All of the rectangles together measure 1250 meters in length.
A textile square with a 25 square meter surface area. We are aware that the area of a square is determined by multiplying one side's length by itself. The square root of 25 square meters, or 5 meters, is the length of one side of the square in this instance.
Secondly, we are aware that the fabric is being cut into 50 cm-wide rectangles. We can use the following formula to determine each rectangle's length:
(Rectangle width) x (Square cloth length) / (Width of square cloth)
The equation in this instance is (50 cm) x (25 m) / (5 m) = 2500 cm or 25 meters.
Therefore, each rectangle is 25 meters long.
We divide the square cloth's length by each rectangle's width to get the total number of rectangles.
25m / 0.5m (50cm) = 50 rectangles.
Finally, we multiply the quantity of rectangles by the average length of each rectangle to determine the total length of all the rectangles:
50 m x 25 m = 1250 m
Therefore, a square piece of fabric that is 25 square meters in size and has been divided into 50 rectangles, each measuring 50 cm wide and 25 meters long.
Therefore the rectangles together measure 1250 meters in length.
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Dean is playing a game with calculators. the 42 participants (including dean) sit in a circle, and dean holds 3 calculators. one calculator reads 1, another 0, and the last one -1. dean starts by pressing the cube button on the calculator that shows 1, pressing the square button on the one that shows 0, and on the calculator that shows -1, he presses the negation button. after this, he passes all of the calculators to the next person in the circle. each person presses the same buttons on the same calculators that dean pressed and then passes them to the next person. once the calculators have all gone around the circle and return to dean so that everyone has had one turn, dean adds up the numbers showing on the calculators. what is the sum he ends up with?
After completing the full turn around the circle by 42 participants as per given condition and number showing on the calculator the sum ends up with 0.
As given in the question,
Total number of participants = 42
Number of calculator = 3
Calculator that reads 1 dean pressed cube button
1³ = 1
Calculator that reads 0 dean pressed square button
0² = 0
Calculator that reads -1 dean pressed negation button
-(-1) = 1
Same activity repeated 42 times in the circle at the end number showed on the calculator are
Calculator reads 1 show 1
Calculator reads 0 show 0
Calculator reads -1 show -1
Sum of the three numbers are
= 1 + 0 + (-1)
= 0
Therefore, sum of the three numbers showing at the end on the calculator is equal to 0.
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Select all the correct answers.
Which three pairs of side lengths are possible measurements for the triangle?
45
B
45
с
AB= 6, AC=6√/2
BC=7√2, AC = 14
AB= 11, AC = 22
BC=8, AC = 8√3
AB= 15, BC = 15
AB= 16, AC=16
Submit
Answer:
AB = 6, BC = 6
AB = 4, AC = 4√2
BC = 2√2, AC = 4
(if im not wrong)
when serenity goes bowling, her scores are normally distributed with a mean of 195 and a standard deviation of 14. what is the probability that the next game serenity bowls, her score will be between 183 and 218, to the nearest thousandth?
The probability that in the next game of serenity bowls, her score will be between 183 and 218 is 73.14%
Given that,
Mean = 195
Standard deviation = 14
Thus, the probability between 183 and 218 is the ρ value of z when x = 195
Subtracting by the ρ value of z when x = 183
so, x = 218
z = 218-195/14 = 1.64
when x = 183
z = 183-195/14= -0.85
Thus, z value is 1.64 then the probability is 0.94950 and when z value is -0.85 then the probability is 0.21886
Now, 0.94950 - 0.21886 = 0.73064
Therefore, The probability that in the next game of serenity bowls, her score will be between 183 and 218 is 73.14%
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a password is to be 4 to 6 characters long. the first character must be a digit but not 0. the rest of the characters can be any letter or digit. how many such passwords are possible?
On solving the provided question we can say that on permutation choose which two of the six positions contain the two digits = 685464000
what is permutation?The permutation of a set in mathematics is essentially the rearranging of its elements if the set is already ordered, or the arrangement of its members in a linear or sequential order. The act of altering the linear order of an ordered set is referred to as a "permutation" in this context. The mathematical calculation of the number of possible arrangements for a given set is known as permutation. Permutation, in its simplest form, refers to the variety of possible arrangements or orders. The placement of the elements matters with permutations. The placement of items in a specific order is known as a permutation. Here, the set's components are sorted in either chronological order or linear order.
Assuming we regard upper and lower case letters as different, there are 52^4 ways = 7311616 ways
sequences of four letters and 100 sequences of two digits
there are 15 ways choose which two of the six positions contain the two digits = 685464000
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Answer the screenshot
The polynomial of degree 3 with the given zeros and a leading coefficient of 1 is:
P(x) = x^3 - 5x^2 - 14x
How to find the polynomial?Remember to do one post per question, I will answer the first one.
We know that for a polynomial of degree N with the given N zeros:
{x₁, x₂, ..., xₙ}
We can write the polynomial as:
P(x) = a*(x - x₁)*(x - x₂)*...*(x - xₙ)
Where the leading coefficient is a.
Here the degree of the polynomial is 3, and the 3 zeros are:
-2, 0, 7
And the leading coefficient is 1.
Then we can write it as:
P(x) = 1*(x + 2)*(x - 0)*(x - 7)
P(x) = (x^2 + 2x)*(x - 7)
P(x) = x^3 + 2x^2 - 7x^2 - 14x
P(x) = x^3 - 5x^2 - 14x
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Find the solutions of the given equation.
25x² +64 = 289
O A. x =
-√√3, √3
OB.
x =
-9,9
OC.
x = -3, 3
O D. x = -3√3, 3√/3
The solution of the given equation is x = -3,3. Hence option C is the correct option.
What is a quadratic equation?
A quadratic equation is any equation in algebra that can be rearranged in a standard form where x represents an unknown value and a, b, and c represent known numbers, with a ≠ 0.
The number of solutions of a quadratic equation is 2. The degree of a quadratic equation is also 2.
Given equation is
25x² +64 = 289
Subtract 64 from both sides of the equation:
25x² +64 -64 = 289 -64
25x² = 225
Divide both sides by 25:
25x²/25 = 225/25
x² = 9
Take square root on both sides:
√x² = √9
x = ±3.
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10001000 students took a test and the scores are normally distributed, with a mean of 7676 and standard deviation of 55. approximately how many students scored between 8181 and 8686?
The number of students who scored between 8181 and 8686 can be calculated using the z-score formula to find standard deviation.
How is this calculated?z1 = (8181-7676)/55 = 1.89
z2 = (8686-7676)/55 = 3.04
Using a standard normal table, the area under the curve between these two z-scores is approximately 8.5%. So, we can estimate that about 850,085 students scored between 8181 and 8686. We find the z-score of 8181 and 8686 and calculate the area under the standard normal distribution curve between these z-scores.
What is the difference between a standard normal distribution and a non-standard normal distribution?A standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1, while a non-standard normal distribution has a different mean and/or standard deviation. The z-score formula is used to convert a non-standard normal distribution to a standard normal distribution, so that the properties of the standard normal distribution can be applied, such as using a standard normal table to find areas under the curve.
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x³ = x² + 20x how do you solve this by factoring?
Answer:
Factors of x are 0, 5, and -4.
Step-by-step explanation:
⇒ x³ = x² + 20x
⇒ x³ - x² - 20x = 0
⇒ x (x² - x - 20) = 0
⇒ x ( x² - 5x + 4x - 20) = 0
⇒ x ( x ( x - 5) + 4 ( x - 5)) = 0
⇒ x (x - 5) (x + 4) =0
⇒ x = 0, 5, and -4
Answer: x = 5
x = -4
x = 0
Step-by-step explanation:The first term is, x2 its coefficient is 1 .
The middle term is, -x its coefficient is -1 .
The last term, "the constant", is -20
Step-1 : Multiply the coefficient of the first term by the constant 1 • -20 = -20
Step-2 : Find two factors of -20 whose sum equals the coefficient of the middle term, which is -1 .
-20 + 1 = -19
-10 + 2 = -8
-5 + 4 = -1 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and 4
x2 - 5x + 4x - 20
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-5)
Add up the last 2 terms, pulling out common factors :
4 • (x-5)
Step-5 : Add up the four terms of step 4 :
(x+4) • (x-5)
Which is the desired factorization A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well. Solving x2-x-20 = 0 by Completing The Square .
Add 20 to both side of the equation :
x2-x = 20
Now the clever bit: Take the coefficient of x , which is 1 , divide by two, giving 1/2 , and finally square it giving 1/4
Add 1/4 to both sides of the equation :
On the right hand side we have :
20 + 1/4 or, (20/1)+(1/4)
The common denominator of the two fractions is 4 Adding (80/4)+(1/4) gives 81/4
So adding to both sides we finally get :
x2-x+(1/4) = 81/4
Adding 1/4 has completed the left hand side into a perfect square :
x2-x+(1/4) =
(x-(1/2)) • (x-(1/2)) =
(x-(1/2))2
Things which are equal to the same thing are also equal to one another. Since
x2-x+(1/4) = 81/4 and
x2-x+(1/4) = (x-(1/2))2
then, according to the law of transitivity,
(x-(1/2))2 = 81/4
We'll refer to this Equation as Eq. #4.2.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
(x-(1/2))2 is
(x-(1/2))2/2 =
(x-(1/2))1 =
x-(1/2)
Now, applying the Square Root Principle to Eq. #4.2.1 we get:
x-(1/2) = √ 81/4
Add 1/2 to both sides to obtain:
x = 1/2 + √ 81/4
Since a square root has two values, one positive and the other negative
x2 - x - 20 = 0
has two solutions:
x = 1/2 + √ 81/4
or
x = 1/2 - √ 81/4
Note that √ 81/4 can be written as
√ 81 / √ 4 which is 9 / 2
A grocery store sells a bag of 6 oranges for $5.22. What is the cost of oranges, in dollars per orange?
Let f(x) = x³ + 2x² + 7x - 11 and g(x) = 3f(x). Which of the following describes g as a
function of f and gives the correct rule?
A.) horizontal compression; g(x) = 3x³ + 6x² + 21x - 33
B.)horizontal stretch; g(x) = 27x3 + 18x² +21x - 11
C.)vertical stretch; g(x) = 3x3 + 6x² +21x - 33
D.)vertical compression; g(x) = 27x³ + 18x² + 21x - 11
Therefore , the solution of the given problem of function comes out to be the function f(x) = x³ + 2x² + 7x - 11 = -1 and g(x) = 3f(x) = -3
what is function?The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope.
Here,
Given:
we have been provided with -
f(x) = x³ + 2x² + 7x - 11
so, x = 1
f(x) = 1 +2 +7 -11= -1
g(x) = 3f(x) = -3
Therefore , the solution of the given problem of function comes out to be the function f(x) = x³ + 2x² + 7x - 11 = -1 and g(x) = 3f(x) = -3
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what is the probability that the request is received by this server within the first 5 minutes (300 seconds) after the hour?
The probability that the request is received by the server within the first 5 minutes (300 seconds) after the hour would depend on the rate at which requests are made to the server, as well as any other factors that may affect the timing of requests.
In order to find this probability, you would need additional information such as the average rate of requests per second or minute, and the distribution of request timing.
If the requests are Poisson distributed with a mean rate of λ requests per second, the probability that a request is received within the first 5 minutes (300 seconds) after the hour is
P(X<=300) = 1- e^(-300λ)
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A rectangular swimming Pool is twice as long as it is wide. A small concrete walkway surrounds the pool. The walkway is a constant 2 feet wide and has an area of 196 square feet. Find the dimensions of the pool.
Answer:
Let x be the width of the pool. Then the length of the pool is 2x, since it is twice as long as it is wide.
The area of the pool is (2x)(x)=2x^2
The total area of the pool and the walkway is 2x^2+196 square feet.
We can set up the equation using this information:
2x^2 + 22x = 196
Where 22x is the area of the walkway, 22x = 2x * 2 = 4x
2x^2 + 4x = 196
2x^2 + 4x - 196 = 0
Using the quadratic formula to solve the equation above:
x = (-b ± √(b^2 - 4ac))/2a
x = (-4 ± √(4^2 - 42196))/2*2
x = (-4 ± √(16 - 1568))/4
x = (-4 ± √(-1552))/4
Since x is width of the pool, it cannot be a negative value, the x value that is negative must be rejected. Therefore x = (-4 + √1552)/4 = 8
The width of the pool is 8 feet and the length is 2x = 2*8 = 16 feet
For every 4 girls in Mr Hegarty's class there are 5 boys. What is the ratio of boys to girls in the class?
Give your answer in its simplest form.
Answer:
5:4
Step-by-step explanation:
girls = 4
boys = 5
ratio = boys:girls = 5:4
HOPE THIS HELPED
Ben is x cm tall.
Kieran is 8 cm taller than Ben.
Bianca is 2 cm shorter than Ben.
Write an expression, in terms of x, for the mean of their heights in centímetres.
Give your answer in its simplest form.
hope this helps you understand !!
Answer:
x + 2
Step-by-step explanation:
Ben : x cm
Kieran: (x + 8) cm
Bianca: (x - 2) cm
Mean of their heights = [tex]\frac{Sum of their heights}{Number of people} = \frac{x + (x + 8) + (x - 2)}{3}[/tex]
= [tex]\frac{x + x + 8 + x - 2}{3}[/tex] (Expand the brackets)
= [tex]\frac{x + x + x + 8 - 2}{3}[/tex] (Bring all the like terms together)
= [tex]\frac{3x + 6}{3}[/tex] (Simplify the two sets of like terms)
= [tex]\frac{3(x + 2)}{3}[/tex] (Extract the common factor '3' in the numerator)
= (x + 2) cm ([tex]\frac{3}{3} = 1[/tex])
Graph x = -4 on the graph below. What is the domain of x = -4? What is the range of x = -4?
Answer:The graph of x = -4 is a vertical line located 4 units to the left of the y-axis.
The domain of x = -4 is the set of all real numbers, since any real number can be plugged into x = -4 and the equation will be true. This is because x = -4 is a vertical line and not a function, it cuts the y-axis at one point, so it doesn't matter what value you put on x it will always be -4.
The range of x = -4 is a single point on the y-axis, y = -4.
Step-by-step explanation:
Determine the value of X
The two angles are (x+10) and the other number is 96
Answer: 43
Step-by-step explanation:
x+x+10 = 96
2x = 86
x = 43
you need to find the height of the cylinder
TSA = 2πrh + πr² (r = 40/2 = 20)
4715 = 40πh + 400π
4715/(40π) = h + 10
≈ 37.5 = h + 10
h = 27.5 cm
Hope this helped.
Answer:-
h = 17.52cm
Step-by-step explanation:
To find the height, we'll use the formula for a surface area of a cylinder.
[tex]\boxed{\sf SA=2\pi rh+2\pi r^2}[/tex]
Since the diameter is 40 cm, than the radius is :-
[tex]\sf r=\cfrac{d}{2}[/tex][tex]\sf r=\cfrac{40\;cm}{2}[/tex][tex]\sf r=20cm[/tex]Now, let's substitute the values to the SA formula:-
[tex]\sf 4715\;cm^2=2\pi (20cm)h+2\pi (20cm)^2[/tex]
[tex]\sf 4715cm^2=40\pi cmh+800cm^2\pi[/tex]
[tex]\sf \cfrac{4715cm^2-800cm^2\pi }{40\pi cm} =\cfrac{40\pi cm(h)}{40\pi cm}[/tex]
[tex]\sf h=\cfrac{2,201.725877cm^2}{40\pi cm}[/tex]
[tex]\sf h=17.52\; cm[/tex]
____________________
Hope this helps!
Have a great day!
A region satisfies the inequalities 2 ≤ x ≤ 6 and 3 ≤ y ≤a. What value of a would give the region an area of 24 square units?
Answer: a = 9
Step-by-step explanation:
The given figure formed is a rectangle.
Area of given region (Yellow region) = 24 [tex]unit^{2}[/tex]
Length (l) = 6-2 = 4 units
Breadth (b) = a-3 units
Area = l×b
24 = 4 x (a-3)
6 = a-3
a = 9 units
Sarah, gene, and paul are proposing plans for a class fundraiser. each presents
his or her proposal for the amount of money raised, y, for x number of
hours worked, in different ways.
We can draw the conclusion that linear functions can be used to represent each of the ideas. Due to the fact that each proposal's linear function has an initial value, the class now has money in its accounts (b).
What does "Linear Function" mean?A linear function is denoted by the equation y = mx + b, where m is the slope or unit rate between the two variables, x and y, and b is the beginning value or y-intercept.
The initial value is b.
A linear function is a graph with straight lines.
A unit rate exists for all linear functions (b).
Sarah's suggestion can be expressed by a linear function because the graph that represents it is a straight line.
Gene's Proposal's table displays the unit rate as change in y/change in x = 7. As a result, a linear function can be used to express it.
Paul's idea has a linear function as its equation.
This leads us to the conclusion that linear functions can be used to represent each of the ideas.
Due to the fact that each proposal's linear function has an initial value, the class now has money in its accounts (b).
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Correct Question:
A survey asks students how many children are in their household. Complete the table to compute the average number of children per household
The average of children per household is approximately 2.1387931034482758.
What is average ?
In maths, the average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values.
To compute the average number of children per household, you would add up the total number of children in all the surveyed households and divide that number by the total number of households surveyed. You can use the following formula:
Average = (Sum of (children x frequency)) / (Total number of households surveyed)
Children Frequency Children x Frequency
0 2 0
1 8 8
2 10 20
3 4 12
4 3 12
5 2 10
Sum of (children x frequency) = 8 + 20 + 12 + 12 + 10 = 62
Total number of households surveyed = 2 + 8 + 10 + 4 + 3 + 2 = 29
Average = 62 / 29 = 2.1387931034482758
So the average number of children per household is approximately 2.1387931034482758
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Find all the zeros of each equation.
[tex]7x^2-144=-x^4[/tex]
The equation 7x² - 144 = -x⁴ has the 4 solutions below:
x = ±3
x = ±4i
How to find the zeros of the equation?
Here we want to solve the equation below:
7x² - 144 = -x⁴
We can redefine the variable:
y = x²
Replacing that we will get:
7y - 144 = -y²
y² + 7y - 144 = 0
So we have a quadratic equation now, the using the quadratic formula we will get:
[tex]y = \frac{-7 \pm \sqrt{7^2 - 4*1*144} }{2} \\\\y = \frac{-7 \pm 25 }{2}[/tex]
Then the two solutions are:
y = (-7 + 25)/2 = 9
y = (-7 - 25)/2 = -16
And we know that:
y = x²
Then:
x = ±√9 = ±3
x = ±√-16 = ±4i
These are the 4 solutions.
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On a separate sheet of papter solve each system by elimination.
Show your work on how to get the solution given for each system.
1) 6x - 4y = 2
-2x + 4y = 18
(5.7)
3) -4x - 12y=-24
-2x - 4y =-10
(3,1)
2) 5x +4y= -8
An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.
What is an expression in math?A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. It is possible to multiply, divide, add, or subtract in math.Unknown variables, numerical values, and arithmetic operators make up an algebraic expression. No symbols for equality or inequality are present.A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression in mathematics.Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the phrase 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated by the arithmetic sign +.Given data :
1 ) 6x - 4y = 2
- 2x + 4y = 18
( 5. 7 )
=
= 6x-4y=2
{-2x+4y=18(5.7)}
= [ -2{1+2y}{3}+4y=18. 5.7 ]
= [tex]\frac{-2+8y}{3}[/tex] = 102.6
= y = 38.725
= x = [tex]\frac{1+2\cdot \:38.725}{3}[/tex]
x = 26.15
2) -4x - 12y=-24
-2x - 4y =-10
(3,1)
Solve the equation for x
x = 12 − 4y
− 24 − 2x−4y = −31
Solve using substitution
−24 −2 (12−4y) − 4y = −31
Simplify
− 48 + 4y = −31
Move the constant to the right side
4y= −3 1− (−48)
Subtract the terms
4y = 17
Multiply both sides
4y × [tex]\frac{1}{4}[/tex] = 17 x [tex]\frac{1}{4}[/tex]
Simplify
4y × [tex]\frac{1}{4}[/tex] = [tex]\frac{17}{4}[/tex]
Substitute the given value of y into the equation x = 12 − 4y
x = 12 − 4 × [tex]\frac{17}{4}[/tex]
Simplify the expression
x=−5
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Answer the screenshot
The domain of the given function f(x) = √(x⁴ - 1) include the following: C. {x|x ≤ -1 or x ≥ 1}.
What is a domain?In Mathematics, a domain simply refers to the set of all real numbers for which a particular function is defined. Additionally, the horizontal extent of a graph represents all domain values (input values) and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.
Next, we would use an online graphing calculator to plot the graph of the given function f(x) = √(x⁴ - 1). By critically observing the graph of this function shown in the image attached below, we can reasonably and logically deduce the following domain:
Domain = (-∞, 1) U (1, ∞)
By using set builder notation, the domain of this function f(x) = √(x⁴ - 1) can be re-written as follows;
Domain = {x|x ≤ -1 or x ≥ 1}.
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Using the standard normal distribution, find the two Z-scores that that form the middle shaded region. The shaded region is symmetric about z = 0. Round your Z-scores to two decimal places.Negative z-score -Positive Z-score
The negative z-score = -0.84 and the Positive Z-score = 0.84.
The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. The shaded region in the question is symmetric about z = 0 and forms the middle part of the distribution.
Standard deviation is a measure of the spread or dispersion of a set of data. It tells us how much the individual observations in a dataset vary from the mean of the dataset.
The formula for the standard deviation of a dataset is:
σ = √( Σ (x_i - μ)^2 / n)
The middle shaded region is known as the central region, it represents the middle part of the distribution, and it covers the area between two Z-scores, one negative and one positive. The area of the central region is typically given as a percentage.
For example, if the shaded region represents 68% of the total area under the standard normal distribution curve, then the two Z-scores that form the boundaries of the shaded region are the Z-scores that correspond to the 16th and 84th percentiles of the standard normal distribution. These Z-scores are -0.84 and 0.84 respectively.
So, the negative z-score = -0.84 and the Positive Z-score = 0.84.
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4 Which number is included in the set of integers that when added to –4 gives a sum of less than zero? Select all that apply. A 3 B 7 C 9 D –2 E 4 F 0
The number included in the set of integers that when added to -4 gives a sum less than zero are 0, -2 and 3
How to find the integers in a word expression?The question wants us to find the numbers included in the set of integers that when added to -4 gives a sum less than zero.
The options are 3, 7, 9, -2, 4 and 0.
Therefore,
let
the number added = x
Hence,
-4 + x < 0
Base on the options, the numbers that fits into the inequality are as follows:
The numbers are 0, -2 and 3.
Therefore,
-4 + 0 < 0
-4 + -2 < 0
-4 + 3 < 0
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Three fathers-Paul, Johnson, and Nicolas have between them a total of 15 children of which 9 are boys. Paul has 3 girls and Johnson has the same number of boys. Johnson has 1 more child than Paul who has 4 children. Nicholas has 4 more boys than girls and the same number of girls as Paul has boys. How many boys each do Nicolas and Paul have?
Answer:
Nicholas has 5 boys, and Paul has 1 boy
Step-by-step explanation:
We will use 3 different variables, p, j, and n. Along with this, if there is a subscript on a variable, it will be either b or g, meaning boy or girl. If there is no subscript, it means both genders. We will start by translating our sentences into linear equations, giving us:
[tex]p + j + n = 15[/tex] (1st Equation)
[tex]p_{g} = j_{b} = 3[/tex] (2nd Equation)
[tex]j = p + 1 (p = 4)[/tex] (3rd Equation)
[tex]n_{b} = n_{g} +4[/tex] (4th Equation)
[tex]n_{g} = p_{b}[/tex] (5th Equation)
Whew! That was a lot. We know that Paul has 4 children, which means Johnson has 5 children. Which means Nicolas has 6 children. We know that Paul's girl count is 3 (second equation), meaning that 4 - 3 = Paul has 1 boy. Then, we know that Nicholas has:
b = g + 4 and b + g = 6
So, we substitute the first equation into the second equation, giving us:
g + 4 + g = 6
2g = 2
g = 1
So, Nicholas has one girl, meaning he has 5 boys.
So, Nicholas has 5 boys, and Paul has 1 boy.
Hope this helped!
Subtract 1/2 and 2/4 using fraction strips
Answer:
0
Step-by-step explanation:
1/2 = 2/4
1/2-2/4 = 0
Find the area of the shaded portion if we know the outer circle has a diameter of 4 m and the inner circle has a diameter of 1. 5 m. A Circle
The area of the shaded portion is given by the difference between the area of the outer circle and the area of the inner circle.
First, let's find the areas of the circles:
Outer Circle: Area = πr^2 = π (2)^2 = 4π square meters
Inner Circle: Area = πr^2 = π (0.75)^2 = 0.5625π square meters
Area of shaded portion = Area of outer circle - Area of inner circle = 4π - 0.5625π = 3.4375π square meters
So the area of the shaded portion is approximately 10.8 square meters.
Quizz guyz •^•
What is the minimum length runway needed to accommodate airplanes that can accelerate uniformly at 2.7 m/s2 and must reach a ground velocity of 64 m/s before they can?
• Use Method
• Neat
• No nonsense
• No alien language
Notes : Hi, I'm actually originally from Indonesia, sorry if my words are a bit lacking. Greetings from Indonesia guys
Answer:
758.295 meters
Step-by-step explanation:
If for any reason my answer is wrong, feel free to correct me.
As per your question,
The airplanes accelerate uniformly at 2.7 meters per second^2
And they must reach a ground velocity of 64 m/s.
Therefore
S(Displacement) = u(initial velocity) x time + 1/2(acceleration x time^2)
Initial Velocity = 0 m/s(airplane is at rest)
Acceleration is 2.7m/s^2
Time = ?
Acceleration = Final Velocity - Initial Velocity / Time(t)
2.7 m/s^2 = 64 m/s - 0 m/s / t
2.7(t) = 64
t = 64/2.7
t = 23.703703... rounded to 23.7
S = 0(23.7) + 1/2[2.7 x (23.7)^2]
S = 1/2(2.7 x 561.7) 561.69 is the original answer rounded to 561.7
S = 758.295 meters
Final Answer - An airport would require a runway of minimum length of 758.295 meters to accommodate aircraft of the respective specifications.
2.7 m/s^2 = 64 m/s 0 m/s/t
2.7(t) = 64
t = 64 ÷ 2,7
t = 23.703
or => 23,7
S = 0×(23.7) + 1/2[2,7 × (23,7)²]
S= 1/2(2.7 × 561.7)
S = 758.295 meters
In conclusion:the speed of the plane is 758.295 meters
The number four letter combination that can be formed with the English alphabet is 26 to the fourth power. The number of six letter combination that can be formed is 26 to the sixth power. how many times more six letter combinations can be formed than four letter combinations.
The times more six letter combinations can be formed than four letter combinations will be 26² times.
How to calculate the scientific notation?It should be noted that scientific notation is a method of displaying very large or very small numbers in a more simplified format. We know that entire numbers can be extended indefinitely, but such large numbers cannot be written on a piece of paper.
Furthermore, the numbers in the millions place after the decimal required to be represented in a simpler format. As a result, representing a few integers in their expanded form is challenging. As a result, we employ scientific notation.
In this case, the number four letter combination that can be formed with the English alphabet is 26 to the fourth power. The number of six letter combination that can be formed is 26 to the sixth power.
The number of times more six letter combinations can be formed than four letter combinations will be:
= 26^6 / 26^4
= 26^2
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Answer:
26^2
Step-by-step explanation:
