The number of ways such that three penguins and six puffins stand in line so that all the puffins stand together is 17,280.
We are given two animals. The number of penguins is 3. The number of puffins is 6. We need to find out the number of ways that three penguins and six puffins can stand in line so that all the puffins can stand together.
We will use the concepts of permutations and combinations. We will make a bundle of all the puffins as a single entity.
The number of ways to arrange 6 puffins among themselves is 6! = 720. The number of ways to arrange 3 penguins and a bundle of puffins is (3 + 1)! = 4! = 24.
The total number of ways to form the line is the product of the above-mentioned calculation.
N = 720*24
N = 17,280
Hence, the number of ways such that three penguins and six puffins stand in line so that all the puffins stand together is 17,280.
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What is the solution of the simultaneous equations 3x 2y 14 and 4x 3y 13?.
The solution of simultaneous equations is x=4 and y = -1.
What are Simultaneous equations?
Simultaneous equations are two or more algebraic equations with the same unknown variables and the same value of the variables satisfies all such equations.
We can solve simultaneous equations by various methods. here we will solve it by elimination method.
Here we have two simultaneous equations
3x -2y = 14 --- (i)
and 4x + 3y = 13---(ii)
Now multiplying (i) by 3 and (ii) by 2 we get
9x -6y = 42 and 8x + 6y = 26.
Now adding both we get
17x = 68 ⇒ x = 68/17 ⇒ x = 4.
Substituting the value of x in (i), we get
3*4 - 2y = 14 ⇒ -2y = 14-12 = 2 = -2/2 ⇒ y = -1.
Therefore, the values of x and y are 4 and -1 respectively .
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NOTE : The question given here is not complete. The complete question is given below.
Question: What is the solution of the simultaneous equations 3x- 2y= 14 and 4x+ 3y= 13?.
The average age of a class of 25 students is 10 years and the average age of another class of 30 students is 15 years. Find the average age of students of the two classes.
The average age of the two classes is 12.73 yrs.
How do we calculate average?Average This is the arithmetic mean, which is computed by adding a set of integers and then dividing by the number of numbers in the set.The average is just the sum of all the numbers divided by the total number of values. The mathematical average of a group of two or more data values is defined as a mean. Average is also known as mean or arithmetic mean. Mean is merely a way of describing the sample's average.Total age of 25 students =25×10=250years.
Total age of 30 students =30×15=450years
∴ Total age of 55 students =250+450=700years
∴ Required For 55 students = 700/55 = 12.73 yerars
∴ The average age of the two classes is 12.73 yrs.
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There are a total of 58 schools and 23,581 students attend those schools. Sarah only works in 23 of those schools, how many students has Sarah worked with?
If Sarah only works in 23 of those schools then Sarah worked with 9,351 students.
Given, There are a total of 58 schools and 23,581 students attend those schools. Sarah only works in 23 of those schools
now, as 58 schools = 23581 students
1 school = 23581/58 students
now,
23 schools = 23× 23581/58 students
23 schools = 9,351 students
So, Sarah worked with 9,351 students.
Hence, Sarah worked with 9,351 students.
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Can you guys help me with my work, please?
The image point of (-9, -5) after applying this translation rule (T₋₅, ₀) and dilation (D₂) is (-28, -10).
What is a translation?In Mathematics, the translation of a geometric figure to the left simply means subtracting a digit from the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is translated up simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image or parent function.
Mathematically, a horizontal translation to the left is modeled by this mathematical expression g(x) = f(x + N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical expression g(x) = f(x) + N.
Where:
N represents an integer.g(x) and f(x) represent a function.By applying the transformation rule T₋₅, ₀ to the pre-image point (-9, -5), we have:
(x, y) → (x − 5, y + 0)
(-9, -5) → (-9 − 5, -5 + 0) = (-14, -5)
Next, we would apply a dilation (D₂) by using a scale factor of 2:
(x, y) → (kx, ky) = (2x, 2y)
(-14, -5) → (2(-14), 2(-5)) = (-28, -10).
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i need help pleaseee!!!
Answer: x = 57
Step-by-step explanation:
Since CD = AC, triangle ACD is isosceles, therefore
ADC = DAC
ADC + DAC + 112 = 180
ADC + DAC = 180 -112 = 68
ADC + DAC = 68/2 = 34
DEB = 180 - 34 - 23 = 123 (sum of interior angles of a triangle = 180)
Therefore, x = 180 - 123 = 57 (DEB and x are supplementary angles)
(1 point) find the minimum sample size needed to be 99% confident that the sample variance is within 50% of the population variance.
The minimum sample size need for the given condition is 14
What is Confidence Level in Statistics?
The proportion of likelihood, or certainty, that the confidence interval will include the real population parameter when a random sample is drawn numerous times is referred to as the confidence level.
Solution:
The minimum sample sixe required when,
Confidence Level = 99%
Variance = 50%
Generally going through the table
Minimum sample size is
X = 14
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how do i put SIF into standard form?
y=5/4x+3/4
The standard form of the given equation is 5x - 4y = -3.
What is a standard form of an equation?
The standard form for linear equations in two variables is Ax+By=C.
What is a slope intercept form?
The slope-intercept form is the way to write a line's equation so that the y-intercept (where the line crosses the vertical y-axis) and slope (steepness) are instantly visible. This form is frequently known as the y = mx + b form.
Here, we have
y = 5/4x+3/4
we have to convert this equation into standard form
y - 5/4x = 3/4
y - 5/4x - 3/4 = 0
4y - 5x - 3 = 0
4y - 5x = 3
5x - 4y = -3
Hence, the standard form of the given equation is 5x - 4y = -3.
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What number should fill in the blank? 36 x 8 =_________+6)x 8
The number to be filled in the blank is 30
How to calculate the missing number?Let us consider the number in the blank = x
Rewriting it as a linear equation,
36 * 8 =( x + 6 )8
288 = ( x + 6) 8
288 /8 = x + 6
36 = x + 6
x = 36- 6
x = 30
The number to be filled in the blank is 30
What is a linear equation?A linear equation is one that has a degree of 1 as its maximum value. Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. Both linear equations with one variable and those with two variables exist. Ax+ B = 0, where A and B are both real integers, and x is the only variable, is the standard form or general form of a linear equation in one variable. A vertical line that is parallel to the y-axis is formed on the graph of a linear equation with one variable, x, and vice versa.To learn more about linear equation, refer:
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which expression represents the product if 3 and 7
Answer:
3X7
Step-by-step explanation:
product means to multiply
In the given relation, what domain value corresponds to the range value 4?
{(-1,2), (-2,4), (2,5), (0,-2), (2,0)}
a. 0
b. 2
c. -2
d. 4
Lora' phone record data for creen time each week. Lat week, he ued 840 minute. Thi week, Lora ued 504 creen time minute on the phone. Calculate the percent decreae in creen time thi week. 17%
34%
40%
67%
The percent of decrease in screen time this week is 40%. correct option is (C).
given that
lora's screen time last week is 840 minutes
lora's screen time this week is 504 minutes
let's calculate the percentage decrease
decrease = 504-840
decrease = -336
percentage decrease = (-336/840) * 100
= -0.4*100
=-40
percentage of decrease is 40%
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The question was incomplete. Check below the complete question.
Lora' phone record data for creen time each week. Lat week, he ued 840 minute. Thi week, Lora ued 504 creen time minute on the phone. Calculate the percent decreae in creen time thi week.
a. 17%
b. 34%
c. 40%
d. 67%
-5
Graph y=-3x + 5
10
5
Check it
10
Answer:
See the attached graph.
Step-by-step explanation:
Pick any two values of x that are on the x axis and compute the values of y using the equation. I'll pick x values of -1 and 2 for illustration.
x=-3x + 5
X Y
-1 2
2 -1
Plot those poins and then connect them with a ruler to form the line for y = -3x + 5
Se the attached graph.
Senja earns $46,200 a year. Her exemptions total $2,900. This year she can deduct $5,000 for business expenses. She also has $2,500 in deductions for medical expenses. What is Senja's taxable income?
The amount that would be Senja's taxable income would be = $38,700
What is taxable income?This is the total income of an individual after the removal of discounts and exemptions from which such is expected to pay a certain percentage of tax.
The amount she earns a year = $46,200
Lat years total deductions = $2,900.
Deductions for business expenses = $5,000
Deductions for medical expenses = $2,500.
The total deductions for this year = $7,500
Therefore, the amount this year that is taxable income for Senja = $46,200 - $7,500 = $38,700
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You help me and my mom we need you more
Answer:
Please give a question to answer. Nothing has been included to answer.
Step-by-step explanation:
if points x,y, and z are collinear, and the slope between ponys y and z is -4. What is the slope between points x and y
Answer:
-4
Step-by-step explanation:
If the points are collinear, then all the points are on the same line. Any two points will have the same slope.
x and y, x and z, y and z, all have the same slope, -4.
Multiply 6.75 x 10 to the 6th power and 1.2 × 10 to the 6th power
Value for multiplication of 6.75 x 10⁶ and 1.2 × 10⁶ : 8.1 x 10¹²
What is Multiplication?
The process of finding the sum of two or more numbers is known as multiplication. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of the same size, we employ multiplication.
The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
We have the given values to multiply:
6.75 x 10⁶ and 1.2 × 10⁶
Now,
= 6.75 x 10⁶ x 1.2 × 10⁶
= (6.75 x 1.2) x (10⁶ x 10⁶)
= (8.1) x 10⁽⁶⁺⁶⁾
= 8.1 x 10¹²
Hence, the value of multiplication of 6.75 x 10⁶ and 1.2 × 10⁶ is 8.1 x 10¹²
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A regular polygon has 16 sides. If one of its angles measures (5h − 29)°, what is the value of h?
h = 56.5
h = 37.3
h = 33.6
h = 9
Answer:
(b) h = 37.3
Step-by-step explanation:
You want the value of h if an angle of a regular 16-gon is given as (5h-29)°.
AngleThe interior angle measure of a regular n-gon is given by ...
θ = 180° -360°/n
For n=16, the interior angle measure is ...
θ = 180° -360°/16 = 157.5°
Value of hThe value of h can be found by solving the equation ...
5h -29 = 157.5
5h = 186.5 . . . . . . add 29
h = 37.3 . . . . . . . divide by 5
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Students at a sports college choose activities for games.
In Year 7 they chose between rounders and athletics in the ratio 1 : 4.
There are 60 students in Year 7.
Work out how many chose athletics.
Answer: 48 students
Step-by-step explanation: 1+4=5
60÷5=12
12x4=48
PLEASE HELPP!!!! Bob has $12.75 and plans to purchase snow cones for his friends at $1.25 each. If he needs to save at least $8.75 to pay for lunch, how many snow cones can he buy. Use the inequality below to help answer.
Answer:
Bob can buy no more than 3 snow cones.
Step-by-step explanation:
[tex]12.75 - 1.25c \geqslant 8.75[/tex]
[tex] - 1.25c \geqslant - 4[/tex]
[tex]1.25c \leqslant 4[/tex]
[tex]c \leqslant 3.2[/tex]
So Bob can buy up to 3 snow cones.
liter balloon that already contained 2.51 moles of argon. What
Sally adds 3.13 moles of argon to a 5.29
is the volume of the balloon after the addition of the extra gas?
The volume of the balloon after the addition of the extra gas is 11.87 liters
The initial volume of the balloon = 5.29 liters
Initial quantity of argon in the balloon = 2.51 mole
Here we have to use the unitary method
The volume of the 1 mole of argon = The initial weight of the balloon / Initial quantity of argon in the balloon
Substitute the values in the equation
The volume of the 1 mole of argon = 5.29 / 2.51
= 2.11 liters
Additional argon added = 2.51 mole
Total quantity of argon = 2.51 + 3.13
= 5.64 mole
The volume of the 5.64 mole of argon = 5.64 × 2.11
= 11.87 liters
Hence, the volume of the balloon after the addition of the extra gas is 11.87 liters
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Guadalupe is scuba diving four minutes ago he was at -3 feet now is at -15 feet what is the difference between in the two depths
The difference between the depth at 3 minute ago and the depth now is 12 feet.
What is difference in mathematics?
Difference in mathematics is produced by one of the most important mathematical operations, which is obtained by deleting two numbers. It displays the difference between two numbers. The objective of finding the difference in math is to ascertain how many numbers there are between the two specified numbers. In terms of notation, there is a negative difference (-).
The depth 3 minute ago was -3 feet,
The depth now is -15 feet.
subtracting the depth now from the depth 3 minute ago,
-3 -(-15)
= 12 feet
Therefore, the difference is 12 feet.
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u - 9.7 < -8.8 Solve the inequality for u.
Simplify your answer as much as possible.
The value of the inequality u - 9.7 < -8.8 is u < 0.9.
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
Here, the inequality is given as:
u - 9.7 < -8.8
Collect like terms
u < -8.8 + 9.7
u < 0.9
The value is u < 0.9.
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The total amount owed by Erica after 5 years is $10865
How to determine the total amount in five years?From the question, we have the following parameters:
Amount borrowed, P = $5300Interest rate on the loan, R = 8%Duration to repay the loan, t = 6 yearsNumber of times the loan is compounded in a year, n = 12, i.e. compounded monthlyAlso from the question, the formula to determine the compound interest formula to be represented as:
A = P(1 + r/n)^nt
Where the values of the variables have been stated above
Solving further, we replace the variables with their values in the above equation
So, we have the following representation
A = 5300 * (1 + (8%/12))^(6*12)
Evaluate the expression
A = 10865
Hence, the value of the amount after 6 years is $10865
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What scale factor was used to enlarge uvw to klm
The scale factor that was used to enlarge the triangle uvw to klm is 4/3
How to determine the scale factor that was used to enlarge the triangles?The triangles that complete the question are added as an attachment
From the attached triangles, we have the following side lengths:
Triangle UVW
UV = 9 units
VW = 15 units
Also, we have
Triangle KLM
KL = 12 units
LM = 20 units
Because the triangle was enlarged from triangle UWV, it is expected that the side length of KLM will be greater than the corresponding side length of UVW
The scale factor of dilation is then calculated using the following scale factor formula
Scale factor = Side length of KLM divided by Side length of UWV
Mathematically, we have
Scale factor = KLM/UVW
Substitute the known values in the above equation, so, we have the following representation
Scale factor =20/15
Evaluate the quotient
Scale factor = 4/3
Hence, the scale factor is 4/3
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3-1/6-(-1 3/10) please help
Answer:
3-1/2 - (-1 3/10)
Convert the number
3- 1/6 - (-13/10)
Determine the sign
3- 1/6 + 13/10
Transform the expression
90-5+39
_______
30
Calculate
124/30
Simplify
62/15
Answer
62/15
Y=x+3\x-2
Deg. Of numerator___
Deg. of denominator___
Optional?
Horizontal Asymptote ____
Vertical asymptote ____
The solution to the questions are
The degree of the numerator is 1The degree of the denominator is 1The horizontal asymptote is y = 1The vertical asymptote is x = 2The degree of the numeratorThe function is given as
y = (x + 3)/(x - 2)
The numerator of the function is
x + 3
The above expression is a linear expression
So, the degree is 1
The degree of the denominatorThe function is given as
y = (x + 3)/(x - 2)
The denominator of the function is
x - 2
The above expression is a linear expression
So, the degree is 1
The vertical asymptoteThe function is given as
y = (x + 3)/(x - 2)
Set the numerator to 0
x +3 = 0
Evaluate
x = -3
The horizontal asymptoteThe degree of the numerator is 1
So, the horizontal asymptote is y = 1
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Jay has a 50 gallon water tank. He fills the tank with a garden hose at a rate of 8. 2 gallons per minute. There are 9 gallons of water in the tank
What is the maximum amount of time Jay can add water without causing the tank to overflow?
The maximum amount of time Jay can add water without causing the tank to overflow is 5 minutes.
Given:
Jay has a 50 gallon water tank. He fills the tank with a garden hose at a rate of 8. 2 gallons per minute.
There are 9 gallons of water in the tank.
water tank to fill = water tank capacity - water in the tank.
= 50 - 9
= 41 gallons.
Time = 41 / 8.2
= 41 / 82/10
= 41*10 / 82
= 10/2
= 5 minutes.
Therefore the maximum amount of time Jay can add water without causing the tank to overflow is 5 minutes.
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ANSWER FOR BRAINLIST DUE TODAY!
Answer:
a. Draw two lines which intersect each other somewhere on the graph.
b. Draw two parallel lines.
What is -3 1/3 ÷ 9? It would be nice to have the answer. Like really nice. I never even done this before.
Answer:
-0.37 or -37/100
Step-by-step explanation:
On a calculator, take the fraction, and divide the 1 by the 3:
1 divided by 3 = 0.33.
So, we have -3.33 divided by 9.
Let's use the calculator to find the final answer:
-0.37
To convert this to a fraction, we have to convert -0.37 to -37 and find the common 10. So, 1 is less than 37 in this term. Same with 10. But, 100 will work:
37/100
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 12 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Answer:
-10/27
Step-by-step explanation:
so to divide fractions first we turn them into improper fractioms
-3 1/3 ÷9
-10/3÷9/1
now we use skip flip mutliply to find the answer where we keep the first term the same then flip the second fraction and then mutliply
-10/3÷9/1
-10/3 × 1/9
-10/27
hopes this helps please mark brainliest
For the following right triangle, find the side length x. Round your answer to the nearest hundredth.
20
12
X
The side length [tex]x = \sqrt{444}[/tex] => x = 21
What are the properties of right triangle?The right angle, or 90°, is always one angle.
The hypotenuse is the side that will be 90° away from the other angle.
The longest side is always the hypotenuse.
The other two inside angles will add up to 90 degrees.
Also known as base and perpendicular are the other two sides that are close to the right angle.
The first two sides of the triangle are :
1st angle = 20°
2nd angle = 12°
Thus by using the Pythagoras theorem ;
20² + 12² = x²
400 + 144 = x²
this implies , 444 = x²
Taking square roots on both sides we get
[tex]x = \sqrt{444}[/tex]
x = 21
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