the base of the triangleh is the height of the triangleThe base of the triangle = 3 - 0 = 3
The vertical height of the triangle = 5 - 1 = 4
Area = ¹/₂ x 4 x 3
Area = 6 sq units.
Thus, the area of the triangle is a function of base and height.
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how do u graph the solution y=2x-1 iready
Answer:
Step-by-step explanation:
y=mx+b
m= slope and b= y intercept
you'll start with a point on the y axis on -1
and the slope will go up so towards the right corner up but 2/1 points
Ciara needs 4 yards of fabric for a dress. She already had 2 1/4 yards of fabric Convert 32/5 to a mixed number
please answer all 3 questions
1. The equation of the form y = a • bˣ is y = 81 x (¹/₃)ˣ
2. His stamp should be worth approximately $7,851.47 after 6 years.
3. The equation of the form y = a • bˣ is y = (¹/₁₆) x 2²ˣ ⁺ ⁵
How did we get our values?1. One will see that y is decreasing by a factor of 3 as x increases by 1. Therefore, we can write the equation as:
y = 81 x (¹/₃)ˣ
2. The increase in value of the stamp can be calculated using the formula:
V = P(1+r)ᵗ
where V is the future value, P is the present value, r is the annual interest rate as a decimal, and t is the number of years.
Substituting the given values:
V = 4900(1+0.075)⁶
V ≈ $7,851.47
Therefore, the stamp should be worth approximately $7,851.47 after 6 years.
3. One will see that y is increasing by a factor of 2 as x increases by 1. Therefore, we can write the equation as:
y = (1/16) x 2²ˣ ⁺ ⁵
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What are the solutions to the system of equations graphed?
Answer:
(- 2, 0 ) , (1, - 3 )
Step-by-step explanation:
the solutions to the system of equations are at the points of intersection with the curve and the straight line.
points of intersection are at (- 2, 0 ) and (1, - 3 ) , then
solutions are (- 2, 0 ) , (1, - 3 )
The cosine of θ is −0.95. What is sin(θ)?
The value of sin(θ) is 0.31 and it lies in the third and fourth quadrants. if the value of the cosine of θ is −0.95.
cos(θ) = -0.95
To calculate the value of sin(θ), we can use the Pythagorean theorem:
[tex]sin^{2}[/tex] (θ) +[tex]cos^{2}[/tex] (θ) = 1
We can rearrange the Pythagorean identity to solve for sin(θ):
[tex]sin^{2}[/tex] (θ)= 1 - [tex]cos^{2}[/tex]
sin(θ) = ±[tex]\sqrt{1-cos^{2}}[/tex] *(θ)--------- (equation 1)
Substitute the value of the cosine of θ = −0.95 in Equation 1
sin(θ) = ±[tex]\sqrt{1-cos^{2}}[/tex] *(θ)
sin(θ) = ±[tex]\sqrt{(1 - 0.9025)}[/tex]
sin(θ) = ±[tex]\sqrt{0.0975}[/tex]
The positive value determines that the value is in the first and second quadrants, Negative shows the third and fourth quadrants.
sin(θ) = [tex]\sqrt{ 0.0975}[/tex]
sin(θ) = 0.312
Therefore, we can conclude that the value of sin(θ) is 0.312.
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Work out the area of the shaded shape on the millimetre (mm) grid.
State the units with your answer.
The diagram is not drawn to scale.
The requried area of the shaded shape is 5 square millimeters.
From the figure,
The area of the green shaded area is given by:
The area of a single square is given as = 1 * 1 = 1 square millimeters.
Now there is 5 square in the shaded region, So the area is given as:
= 5 * 1 = 5 square millimeters.
Thus, the requried area of the shaded shape is 5 square millimeters.
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Diondra wants to know the most popular movie of this year but is unsure of the best way to determine this answer. Which of the following questions would Diondra ask that does NOT allow for variability?
Which movie did her best friend like the most?
How many awards did each movie win?
What is the total dollar amount that each movie made from ticket sales?
How many weeks did each movie play in the theater?
The question that Diondra would ask that does not allow for variability is A. Which movie did her best friend like the most?
How does this question not show variability ?The other three questions ("How many awards did each movie win?", "What is the total dollar amount that each movie made from ticket sales?", and "How many weeks did each movie play in the theater?") all offer metrics by which a movie's popularity could be measured, and those measurements could vary from movie to movie.
However, the question about her best friend's favorite movie depends solely on the opinion of one individual, not a variable measure, and therefore doesn't allow for variability.
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What is the domain of the function
Answer:
xs7
Step-by-step explanation:
Mary has a lemonade stand.Last week she spent $18.00 on supplies,but earned only $12.00.Did Mary make a profit ?Explain and show problem as a mathematical equation.
They need to sell at least 13 cups to gain profits.
Here, we have,
Givens
The initial cost is $1.20.
Each cup of lemonade costs 6 cents to make.
May's children sell 10 cents a cup.
First, we need to represents the cost of their investment.
0.06x = 1.20, because each cup costs 6 cents, and the initial costs of all is $1.20.
That means,
x= 20
They can produced 20 cups.
However, they already sell a cup for 10 cents. So, how many cups they need to sell to gain profits? We need to establish a similar relation,
0.10 x = 1.20
x = 12
This means if they sell 12 cups, they will just cover the investment, that is, zero profits.
Therefore, they need to sell at least 13 cups to gain profits.
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complete question
Mary's children decide to run a lemonade stand to earn some extra money.The cost to start the business is $1.20 and each cup of lemonade costs 6 cents to make. If lemonade sells for 10 cents a cup,how many cups must Mary's children sell to make a profit?----Apply systems of equations
Find the greatest common factor of 56xy and 16y³.
Answer:
8y
Step-by-step explanation:
Lets put these two parts into addition to make it easier.
(y)56x + 16y^2
(8y)7x + 2y^2
8y is the GCF(grates common factor)
Which condition would prove ΔJKL ~ ΔXYZ?
The condition that will prove the two triangles similar is
side JL = 8 * side ZX
angle L = angle Z
What are similar triangles?Similar triangles are triangles which have the similar shape however not necessarily the equal size. More officially, two triangles are comparable if their corresponding angles are congruent and their corresponding aspects are in proportion.
This means that if we had been to scale one triangle up or down uniformly, the ensuing triangle could be much like the original triangle.
In the figure, the scale is 8
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60% of the books in a library are for adults, 5% are for young people and the rest are for children. If there are 280 books for children, how many books are there altogether?
Answer:
800 books
problem solving steps：
adults:60%
young people:5%
children=100%-60%-5%
=35%
35%=280 books
1%=280÷35
=8
100%=800
so,there are 800 books
A triangle has side lengths of 13, 18, and 24. Is it a right triangle?
Answer:
No, it is not a right triangle.
[tex] \sqrt{ {13}^{2} + \ {18}^{2} } = \sqrt{169 + 324} = \sqrt{493} [/tex]
√493 is not equal to 24.
Answer:
it doesn't
Step-by-step explanation:
it doesn't follow pythagoras theorem
a² = b² + c²
Is this negative and odd or even and positive or negative and even and positive and odd?
Answer:
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Step-by-step explanation:
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S and P are the midpoints of the
legs, RT and QU, of trapezoid QRTU.
If QR
TU =
X?
= -6x + 37, PS = x + 33, and
= 2x + 41, what is the value of
The value of x in the trapezoid is 2.
How to find the side of a trapezoid?The mid points of a trapezoid is a line that goes across from the middle of one leg to the middle of the other leg.
Using the mid point theorem, let's find the value of x in the trapezoid as follows:
PS = 1 / 2 (QR + TU)
PS = x + 33
QR = -6x + 37
TU = 2x + 41
Therefore,
x + 33 = 1 / 2 (-6x + 37 + 2x + 41)
x + 33 = 1 / 2 (-4x + 78)
x + 33 = -2x + 39
x + 2x = 39 - 33
3x = 6
divide both sides by 3
x = 6 / 3
x = 2
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What is the scale of the x-axis in this coordinate graph?
A. 1 tick mark represents 0.1 unit
B. 1 tick mark represents 0.2 unit
C. 1 tick mark represents 0.3 unit
D. 1 tick mark represents 0.4 unit
Answer:
B. 1 tick mark represents 0.2 unit
Step-by-step explanation:
Looking at the axis and going over 2 tick marks is .4
.4 /2 = .2
Each tick mark is .2 units
The circle graph shows how Josh's family budgets a total of $6200 for the month.
Housing
$1178
Category
Clothing
Insurance
Transportation
Taxes
$1364
Taxes
Food
$868
$248 Insurance
$186
Utilities
$496
Savings
$434
Find the percentage of the total budgeted for each category listed below.
Percentage
0%
0%
0%
Clothing
Entertainment
$682
The percentage of the total budgeted category is given by
a) Clothing : 12 %
b) Insurance : 3 %
c) Taxes : 22 %
Given data ,
Let the percentage value be represented as A
Now , the value of A is
Let the total budgeted amount be = $ 6,200
Now , the amount for clothing = $ 744
So , the percentage for clothing = 744 / 6200 = 12 %
And , the amount for insurance = $ 186
Now , the percentage for insurance = 186 / 6200 = 3 %
And , the amount for taxes = $ 1,364
So , the percentage for taxes = 1364 / 6200 = 22 %
Hence , the percentages are solved
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