Solving and simplifying the potenciation, we get 3⁹
Potentiation simplificationAs the bases presented are multiple, we can reduce it to the common base 3.
To do this, replace 9 with the equivalent in base 3.
That is, 3².
Then, apply the property of multiplying like bases, adding the exponents.
[tex]\begin{array}{l}\sf 9^{2} \times 3^{5}=[?]\\\raisebox{4pt}{$\sf \big(3^{2}\big)^{\!2} \times 3^{5}=[?]$}\\\sf 3^{4} \times 3^{5}=[?]\\\sf 3^{4+9} = [?]\\\sf 9^{2} \times 3^{5} = 3^{9}\end{array}[/tex]
So, the result found is 3⁹
Alternatively, the result can be written as 1.9683×10⁴, in scientific notation
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Identify the expression and the value equivalent to 4 times 3 cubed.
The value equivalent tο the expressiοn "4 times 3 cubed" is 108.
What is Algebraic expressiοn ?Algebraic expressiοn can be defined as cοmbinatiοn οf variables and cοnstants. An algebraic expressiοn is a mathematical phrase that can cοntain numbers, variables, and mathematical οperatiοns such as additiοn, subtractiοn, multiplicatiοn, and divisiοn.
It is a cοmbinatiοn οf numbers, variables, and symbοls arranged in a meaningful way tο represent a mathematical statement οr relatiοnship.
The expressiοn "Fοur times Three cubed" means that we shοuld first cube the number 3, and then multiply the result by 4.
Tο cube 3, we multiply it by itself three times :
[tex]3^3 = 3 * 3 * 3 = 27[/tex]
Next, we multiply this result by 4:
4 * 27 = 108
Therefοre, the value equivalent tο the expressiοn "4 times 3 cubed" is 108.
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evaluate 2(s + t)^3 - 6 when s = 3 and t = 2
The value of 2(s + t)^{3} - 6 is 244.
What is an equation?
In mathematics, an equation is a statement that asserts the equality of two expressions, usually separated by an equals sign (=).
For example, the equation 3x + 5 = 11 asserts that the expression 3x + 5 is equal to the expression 11. An equation can have one or more variables, which are typically represented by letters. In the example above, x is the variable.
To evaluate 2(s + t)^{3} - 6 when s = 3 and t = 2, we can substitute 3 for s and 2 for t in the expression and simplify.
So we have:
2(s + t)^{3} - 6 = 2(3 + 2)^{3} - 6 (substituting s = 3 and t = 2)
= 2(5)^{3} - 6 (evaluating the expression inside the parentheses)
= 250 - 6 (cubing 5 and multiplying by 2, and then subtracting 6)
= 244 (subtracting 6 from 250)
Therefore, when s = 3 and t = 2, the value of 2(s + t)^{3} - 6 is 244.
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(-8x^2+10x+4)-(-4x+10)
Answer: -2(x-1)(4x-3)
Step-by-step explanation: because im just that guy
Find the cardinal number for the set A={Pacific,Indian,Atlantic,Gulf of Mexico}.
Answer:
4
Step-by-step explanation:
The cardinality of a set is the number of elements in the set.
Therefore, the cardinal number for the set A={Pacific, Indian, Atlantic, Gulf of Mexico} is 4, since it has four elements.
A ladder leans against the wall of a building. The ladder measures
55 inches and forms an angle of 63 with the ground. How far from
the ground, in inches, is the top of the ladder? How far from the
wall, in inches, is the base of the ladder? Round to two decimal
places as needed.
Can anybody sugges me a math and science week theme?
We can suggest the following three themes for a math and science week, combining the two fields and exploring current events and issues:
Exploring the Cosmos: This theme could focus on space exploration and the science and math behind it. Activities could include stargazing, rocket building, and discussions of the latest discoveries in space science.Sustainable Solutions: This theme could center on environmental science and the math and science needed to create sustainable solutions. Activities could include hands-on experiments with renewable energy sources, discussions of climate change and its impacts, and exploration of innovative solutions to environmental challenges.Math and Science in Everyday Life: This theme could highlight the ways in which math and science impact our daily lives. Activities could include examining the science behind cooking and nutrition, exploring the math involved in financial planning and budgeting, and discussing the science of medicine and health.How to find a themeHere are a few steps you can follow to find a theme:
Brainstorm: Start by brainstorming ideas for possible themes. You can involve others in the brainstorming process, such as colleagues, students, or community members. Write down any ideas that come to mind, no matter how big or small.Identify key topics: Look for common themes or topics that emerge from your brainstorming session. Are there particular areas of science or math that people seem interested in? Is there a particular focus or goal that you want to achieve with your science and math week?Narrow down your choices: Once you have identified key topics, narrow down your choices to a few that seem the most compelling. Consider factors such as feasibility, relevance to your audience, and potential impact.Develop a plan: Once you have selected a theme, develop a plan for your science and math week. Determine the activities and events that will be included, the resources and materials needed, and the timeline for implementation.By following the steps above, you can figure out a theme for yourself. If you wish, use one of the themes already suggested above.
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Solve the indicated quantity
The value of x is equal to 35° and the measure of the angle between points AY, m∠AND is equal to 80°.
How to evaluate for the x and the angle m∠ANDFrom the question, we observe that the larger angle between m∠ANY consists of the two angles between m∠AND and m∠YND, so we shall sum the two small angles and equate the result to the larger angle to solve for the value of x as follows:
2x + 10 + 30 = 110°
2x + 40 = 110
2x = 110 - 40 {subtract 40 from both sides}
2x = 70
x = 70/2 {divide through by 2}
x = 35°
so we can evaluate for the angle between m∠AND as follows:
m∠AND = 2(35) + 10
m∠AND = 70 + 10
m∠AND = 80°
In conclusion, the value of x is equal to 35° and the measure of the angle between points AY, m∠AND is equal to 80°.
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Maria has been tracking the number of songs she has
downloaded on her smart phone for the past several
months. Use the scatterplot and line of best fit below to
help her determine when she will reach 10,000 songs?
Answer:
The answer of the given question based on the scatterplot for determining when she will reach 10,000 songs the answer is Maria will reach 10,000 songs in approximately 13.33 months, or about 14 months.
What is Slope?Slope is measure of steepness or incline of line. In geometry and mathematics, slope is defined as ratio of the change in y-coordinates to change in x-coordinates between two distinct points on line. This is often represented by letter "m".
To determine when Maria will reach 10,000 songs, we need to find the point on the line of best fit where the y-value is 10,000.
From the scatterplot, we can estimate that the line of best fit intersects the y-axis at approximately 2000. This means that the initial number of songs downloaded was 2000.
Next, we need to find the slope of the line of best fit. Let's choose the points (5, 6500) and (10, 9500).
The slope of the line passing through these two points is:
slope = (y2 - y1)/(x2 - x1) = (9500 - 6500)/(10 - 5) = 600 songs per month
This means that Maria is downloading 600 songs per month on average.
Finally, we can use the slope-intercept form of a line to find the x-value when the y-value is 10,000:
y = mx + b
10,000 = 600x + 2000
8000 = 600x
x = 13.33
Therefore, Maria will reach 10,000 songs in approximately 13.33 months, or about 14 months.
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Find the solution to the differential equation: dy/dt=0.4(y−200) when y=40 and t=0
As a result, y = 200 + 160[tex]e^{(0.4t)}[/tex] is the answer to the provided differential equation with starting conditions of y = 40 and t = 0.
What equation of number would that be?A mathematical statement that shows the equivalence of a couple of equations is what an equation at algebra means. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are split by the 'equal' symbol.
The given differential equation is:
dy/dt = 0.4(y - 200)
To solve this differential equation, we need to separate the variables and integrate:
dy/(y - 200) = 0.4 dt
Integrating both sides, we get:
ln|y - 200| = 0.4t + C
where C is the constant of integration.
To determine the value of C, we use the initial condition that y = 40 when t = 0:
ln|40 - 200| = 0.4(0) + C
ln|-160| = C
C = ln(160)
Thus, the equation becomes:
ln|y - 200| = 0.4t + ln(160)
Taking the exponential of both sides, we get:
|y - 200| = [tex]e^{(0.4t+ln(160))}[/tex] = 160[tex]e^{(0.4t)}[/tex]
Simplifying, we get:
y - 200 = ±160[tex]e^{(0.4t)}[/tex]
y = 200 ± 160[tex]e^{(0.4t)}[/tex]
Using the initial condition that y = 40 when t = 0, we can determine the value of the constant of integration:
40 = 200 ± 160[tex]e^{(0.4(0))}[/tex]
40 = 200 ± 160
Solving for the two possible values of y, we get:
y = 360 or y = 40
Therefore, the solution to the given differential equation with the initial condition y = 40 and t = 0 is:
y = 200 + 160[tex]e^{(0.4t)}[/tex]
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what is 4+2+3+5+6+7+5+6+1+9
Answer:
Step-by-step explanation:
Awnser=48
Determine the measurement of EF.
EF = 3.47
EF = 3.16
EF = 1.39
EF = 1.1
the answer is "EF = 3.16". According to condition of Similar triangles.
How to solve these problem?
To solve this problem, we will use the property of similar triangles, which states that corresponding angles of similar triangles are equal, and their corresponding sides are proportional.
First, we need to find the ratio of the sides of the two triangles. We can do this by dividing the length of one side of triangle ABC by the corresponding side of triangle DEF. Let x be the length of EF, then:
AB/DE = BC/EF = CA/DF
Substituting the given values, we get:
11/4.4 = 7.9/x = 7.6/(DE + x)
Solving for x, we get:
x = 3.16
Therefore, EF = 3.16.
Hence, the answer is "EF = 3.16".
Note that we can also check our answer by verifying that the corresponding sides of the two triangles are proportional using the ratios we found:
AB/DE = 11/4.4 = 2.5
BC/EF = 7.9/3.16 = 2.5
CA/DF = 7.6/(4.4+3.16) = 2.5
Since the ratios are all equal, we can conclude that the triangles are similar.
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If 0 equal number on picture
Answer:
sin -1/2 cos sqrt3/2
Step-by-step explanation:
UNIT CIRCLE
79.9 is 99% of what
Answer:80
Step-by-step explanation:
if 79.9 Is 99% of the unknown number the other 1% would be 80
In the figure.
Find m
Answer:
Step-by-step explanation:
6
A man owes (a) $10,000 due in three months and (b) $20,000 due in seven months. He and his creditor agree to settle the obligations by two equal payments, one in five months and the other in 11 months. Find the size of each payment if money is worth 6% find :
1-the comparison date is 11 months hence.
2-the comparison date is now
3-the comparison date is 3 months
Answer:
Pls mark as brainliest
Step-by-step explanation:
To solve this problem, we can use the concept of present value of money. We want to find the equal payments that will settle the obligations in 5 and 11 months, respectively, and we know the amounts and due dates of the obligations.
Using a 6% interest rate, we can find the present value of each obligation on each comparison date, and then solve for the unknown equal payments.
Comparison date is 11 months hence:
The present value of $10,000 due in 3 months at a 6% interest rate is:
PV1 = $10,000/(1 + 0.06 * 3/12) = $9,703.70
The present value of $20,000 due in 7 months at a 6% interest rate is:
PV2 = $20,000/(1 + 0.06 * 7/12) = $19,003.22
To settle these obligations with two equal payments, we can set up the equation:
PV1/(1 + 0.06 * 8/12) + PV2/(1 + 0.06 * 4/12) = x + x/(1 + 0.06 * 6/12)
where x is the size of each payment.
Simplifying the equation, we get:
9703.70/1.04 + 19003.22/1.02 = 2.5x
Solving for x, we get:
x = $8,102.67
Therefore, each payment should be $8,102.67.
Comparison date is now:
The present value of $10,000 due in 3 months at a 6% interest rate is:
PV1 = $10,000/(1 + 0.06 * 3/12) = $9,703.70
The present value of $20,000 due in 7 months at a 6% interest rate is:
PV2 = $20,000/(1 + 0.06 * 7/12) = $19,003.22
To settle these obligations with two equal payments, we can set up the equation:
PV1 + PV2/(1 + 0.06 * 4/12) = x + x/(1 + 0.06 * 6/12)
where x is the size of each payment.
Simplifying the equation, we get:
9703.70 + 19003.22/1.02 = 2.5x
Solving for x, we get:
x = $8,556.54
Therefore, each payment should be $8,556.54.
Comparison date is 3 months:
The present value of $10,000 due in 3 months at a 6% interest rate is:
PV1 = $10,000
The present value of $20,000 due in 7 months at a 6% interest rate is:
PV2 = $20,000/(1 + 0.06 * 4/12) = $19,508.67
To settle these obligations with two equal payments, we can set up the equation:
PV1/(1 + 0.06 * 8/12) + PV2 = x + x/(1 + 0.06 * 6/12)
where x is the size of each payment.
Simplifying the equation, we get:
10000/1.04 + 19508.67 = 2.5x
Solving for x, we get:
x = $8,433.13
Therefore, each payment should be $8,433.13.
Jonathan works with his dad to earn extra money. His dad uses this expression to determine the amount Jonathan is paid each week, based on the number of hours he works, x. { 7 . 5 x ; 0 ≤ x ≤ 10 75 + 9 ( x − 10 ) ; x > 10 What does the term 9(x – 10) represent? A. the total amount he is paid for the hours over 10 B. the amount he is paid for each hour over 10 C. the number of hours he works each week D. the number of hours he works over 10 each week
The correct answer is Option B, The amount Jonathan is paid for each hour over 10.
The expression { 7 . 5 x ; 0 ≤ x ≤ 10 75 + 9 ( x − 10 ); x > 10 } gives the amount of money Jonathan is paid each week based on the number of hours he works, x. The first part of the expression, 7.5x, applies when x is between 0 and 10, inclusive. The second part of the expression, 75 + 9(x - 10), applies when x is greater than 10.
So, the term 9(x - 10) represents the amount he is paid for each hour over 10. When Jonathan works more than 10 hours, he is paid a flat rate of $75 for the first 10 hours, and then an additional $9 for each hour over 10. Therefore, if Jonathan works x hours and x is greater than 10, then he is paid 9(x - 10) dollars for each hour over 10.
Therefore, the correct answer is B. the amount he is paid for each hour over 10.
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the value of a car is 15000 and depreciates at a rate of 8% per year. what is the exponential equation.
Hope this helps.
Work out the length of AG in the cuboid below.
The length of the AG in the cuboid is 7.56 cm.
Finding the length diagonal of the cuboid:To find the Length of the diagonal AG, we need to find the length of AC. Use the Pythagorean formula to find the length of AC. Now use the trigonometric ratios formulas to find the length of AG.
Here we have a cuboid
Where AD = 23 cm, DC = 18 cm and ∠GAC = 75°
From the right angle triangle, ADC
=> AC² = AD² + DC² [ Using the Pythagorean formula ]
=> AC² = (23)² + (18)²
=> AC² = 529 + 324
=> AC = √853 = 29.20
Hence, the length of AC = 29.20
From the right angle triangle, AGC
=> Cos B = AC/AG
=> Cos 75° = 29.20/AG
=> AG = Cos 75° (29.20)
=> AG = (0.26)(29.20)
=> AG = 7.56
Therefore
The length of the AG in the cuboid is 7.56 cm.
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help algebra 2 blahahahah
The factored representation of the quadratic function 2x² - 10x - 48 is given as follows:
2(x - 8)(x + 3).
How to factor the quadratic function?The quadratic function for this problem is defined as follows:
2x² - 10x - 48
The leading coefficient of 2 is common to all the terms of the expression, hence the expression can be simplified as follows:
2x² - 10x - 48 = 2(x² - 5x - 24).
The term with the square of x can be simplified as follows:
x² - 5x - 24 = (x - 8)(x + 3).
Meaning that x = 8 and x = -3 are the roots of the quadratic function, hence, considering the leading coefficients and the linear factors, the simplified expression is given as follows:
2x² - 10x - 48 = 2(x - 8)(x + 3).
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The factorization of the quadratic equation is:
y = 2*(x + 3)*(x - 8)
How to factor the quadratic equation?Here we have the quadratic equation:
2x^2 - 10x - 48
To factorize it, we need to find the roots of the quadratic, to do so we need to solve the equation:
y = 2*x^2 - 10*x - 48 = 0
2x^2 -10x - 48 = 0
Dividing by 2 in both sides we will get:
(2x^2 - 10x - 48)/2 = 0/2
x^2 - 5x - 24 = 0
Now we can use the quadratic formula to get the roots:
[tex]x = \frac{5 \pm \sqrt{(-5)^2 - 4*1*-24} }{2} \\\\x = \frac{5 \pm 11}{2}[/tex]
The roots are:
x = (5 + 11)/2 =8
x = (5 - 11)/2 = -3
Then the factorization will be:
y = 2*(x - (-3))*(x - 8)
y = 2*(x + 3)*(x - 8)
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What is the slope of the line given the ordered pairs (1, 4) and (2, 7)?
A student calculated a value to be $38.06 when they should have rounded up to $38.07. What is the percent error in their calculation?
Answer:
To calculate the percent error, we need to find the absolute difference between the correct value and the measured value, divide that by the correct value, and then multiply by 100 to get a percentage.
The absolute difference between the correct value and the measured value is:
$38.07 - $38.06 = $0.01
Dividing this by the correct value ($38.07) gives:
$0.01 / $38.07 ≈ 0.0002626
Multiplying by 100 gives the percent error:
0.0002626 x 100% ≈ 0.02626%
Therefore, the percent error in the student's calculation is approximately 0.02626%.
The percent error in the student's calculation is 2.63%.
Explanation:To calculate the percent error, we need to find the absolute difference between the student's calculated value and the correct value, which is $38.07. The absolute difference is $0.01. To find the percent error, we divide the absolute difference by the correct value and multiply by 100. Percent Error = (|Correct Value - Calculated Value| / Correct Value) * 100. Percent Error = (0.01 / 38.07) * 100. Percent Error = 0.0263 * 100. Percent Error = 2.63%. Learn more about percent error here:https://brainly.com/question/13270722
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I need help with this assignment
The names of the column headers in the table indicates that the function c(x) = q(x) ÷ m(x), where q(x) and m(x) are whole numbers, indicates that the function c(x) is a rational function.
What is a rational function?Rational functions are functions that consists of a ratio of polynomial functions. A rational function, f(x), consists of the functions g(x) and h(x), such that f(x) = g(x)/h(x), where h(x) ≠ 0.
The input variable of the functions is; x
The functions in the question are; q(x) and m(x)
The function c(x) is; c(x) = q(x) ÷ m(x)
The function c(x) is composed of two functions q(x) and m(x), that are together presented as a fraction, which indicates that c(x) is a rational function.
The type of function represented by the function c(x) is therefore;
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which uses th GFC to generate an expression equivalent to 2.4x - 12
The GCF (Greatest Common Factor) of 2.4x and 12 is 2.4. Therefore, we can write: 2.4x - 12 = 2.4(x - 5)
What is expression ?
In mathematics, an expression is a combination of symbols and/or numbers that represents a mathematical quantity or relationship. It can be a simple numerical value or a more complex arrangement of terms and operations.
To generate an expression equivalent to 2.4x - 12 using the GCF, we need to find the largest common factor between the terms 2.4x and 12.
First, we can simplify 2.4x by dividing both the numerator and denominator by 0.4, which gives us:
2.4x = 6x
Now, we can find the GCF between 6x and 12, which is 6. We can factor out this GCF from both terms to get:
2.4x - 12 = 6(x - 2)
So, the expression equivalent to 2.4x - 12 using the GCF is 6(x - 2). This expression represents the same quantity as 2.4x - 12, but is simplified and factored.
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How much money should be deposited today in an account that earns 2.5% compounded monthly so that it will
accumulate to $13,000 in 4 years?
i Click the icon to view some finance formulas.
Answer: We can use the formula for the future value of an annuity with monthly compounding to determine how much money should be deposited:
FV = P * ((1 + r/n)^(n*t) - 1) / (r/n)
where:
FV = future value (the amount we want to accumulate, which is $13,000 in this case)
P = periodic payment (the amount we need to deposit each month)
r = annual interest rate (2.5% in this case)
n = number of compounding periods per year (12 for monthly compounding)
t = number of years (4 in this case)
We want to solve for P, so we can rearrange the formula as follows:
P = FV * (r/n) / ((1 + r/n)^(n*t) - 1)
Substituting the given values, we get:
P = 13000 * (0.025/12) / ((1 + 0.025/12)^(12*4) - 1)
Calculating this expression gives us:
P = $279.27 (rounded to the nearest cent)
Therefore, we need to deposit $279.27 each month for 4 years in an account that earns 2.5% compounded monthly in order to accumulate $13,000. Alternatively, if we want to make a single deposit today, we can multiply this monthly amount by 12 and then by 4, which gives us:
P = $13,414.08 (rounded to the nearest cent)
Therefore, we need to deposit $13,414.08 today in an account that earns 2.5% compounded monthly in order to accumulate $13,000 after 4 years.
Step-by-step explanation:
Which of the following is unique in Inditex SA's value chain?
Only sales staff provide new product ideas.
O Manufacturing facilities are geographically close to headquarters.
O Products are shipped directly to warehouses.
Only designers provide new product ideas.
Therefore , the solution of the given problem of unitary method comes out to be the additional choices are not exclusive to Inditex's value chain and are frequently used by other businesses in the sector.
An unitary method is what?By combining what was learned and implementing this variable technique, which also includes all supplemental information from two people who used a particular tactic, the task can be finished. In other words, if the desired result occurs, either the entity specified expression in the computation will be acknowledged, or both of the expression's crucial processes will actually skip the colour. A refundable fee of Rupees ($1.01) may be needed for forty pens.
Here,
The fact that goods are delivered straight to warehouses distinguishes Inditex SA's value chain from other companies.
As a result, lead periods are shortened and inventory costs are kept to a minimum during the quick and effective distribution of goods to retail stores. Fast fashion is this method, and it has been a major factor in Inditex's success in the fashion sector.
The additional choices are not exclusive to Inditex's value chain and are frequently used by other businesses in the sector.
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Determine the length of x in the triangle. Give your answer to two decimal places. most importantly show the steps, please.
Answer:
x=43.85
Step-by-step explanation:
solution Given.
let the given angle be θ: 20 degree.
It's opposite side is 12.
It's hypotenuse is x.
Since
We have
Sin θ= opposite/hypotenuse
Sin20 degree=12/x
0.34202014332=12/x
doing criss cross multiplication
x=12/0.34202014332
therefore x=43.8570660032
in two decimal form x=43.85
write a sine function in which the amplitude is 2 and its graph has 3 complete cycles on the interval
Sine function in which the amplitude is 2 and its graph has 3 complete cycles on the interval is 2sin3x
Sine Function DefinitionThe sine function in trigonometry is the ratio of the hypotenuse's length to the opposite side's length in a right-angled triangle.
let's imagine the sine function is in form of:Y= A sin( B( X-C))+ D Or Y= A cos( B( X-C))+ D
where,
A is the value of the amplitude
B is the number of cycles between 0 and 2 pi since B is the graph's period, or (2π).
C is the graph's horizontal movement.
D is the graph's vertical movement.
Given:amplitude=2
number of cycle in the interval=3
Example:
Y= 2 sin 3X
it has an amplitude of 2
There are three cycles of sin between 0 and 2 π
Hence, y=2sin3x is the sine function in which the amplitude is 2 and its graph has 3 complete cycles on the interval.
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Please helppp!! At a hospital there were 460 patients, of these, there were 150 men, 192women and the reminder children. How many more adults were there than children?
Answer:
224 more adults than children
Step-by-step explanation:
150+192=342 adults together
460-342=118 children
342-118= 224
sooo there were 224 more adults than children
Which could be the missing first term
1. If the letters of the word "COMPUTER" are arranged in random, what is the probability that O&E are together?
The probability that O and E are together in a randomly arranged word "COMPUTER" is 0.25, or 25%.
What is probability?Statistics and probability theory both make substantial use of probability, which is a measure of the possibility or chance of an event occurring. A number between 0 and 1, where 0 denotes an event that is impossible and 1 denotes an event that is certain, is used to indicate the likelihood of an occurrence.
We must count the number of favourable possibilities—those that match the event of interest—and divide that number by the total number of potential outcomes in order to calculate the probability of an occurrence.
There are 8 letters in the word, so the total number of arrangements is 8! = 40,320.
For O and E to be together we consider it as a sing letter, thus:
There are 7! ways to arrange the letters of new word.
Now, OE can be written as OE or EO thus:
2 x 7! = 10,080
Now, the probability of O and E together is:
Probability = 10,080 / 40,320
Probability = 0.25
Hence, the probability that O and E are together in a randomly arranged word "COMPUTER" is 0.25, or 25%.
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