There are 325 ways we can write two different letters so that they are in alphabetical order.
A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant (unlike permutations).
A k-combination of a set S is officially defined as a subset of S's k unique elements.
We have 25 ways to have the combo A_
Then 24 ways to have the combo B_
The number of combos = 25 * (26/ 2)
= 25 * 13
= 325 ways
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A drawer contains one pair of brown socks and one pair of white socks. The table shows the possible outcomes, or sample space, for choosing a sock, replacing it, and then choosing another sock.
Given that the drawer includes one pair of brown socks and one pair of white socks, the likelihood of selecting one sock, replacing it, and then selecting another sock is 1/16.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Here,
n(s)=4
n(e)=1
Probability of choosing a sock, replacing it, and then choosing another sock,
=1/4*1/4
=1/16
Probability of choosing a sock, replacing it, and then choosing another sock will be 1/16 as the drawer contains one pair of brown socks and one pair of white socks.
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Question 2
The average distance from Jupiter to the Sun is about 5 x 10^8 miles. The average
distance from Venus to the Sun is about 7 x 10^7 miles.
The average distance from Jupiter to the Sun is about how many times as great as
the average distance from Venus to the Sun?
1. 1.4 times
2.7.1 times
3. 10 times
4. 430,000,000 times
When the average distance from Jupiter to the Sun is about 5 x 10^8 miles and the average distance from Venus to the Sun is about 7 x 10^7 miles. The average distance from Jupiter to the Sun is about 7.1 as great as the average distance from Venus to the Sun.
How to compare the distancesThe distances is compare using the mathematical operation called division,
the procedure is done as follows
= (The average distance from Jupiter to the Sun) / (The average
distance from Venus to the Sun)
= 5 x 10^8 miles / 7 x 10^7 miles.
= 7.14285
= 7.1
the comparison showed that the distance from Jupiter to Sun is 7.1 times greater than the distance form Venus to Sun
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Janet made 7 1/3 pounds of trail mix. If she puts 1 5/6 pounds into each bag, how many
bags can Janet fill?
when finding 6.1 divided by 0.1 how is the decimal point moved?
well, let's just divide them anyway and check it out.
hmmm 6.1 ÷ 0.1, well, when dividing decimals, we can first check the decimals on each hmmm 6.1 has one decimal and 0.1 has one decimal, so for the one decimal on 6.1 0.1 gets one "0" and for each decimal on 0.1, 6.1 gets one "0".
That means we can change the values with no dots to say 610 and 10, so we end up with a division of 610 ÷ 10 = 61. We can write that as 61.0 hmmm woopsie, the dot moved to the right by one slot.
Andrew invests $2834 in a savings account with a fixed annual rate of 2.5% compounded daily. What will the account balance be after 28 years?
The account balance(i.e. compound amount) will be $5706.84 after 28 years.
What is daily compounded interest?
Daily compounded interest is defined as an interest that is accrued daily and is computed by charging interest on principal plus interest earned daily. Due to the frequent compounding, daily compounded interest is higher than interest compounded on a monthly or quarterly basis.
Given, Principal = $2834
the annual rate = 2.5% = 0.025
time = 28 years
For compounded daily, n = 365
Now, the compound amount is calculated by
[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]
or, A = [tex]2834(1 + \frac{0.025}{365} )^{365*28}[/tex]
A = $5706.84
Hence, the account balance will be $5706.84 after 28 years.
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If [tex]$4^x = 3$[/tex], what is [tex]$4^{2x-2}?$[/tex]
[tex]4^x=3 \\\\[-0.35em] ~\dotfill\\\\ 4^{2x-2}\implies 4^{2x}\cdot 4^{-2}\implies (4^x)^2\cdot \cfrac{1}{4^2}\implies \cfrac{(4^x)^2}{16}\implies \cfrac{(3)^2}{16}\implies \cfrac{9}{16}[/tex]
One of the roots of the equation 10x^2-33x=c=0 is 5.3. Find the other root and the coefficient c.
Answer:
another root=-2,c=-106
Step-by-step explanation:
let q and r be two roots of eqn 10x²-33x-c=0,--(1)
then,q=5.3
comparing eqn--(1) with ax²+bx+c=0,we get
a=10,b=-33,C=-c
we know,
q+r=-b/c
or,5.3+r=33/10
or,53+10r=33
or,10r=-20
or,r=-2
hence, another root=-2
again,we know
q×r=-C/a
or,5.3×-2=c/10
or,-106=c
hence,c=-106.
If 65% of a number is 208 and 15% of the same number is 48, find 80% of that number.
The number is 320 and 80 % of the number is 256
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the equation A is
65% of a number is 208 and 15% of the same number is 48
So , 65% of n = 208 be equation (1)
15% of n = 48 be equation (2)
Now , on simplifying the equations , we get
( 15 / 100 ) x n = 48
15n/100 = 48
Multiply both sides by 100 . we get
15n = 4800
Divide by 15 on both sides of the equation , we get
n = 320
The number n can also be determined by
( 65% - 15% ) of n = 208 - 58
50 % of n = 160
So , 100 % on n = 160 x 2
n = 320
Therefore , the number n is 320
Now , the 80 % of the number n is A = 80/100 x 320
A = 320 x 0.8
A = 256
Therefore , the value of A is 256
Hence , The number is 320 and 80 % of the number is 256
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X is a normally distributed random variable with mean 26 and standard deviation 1.
What is the probability that X is between 24 and 28?
Use the 0.68-0.95-0.997 rule and write your answer as a decimal. Round to the nearest
thousandth if necessary.
Answer: give me brainliset
(
X
>
42
)
=
P
(
Z
>
−
1.1429
)
=
1
−
P
(
Z
<
1.1429
)
=
1
−
Φ
(
1.1429
)
=
1
−
0.8729
(from tables)
=
0.1271
Step-by-step explanation:
Order these numbers from least to greatest.
1.4 comma space 1.04 comma space 16 over 10 comma space 1 1 half
Answer:
1.04, 1.4, 1.5 (one and a half), 10, 16
Answer:
1.04, 1.4, 1.5, 1.6
Step-by-step explanation:
1 1 half = 1.5
16 over 10 = 1.6
hope this helps!
What is the solution of the equation?:
-2(3x+1)-2x=-4(2x)-4
it doesn't have solution
Find the x- and y-intercepts of the graph of -3x + y = 6. State each answer as an
integer or an improper fraction in simplest form.
Answer:
X-intercept : (-2,0)
Y-intercept : (0,6)
Answer:y-intercept (0,6),x-intercept (-2,0)
Step-by-step explanation:
To find the y-intercept set x=0
-3(0)+y=6
y=6
y-intercept (0,6)
To find the X-intercept set y=0
-3x+0=6
-3x=6
x=-2
x-intercept (-2,0)
Tyee has 39 m of fencing to build a three-sided fence around a rectangular plot of
land that sits on a riverbank. (The fourth side of the enclosure would be the river.)
The area of the land is 169 square meters. List each set of possible dimensions (length
and width) of the field.
The dimensions of a building to be fenced off around a rectangular parcel of land are 10.5 meters and 21 meters.
How come it's called a rectangle?The Latin word rectus, which meaning "right" or "straight," is the source of the English word "rectangle." The straight sides of a rectangle are a result of its right angles. Rectitude, which refers to moral uprightness, is another term with the same root.
Explanation:
The size of a rectangle
lw = area of rectangle
where,
= length
= width
Thus, perimeter equals 2w plus l.
42 = 2w + l
l = 42 - 2w
Hence,
area = w (42- 2w)
180 = 42w - 2w²
-2w² +42w - 180 = 0
-w² + 21w - 180 = 0
The following is where to find the dimension w;
w = - b / 2a
where
a = -1
b = 21
w = - 21 / 2 × -1
W=10.5 meters.
Then,
l = 42 - 2w
l = 42 - 2(10.5) (10.5)
l=21 meters .Consequently, the measurements are 10.5 meters and 21 meters.
The dimensions of a building to be fenced off around a rectangular parcel of land are 10.5 meters and 21 meters
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what is the probability that an electron will tunnel through a 0.50 nm air gap from a metal to a stm probe if the work function is 4.0 ev?
The probability that an electron will tunnel through a 0.50 nm air gap from a metal to a STM probe if the work function is 4.0 eV is 3.4 × 10^-5
The air gap from a metal to a STM = 0.50 nm
The work function = 4.0 eV
The probability is the ratio of the number of favorable outcomes to the total number of outcomes
The probability = Number of favorable outcomes / Total number of outcomes
The value of η = h / [tex]\sqrt{2m(U_0-E)}[/tex]
Substitute the values in the equation
= [tex]\frac{1.05(10^{-34})}{\sqrt{2(9.11(10^{-31})(4(1.6)(10^{-19})} }[/tex]
Do the arithmetic operation
= 0.0972 nm
The probability = exp (-1 / 0.972)
= 3.4 × 10^-5
Therefore, the probability is 3.4 × 10^-5
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0.27 times 35 = 9.45 because i just said so bye
Answer:
Yes, you're right.
Step-by-step explanation:
Just by doing the math, 0.27 times 35 is 9.45.
Plugging it in a calculator also says it's 9.45.
The general form of an parabola is 4y2 + 40y + 3x + 103 = 0
What is the standard form of the parabola?
The standard form of the parabola is x = -4/3y² -40/3y -103/3
What is parabola?
A parabola is an approximately U-shaped, mirror-symmetrical planar curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. One way to describe a parabola is with a point and a line.
x = -4/3(y +5)² -1
Solve for x.
x = (4y² +40y +103)/(-3)
x = -4/3y² -40/3y -103/3 . . . . 'standard form' in the US
__
Taking our clues from the graph*, we can write the vertex form equation as ...
x = -4/3(y +5)² -1 . . . . . . 'standard form' in other places
____
* The vertex is (-1, -5), so for some leading coefficient, the equation will be ...
x = a(y -(-5))² +(-1) = a(y +5)² -1
The value of 'a' is the scale factor. Here, that is the difference between the parabola value (x = -2 1/3) and the vertex value (x = -1) one unit away from the vertex.
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The diameter of a circle is 6 cm. Find its area to the nearest whole number.
Answer:
28.26
Step-by-step explanation:
A=3.14r^2
A=3.14(3)^2
A=3.14(9)
A=28.26
Answer: 28 cm
Step-by-step explanation: Area=π·r² and diameter =2r
So if we need to find what our radius is. As shown by d=2r our radius is 1/2 our diameter. If our diameter is 6cm our radius is 3cm.
Now plug 3cm into A= 2πr²⇒ A= 2(3.14)(3²) = 28.26
Now round to the nearest whole number ⇒ 28.
O
Nolan is going to a carnival that has games and rides. Each game costs $2.50 and
each ride costs $3.50. Nolan spent $52.50 altogether on 17 games and rides. Write a
system of equations that could be used to determine the number of games Nolan
played and the number of rides Nolan went on. Define the variables that you use to
write the system.
Answer: g + r = 17
2.5g + 3.5r = 52.5
Step-by-step explanation: Let g be the number of games Nolan played and r be the number of rides Nolan went on. We can write the following system of equations to represent the problem:
g + r = 17
2.5g + 3.5r = 52.5
We can solve this system of equations using elimination, substitution, or graphing.
What value of x makes the equation 1/2(5x+16)-3/2(x-8)=-4 true
Answer:
x=-24
Step-by-step explanation:
you would solve for x
1) multiply the equation out
2) put x on one side by subtracting and adding on each side (make sure to balance it out)
3) divide or multiple by the number on the number on the x
5/2x + 8 - 3/2x + 12 = -4
5/2 x - 3/2 x + 8 + 12 = -4
x + 20 = -4
x = -24
Element x decays radioactively with a half life of 8 minutes. If there are 170 grams of element x, how long, to the nearest tenth of a minute, would it take the element to decay to 5 grams?.
A time of 40.7 minutes is taken for 170 grams of element X to decay to 5 grams.
What is radioactive decay?
The release of energy in the form of ionizing radiation occurs during radioactive decay.
Ionizing radiation can harm DNA in genes and tissues because it can affect the atoms in living things.
We know that decay behaves exponentially and follows this model
[tex]m(t) = m_{0} . e^{t/T} \\[/tex]
The time constant can be described in terms of half-life (t1/2), in minutes, through the following expression
T = t1/2 /In2
If we know that t1/2 = 8 min , m₀ = 170g and m(t) = 5g then the time needed for the decay is:
τ ≈ 11.541 min
t = -τ .In m(t)/m₀
t ≈ 40.698 min
A time of 40.7 minutes is taken for 170 grams of element X to decay to 5 grams.
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[tex]10x+6y=0\\\-7x+2y=31[/tex]solve the system by using substitution or elimination
The value of x= 93/11 and y=-155/11 when the system of equation are 10x+ 6y=0 and 7x+ 2y=31.
Given that,
The system of equation are 10x+ 6y=0 and 7x+ 2y=31.
We must resolve the equation system.
We know that,
Take the system of equations.
10x+ 6y=0 ------>equation(1)
7x+ 2y=31 ------->equation(2)
Multiply 3 to the equation(2) and subtract with equation(1)
3×(7x+ 2y=31)
21x+ 6y=93
10x+ 6y=0
----------------- (subtract)
11x+0=93
11x=93 (divide)
x=93/11
Substitute x=93/11 in equation(1)
10(93/11)+6y=0
930/11+6y=0
6y=-930/11
y=-155/11
Therefore, The value of x= 93/11 and y=-155/11 when the system of equation are 10x+ 6y=0 and 7x+ 2y=31.
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(a) Find the three consecutive natural numbers whose sum is 66.
(b) Find the three consecutive odd natural numbers whose sum is 39.
Answer:
(a) 21, 22, 23
(b) 11, 13, 15
Step-by-step explanation:
Natural numbers are the set of numbers 1, 2, 3... Not numbers that we think of as fractions or decimals or negative numbers.
Let x = the first number
Let x+ 1 = the second number
Let x+ 2 = the third number
x + x+ 1 + x + 2 = 66 Combine like terms
3x + 3 = 66 Subtract 3 from both sides
3x = 63 Divide both sides by 3
x = 21
Check:
21 + 22 + 23 = 66
Let x + the first number
Let x + 2 = the second number
Let x + 4 = the thirds number
x + x + 2 + x + 4 = 39 Combine like terms
3x + 6 = 39 Subtract 6 from both sides
3x = 33 Divide both sides by 3
x = 11
Check: 11 =+ 13 + 15 = 39
A frog in a hemispherical pod (see fig. ) just floats without sinking into sea water with density 1. 35g / c * m ^ 3 if the pod has radius 6 cm and negligible mass, what is the mass of the frog?.
Thus, the mass of the frog is 48.6π grams when it is in a hemispherical pod which just floats without sinking into sea water.
What is meant by buoyancy?The force imposed on a body by a fluid, such as water or air, in which the body is submerged or immersed is known as buoyancy. This force is equivalent to the mass of the fluid that the body has displaced. In mathematics, buoyancy is defined as the sum of the fluid density, gravitational acceleration, and body volume. Archimedes' principle, which asserts that the buoyant force on an item is equal to the weight of the fluid it displaces, is a name for this connection. A key idea in the study of fluid mechanics, buoyancy has many uses, including the construction of boats, planes, and other floating structures.
How to solve?
V = 2/3 * π * r^3,
V = 2/3 * π * 6^3 = 2/3 * π * 216 = 36π.
F = V * d,
F = 36π * 1.35g/c * m^3 = 48.6π g.
F = m + W,
48.6π g = m + 0 g.
m = 48.6π g.
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What is an equation of the line that passes through the point (5, -8) and is
perpendicular to the line 5x - 4y = 16?
The equation of the line which is perpendicular to 5x - 4y = 16 is [tex]y = -\frac{4}{5}x -4[/tex].
What is Coordinate Geometry?The study of geometry using coordinate points is known as coordinate geometry (also known as analytical geometry). Finding the distance between two points, breaking lines into m:n segments, locating a line's midpoint, computing a triangle's area in the Cartesian plane, and other operations are all feasible using coordinate geometry.
Not all crossing lines are parallel ones. If the intersecting lines satisfy the following conditions, they are said to be perpendicular lines. Following are the two primary characteristics of perpendicular lines:
The intersection of perpendicular lines is always at a right angle.Two lines will always be parallel to one another if they are perpendicular to the same line.Let's say that lines AB and CD are parallel to one another. Line AB has a slope of m1, whereas line CD has a slope of m2.
If and only if the product of the slopes of the two lines equals negative of unity, two lines are perpendicular to one another.
As a result, the following is the formula for the perpendicular's slope:
m1.m2 = -1
The equation of the line be "y = mx + c".
Equation of the line Perpendicular to the line is 5x - 4y = 16
Therefore, 4y = 5x - 16
⇒ [tex]y = \frac{5}{4}x -4[/tex]
Slope of the line Perpendicular to the required line is [tex]\frac{5}{4}[/tex].
Slope of the required ine be m .
Therefore, m * [tex]\frac{5}{4} = -1[/tex]
⇒ [tex]m = -\frac{4}{5}[/tex].
Equation of the line is ,
[tex]y = -\frac{4}{5}x + c[/tex]
The line passes through (5,-8)
Therefore,
[tex]-8 = \frac{-4}{5}*5 + c[/tex]
⇒ c = -4
The equation of the line is [tex]y = -\frac{4}{5}x -4[/tex].
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Which of the following relations between input numbers and output numbers is NOT a function?
send a picture so i know what its asking for
if 14 meter of ribbion cost 19$ how much will 21 meters cost
Answer: 21 meters cost $28.5
Step-by-step explanation:
divide 19 by 14 and multiply by 21
21 meters cost $28.5
Show your work, (I am stuck on this because I’m not smart lol)
Answer:
She needs to get at least 96 on the 4th test to earn an average of at least 90 in the class.
Step-by-step explanation:
(97+78+89+?) divided by 4 at\geq 90
It is divided by 4 because it is the average of 4 test scores.
To Solve: (97+78+89+?) divided by 4 at\geq 90
Multiply by 4 on both sides 97+78+89+? at\geq 360
Isolate variable: ? at\geq 96
PLS HELP SUPER EASYY
The measure of the given angle ∠BDC or x is 55°.
What are angles?An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint.
The Latin word "angulus," which means "corner," is the source of the English term "angle."
The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.
The names of fundamental angles include acute, obtuse, right, straight, reflex, and full rotation.
A geometrical shape called an angle is created by connecting two rays at their termini.
In most cases, an angle is expressed in degrees.
So, we know that:
∠ABC = 80°
∠ABD = 25°
∠BDC = x°
Calculate for ∠BDC:
∠ABC - ∠ABD = ∠BDC
80 - 25 = x
x = 55°
Therefore, the measure of the given angle ∠BDC or x is 55°.
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The diameter of a circle is 12 ft. Find its area to the nearest whole number.
Answer:
77.04
Step-by-step explanation:
A=3.14r^2
a=3.14(6)^2
A=3.14(36)
A=77.04
Answer: 113 ft^2
Step-by-step explanation:
Kona work at a bakery. She baked 3308 muffin. She diplayed the muffin on tray that each hold 12 muffin. How many tray did Kona ue to diplay the muffin?
Using mathematical operations, we know that Kona needs a 276 trays to display all her 3308 muffins.
What are mathematical operations?The process of calculating a value using operands and a math operator is known as a mathematical "operation."
The provided operands or integers must follow certain established rules that are associated with the math operator's symbol.
Addition, subtraction, multiplication, division, and modular forms are the five fundamental operations in mathematics.
So, a tray will be needed to display all the cakes:
The total number of muffins is 3308.
Each tray can have 12 muffins.
The total trays needed are:
3308/12
275.66
Rounding off: 276
Therefore, using mathematical operations, we know that Kona needs a 276 tray to display all her 3308 muffins.
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