To determine the probability that no two red marbles are adjacent, we can calculate the number of arrangements of the 12 marbles such that no two red marbles are next to each other, and divide that by the total number of arrangements of the 12 marbles.
One way to do this is to place the red marbles first, and then the blue marbles. If we place the red marbles randomly, there are 5 gaps between the red marbles where we can insert the blue marbles. Thus, there are 5! = 120 ways to arrange the blue marbles.
Next, we need to determine the number of ways to arrange the red marbles. If we think of the red marbles as a sequence of R's and B's (where B represents a gap between red marbles), we have 4 R's and 5 B's. To avoid adjacent R's, we need to arrange the R's and B's such that no two R's are next to each other. One way to do this is to use the concept of combinations.
There are C(9,4) ways to arrange 4 R's and 5 B's in a sequence of 9 elements. This number can be calculated using the formula for combinations: C(n,k) = n! / (k! (n-k)!). In this case, C(9,4) = 126.
Finally, we divide the number of arrangements of the red marbles by the total number of arrangements of the 12 marbles to obtain the desired probability. The total number of arrangements of the 12 marbles is 12!. Thus, the desired probability is:
P = 126 / (120 * 12!) =
126 / (120 * 479001600)
= approximately 0.0000026
So, the probability that no two red marbles are adjacent is approximately 0.0000026.
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At which point would the graphs of the equations below intersect?
(-2,-1)
(2,-1)
(-1,2)
(-1,-2)
The point at which the graphs of the equations would intersect is given as follows:
(-2, -1).
Which is the point that the two functions would intersect?The point at which the two functions would intersect is the solution to the system of equations in this problem.
The equations are given as follows:
3x - 4y = -2.-6x + 5y = 7.Multiplying the first equation by 2, we have that:
6x - 8y = -4.-6x + 5y = 7.Adding the two equations, the solution for y is obtained as follows:
-3y = 3
3y = -3
y = -1.
Hence the solution for x is obtained as follows:
3x - 4(-1) = -2
3x + 4 = -2
3x = -6
x = -2.
Hence the point is:
(-2, -1).
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determine the term and coefficient of each degree
The polynomial f(x) = x⁷ - x⁵ + 5x - 1 has 4 terms and the highest degree is 7
What is term and coefficient of a polynomialA polynomial is a mathematical expression consisting of variables and coefficients, which are combined using only addition, subtraction, and multiplication.
Term: A term in a polynomial is a single expression that can be added or subtracted to the other terms in the polynomial. A term consists of a coefficient multiplied by one or more variables raised to a power. For example, the term "3x^2" in the polynomial 3x^2 + 2x + 1 is a single term.
Coefficient: A coefficient in a polynomial is a numerical value that multiplies a variable or a set of variables in a term. In the example "3x^2", the coefficient is 3. A coefficient can be a constant value, such as 2 in the term 2x, or a variable, such as x in the term x^2. The coefficient in a polynomial determines the magnitude and the sign of each term in the polynomial.
In the polynomial given;
f(x) = x⁷ - x⁵ + 5x - 1
The term in the polynomial is 4 and the degree of the polynomial is 7 while the leading coefficient is 1
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A company plant to market a model of a plant that is 96 feet and 8 inches long with a wing Spand of 56 feet choose a reasonable scale for this model and find the length and wingspan of the model explain why you chose the scale and why did it
The length of the model is 3.33 feet and the wingspan is 1.87 feet, which are reasonable and manageable sizes for a model of this type.
What is scale conversion?
Scale conversion is the process of determining the size of a model based on the size of the original object being modeled.
One way to determine a reasonable scale for the model is to consider the desired size of the model relative to the actual size of the plane. For example, if we want the model to be 1/30th the size of the actual plane, we can use the following formula to find the length and wingspan of the model:
Model length = Actual length ÷ Scale factor
Model wingspan = Actual wingspan ÷ Scale factor
Using these formulas, the length of the model would be:
Model length = 96 feet + 8 inches ÷ 30 = 3 feet 4 inches ÷ 30 = 3.33 feet
And the wingspan of the model would be:
Model wingspan = 56 feet ÷ 30 = 1.87 feet
The reason for choosing a 1/30th scale factor is that it results in a model that is relatively small but still large enough to show the details of the design. It also provides a good balance between size and detail, allowing the model to be easily handled and displayed while still showcasing the key features of the actual plane.
Using this scale, the length of the model is 3.33 feet and the wingspan is 1.87 feet, which are reasonable and manageable sizes for a model of this type.
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At still Bay Middle School, 3 out of 5 teachers have earned their masters degrees. If there are 30 teachers at the school, how many of them have earned their masters degrees?
Based on the given ratio, the number of teachers at Still Bay Middle School, who have earned their master's degrees, is 18.
What is the ratio?The ratio is the relative size of a value compared to another.
Ratios are depicted as percentages, fractions, or decimals, to show that they are fractional values, representing a portion of a whole.
The ratio of teachers who have earned their master's = 3/5
The total number of teachers at the school = 30
The number of teachers with masters = 18 (30 x 3/5)
The number of teachers without masters = 2/5 (1 - 3/5)
= 12 (30 x 2/5)
Thus, since 3 out of 5 teachers at Still Bay Middle School have earned their master's degrees, the number is 18 if there are 30 teachers at the school.
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you have 7 guests and a round table. in how many different ways can you seat your guests around this table? the ways are considered the same if you can turn one into another by rotating the table with your guests. what if only 5 people can sit at your table at a time?
The number of different ways that 7 guests can be seated is 720 and 5 guests can be seated is 24.
Permutation and combinations:In mathematics, Placing the elements of a set into a certain sequence or order is known as permutation. In other terms, the process of permuting is reordering of the elements of a set if the set is already ordered.
In the case of a round table, the formula for the number of ways that 'n' elements can be arranged is (n - 1)!
Here we have
There are 7 guests and a round table.
By the given formula,
No of different ways that 7 guests can be seated = (7 - 1)! = 6!
= 6 × 5 × 4 × 3 × 2 × 1
= 720
If they are only 5 people
No of different ways that 5 guests can be seated = (5 - 1)! = 4!
= 4 × 3 × 2 × 1
= 24
Therefore,
The number of different ways that 7 guests can be seated is 720 and 5 guests can be seated is 24.
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A car owner pays for new brakes that cost $756.25, with a credit card that has an annual rate of 24.5%. Determine the total amount paid, if the car owner pays $100 a month, until the balance is paid off. A spreadsheet was used to calculate the correct answer. Your answer may vary slightly depending on the technology used. $830.52 $73.76 $892.64 $185.28
The total amount paid for a credit card purchase of $756.25 at an annual rate of 24.5% and monthly repayment of $100, until the balance is paid off, is $829.79.
How is the total amount determined?The total amount paid by the car owner can be determined using an online finance calculator, setting the following parameters.
The total amount paid includes the principal and the interest for the credit.
The payment period will last for 8 months and some days.
I/Y (Interest per year) = 24.5%
PV (Present Value) = $756.25
PMT (Periodic Payment) $-100
Results:
N = 8.298
Sum of all periodic payments = $829.79
Total Interest = $73.54
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Which of the point of blow doesn't lie on the curve y = x^2
The point that does not lie on the curve y = x² is given as follows:
A. (3/2, 9/2).
How to obtain the point that does not lie on the curve?The function for this problem is defined as follows:
y = x².
Hence all the points in the graph of the function have the following format:
(x, x²).
Meaning that the y-coordinate is the square of the x-coordinate.
The square of 3/2 is given as follows:
(3/2)² = 3²/2² = 9/4.
Hence when x = 3/2, y = 9/4, and thus option A gives the point that does not lie on the curve.
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Find the distance between X(−3,−2) and Y(−6,5)
The distance between the points (-3, -2) and (-6, 5) is 7.62 units.
How to find the distance between the two points?We know that the distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula:
d = √( (x₁ - x₂)² + (y₂ - y₁)²)
So here, the distance between (-3, -2) and (-6, 5) will be:
d = √( (-3 + 6)² + (-2 - 5)²)
d = √( 58) = 7.62
The distance between the points X(−3,−2) and Y(−6,5) is 7.62 units.
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Use inductive reasoning to predict the next line in the sequence of computations. Then use a calculator or perform the
arithmetic by hand to determine whether your conjecture is correct.
11x9,091 100,001
22x9,091 = 200,002
33x9,091 = 300,003
44 x 9,091 400,004
Answer:
55 x 9091 = 500,005
Step-by-step explanation:
This checks with a calculator
A certain amount of money is shared between Harvey and Mike in the ratio 4:3. If Mike gets £ 75 less than Harvey, find the total amount of money.(will mark brainliest)
Based on their sharing ratio of 4:3, when Mike gets £ 75 less than Harvey, the total amount of money shared is $525.
How is the total amount determined?The total amount being shared between Harvey and Mike is determined using the arithmetic of ratios.
Firstly, we determine the sum of ratios as 7. Since Mike's share is 3/7, which is less by £75 than Harvey's share, which is 4/7, we find the difference as 1/7 and equate it to £75.
Proportionately, if 1/7 equals £75, the total sum being shared will be equal to $525 (£75 x 7/1)
Sharing ratio between Harvey and Mike = 4:3
Sum of ratios = 7
Let the amount Harvey gets = x
x = 4/7
Let the amount Mike gets = x - 75
x - 75 = 3/7
4/7 - 3/7 = 1/7
1/7 = £75
7 = £525 (£75 x 7/1)
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TRUE or FALSE: Squaring a number and taking the square root are opposites (they undo each other).
Answer:
True
Step-by-step explanation:
Take the square of 3, for example. The answer is 9. If you find its square root, the square root is 3, showing it is true.
Answer: True.
Step-by-step explanation: One thing to be careful of though is when solving equations. When you square values and square root them later, you are opening the door for extraneous solutions. But yes, Squaring and square rooting a value will undo the process and result in the original number.
pls help i need help on this question
Express sin
�
L as a fraction in simplest terms.
Answer:
BELOW
Step-by-step explanation:
For RIGHT TRIANGLES sin (L ) = opposite LEG / Hypotenuse
sin (L ) = 21/35 = 3/5
If a stimulus plus a response results in a satisfying outcome, the probability of that response occurring again ________. Question 24 options: is not affected decreases increases depends on the CS-UCS relationship
The answer is option (C) increases. If a stimulus plus a response results in a satisfying outcome, the probability of that response occurring again increases.
This is called the law of effect, which states that behaviors with positive outcomes are more likely to be repeated in the future.
When a response is followed by a satisfactory outcome, the person is more likely to associate that response with a positive outcome and is more likely to repeat that response in future situations.
This law is based on the concept of reinforcement, ie when an environmental stimulus favors the repetition of a behavior. This law was first proposed by psychologist Edward Thorndike in the early 20th century.
Full question:
If a stimulus plus a response results in a satisfying outcome, the probability of that response occurring again ________.
A. decreases.
B. depends on the CS-UCS relationship.
C. increases.
D. is not affected.
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Express cos a in terms of sin a
Answer:
Step-by-step explanation:
We know that
[tex]sin^2a+cos^2a = 1[/tex],
so if we rearrange that and solve for [tex]cosa[/tex] then we get
[tex]cosa[/tex] = ± [tex]\sqrt{1-sin^2a}[/tex]
A 10 kg ball is 50 meter above the ground. How fast will it be moving when it hits the ground?
Answer:
31.3 m/s
Step-by-step explanation:
v² = v₀² + 2aΔx
v² = 0 + 2(9.8 m/s²)(50 m)
v² = 980 m²/s²
v = √ 980 m²/s² = 31.3 m/s
Notes: ball starts from rest, so v₀ = 0; ball is in free fall, so a = g = 9.8 m/s²; objects in free fall accelerate at the same rate, g, independent of mass.
Evaluate the expression for the given value of the variables.
0.7d - 2.1f=
d= 15, f= 3
0.7d - 2.1f = Answer?
Answer:
16.8
Step-by-step explanation:
First, plug in the values given.
(0.7*15) - (2.1*3)
From there, it's simple math. Multiply what is in the parentheses first,
10.5 + 6.3
then add together the sums
16.8.
Draw a polygon with the given conditions in the coordinate plane. One side of the polygon is drawn for you. Do not retrace the given side.
a triangle with an area of 15 units2
A polygon with the given area is given below.
What is Polygons?Polygons are closed figures which has at least three set of line segments joined together.
The polygon with least number of sides is triangle.
We have to draw a triangle of area 15 unit².
Area of the triangle = [tex]\frac{1}{2}[/tex] × Base × Height
[tex]\frac{1}{2}[/tex] × Base × Height = 15
Base × Height = 30
Let base = 6 units, height = 5 units
We can draw a right triangle this way as shown below.
If we are starting from the point A(0, 0), a length of base of 6 units will be a line segment from A(0, 0) to B(6, 0).
If the height is 5 units, draw a line segment from B(6, 0) to C(6, 5).
Join A to C.
Hence the required triangle is shown below.
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(Show the given data related
to religion of Bagmati Rural Municipality in a Pie chart.
Religious. Number
(Hindu). 31,954
(Buddhist) 25,000
(Christian). 14,000
(Muslim). 5,997
(Others). 3,200
The pie chart for this problem is given by the image presented at the end of the answer.
How to construct a pie chart?A pie chart is constructed in pizza format, considering the percentages of each input data in the problem.
A percentage is calculated as the division of the number of desired outcomes by the number of total outcomes, and then multiplied by 100%.
The percentages for the data-set in this problem is given as follows:
Hindu: 39.9%.Buddhist: 31.2%.Christian: 17.5%.Muslim: 7.5%.Others: 4%.More can be learned about pie charts at https://brainly.com/question/26851221
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Camp cool algebra question number 1.
How many children will be in the camp in 3 years?
Answer:8750
Step-by-step explanation:
I did 5000 times .25(1/4 as a decimal) which equals 1250. Then 1250 times 3(year) equals 3750. 5000 plus 3750 is 8750
Find the length of the midsegment of trapezoid ABCD.
pls show yr work
Answer:26
Step-by-step explanation: Base one plus Base 2 divided by 2
A system of linear equations is graphed below.
Which coordinate point represents the solution?
(2, 2)
(0, 40)
(40, 0)
(20, 20)
Answer:
it could be 20 and 20 or 0 and 40
A 12 meter ladder is inclined against a brick wall at an angle of 15°. If the top of the
ladder reaches the top of the wall, how tall is the wall?
The height of the wall is 3.10 meters
How to determine the lengthIt is important to note the six types of trigonometric identities, they are;
sinecosinetangentcotangentsecantcosecantFrom the information given, we have that;
θ = 15 degrees
Hypotenuse= 12 meters
Opposite side = top of the wall
Let's use the sine identity;
sin 15 = x/12
cross multiply
Find the value
0. 2588(12) = x
Multiply the values
x = 3.10 meter
Hence, the value is 3.10 meters
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Dean is helping his mom make a fence for their rectangular vegetable garden. First, they measure the sides and find that it is 20 feet long and 40 feet wide. Then, they buy fencing from the hardware store. If the store sells fencing in 4-yard packages, how many packages do Dean and his mom need?
Answer:
10 packages
Step-by-step explanation:
To find the number of 4 yard packages for the fencing, we need to find the perimeter of the fence.
Perimeter = 2*(20 + 40)
Perimeter = 2*60 = 120 feet
*It is important to note that the perimeter is in feet and the packages are in yards*
4 yards = 12 feet
120 / 12 = 10 packages
what is 4z−(−3z) ???
Answer:
Step-by-step explanation: Ok so, to simplify the expression, you have 2 know that 2 negatives next to each other is positive, so you add 4z + 3z which gives you 7z.
Hayden has $150 to buy clothing for his part-time job.
He buys 2 shirts that cost $33.75 each and a pair of trousers that costs $45.95.
How much money does Hayden have left?
Answer:
$36.55
Step-by-step explanation:
$33.75 x 2 = $67.50
$67.50 (two shirts) + $45.95 (pair of trousers) = $113.45 (the amount of money spent)
Subtract that from the budget of $150...
$150-$113.45= $36.55 left bro
Answer:
$36.55
Step-by-step explanation:
$33.75 x 2 = $67.50
$67.50 + $45.95 = $113.5
$150-$113.45= $36.55
The answer is $36.55
Hope this Helped! Have a GOOD DAY!!!!!
need help with b and c
a. The real annual interest rate is 1.6%
b. He made $14871 after 25 years in account.
What is the interest rate?
The amount of interest due each period expressed as a percentage of the amount lent, deposited, or borrowed is known as an interest rate. The total interest on a loaned or borrowed sum is determined by the principal amount, the interest rate, the frequency of compounding, and the period of time the loan, deposit, or borrowing took place.
Here, we have
Given: A taxpayer who pays 22% in taxes each year has these two accounts. Account 1: $10000 is placed in a tax-deferred account that pays 2.1% interest compounded annually for 25 years. Account 2: $10000 is placed in a taxable account that pays 3.1% interest compounded annually for 25 years.
b. His real annual interest rate is the interest rate decreased by the product of the interest rate and the tax rate.
Actual annual interest rate = 2.1% - (22% × 2.1%)
= 1.6%
Hence, the real annual interest rate is 1.6%
c. P = $10000 , n= 25, r = 1.6%
Compound interest = p(1+(r/100))ⁿ
= 10000(1+(1.6/100))²⁵
= $14871
Hence, he made $14871 after 25 years in account.
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A grocer has two kinds of nuts. One costs $5 kg and the other costs $4.20 kg . How many kg of each type of nut should be mixed in order to get 60 kg of a mixture worth $4.80kg
45 kg of one nut and 45 kg of another nut should be mixed in order to get 60 kg of a mixture worth $4.80kg.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 7 is an equation.
We have,
One nut = x kg
Cost = $5
Other nuts = y kg
Cost = $4.20
Now,
From the given statement we can make two equations.
x + y = 60
x = 60 - y
Substituting here,
5x + 4.20y = 4.80
5 (60 - y) + 4.20y = 4.80 x 60
300 - 5y + 4.20y = 288
300 - 288 = 5y - 4.20y
12 = 0.8y
y = 12/0.8
y = 15
Now,
x = 60 - 15
x = 45
Thus,
45 kg of one nut and 45 kg of another nut.
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£200 is invested for 10 years at 9 compound interest per annum
After 10 years, the investment of £200 at 9% compound interest per annum would be worth approximately £432.97.
The amount of money that would be obtained after 10 years can be calculated using the formula for compound interest:
A = P * (1 + r/n)^(nt)
Where:
A = final amount
P = initial principal (£200)
r = interest rate (9%)
n = number of times compounded per year
t = number of years invested (10)
For an interest rate compounded annually, n = 1. Plugging in the values into the formula, we have:
A = £200 * (1 + 0.09/1)^(1 * 10)
A = £200 * (1.09)^10
A = £200 * 2.1669
A = £433.38
Therefore, £433.38 would be obtained after 10 years of investing £200 at 9% compound interest per annum.
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13. Find m/VWZ. (5r – 12)° V Y Z (2x - 3)° W X
From the given figure, conclude that ∠VWZ = 27°. This can be solved by using SAS theorem.
What is SAS theorem?The triangles are congruent if two sides and the included angle of one triangle are equivalent to two sides and the included angle of another triangle. Congruent refers to figures that are similar in all respects, primarily in terms of size and shape. Congruence describes how two congruent figures relate to one another.
From the given picture, it is clear that WXYV is a rectangle.
∠VYX = 90°
As we know, ∠YVX + ∠VYX + ∠VXY = 180°
or, 5x - 12° + 90° + 2x - 3° = 180°
or, 7x = 180° - 90° + 15°
or, 7x = 105°
or, x = 15°
thus, ∠VXY = 2x - 3° = 27°
next comparing ΔVYX and ΔYVW we get:
VY = VY
WV = XY
So, ∠VYX = ∠XVW = 90°
From SAS theorem,
ΔVYX ≅ ΔYVW
∠VWX = ∠VXY = 27°
Thus, ∠VWX = 27°
and ∠VWX and ∠VWZ is same.
Therefore, ∠VWZ = 27°
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In a demonstration of the photoelectric effect, suppose that a minimum energy of 4.0×10−19 J (2.5 eV ) is required to dislodge an electron from a metal surface. What is the minimum frequency (and longest wavelength) of radiation for which the detector registers a response?
The minimum frequency of radiation is 0.603 × 10¹⁵ and the longest wavelength is 4.97 × 10⁻⁷.
What is Planck's Equation?Planck's equation is an equation which describes about the amount of spectral radiance radiated by a black body at a certain wavelength in thermal equilibrium.
We have the Planck's Equation,
E = hv,
where E is the energy, h is the Planck's constant = 6.63 x 10⁻³⁴ J and v is the frequency of radiation.
We have in the question E = 4.0×10⁻¹⁹ J
Substituting,
4.0×10⁻¹⁹ = (6.63 x 10⁻³⁴) v
v = (4.0×10⁻¹⁹) / (6.63 x 10⁻³⁴)
= 0.603 × 10¹⁵
Also we have the equation to find the wavelength,
v = c / λ, where c is the speed of the light = 3 × 10⁸ and λ is the wavelength.
λ = c / v = (3 × 10⁸) / (0.603 × 10¹⁵)
= 4.97 × 10⁻⁷
Hence the minimum frequency and the longest wavelength of radiation for which the detector registers a response are 0.603 × 10¹⁵ and 4.97 × 10⁻⁷ respectively.
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