The length of CF is given as 45 cm
How to solve for the length of CFSince AE is the altitude of the parallelogram ABCD, it is perpendicular to the base DC. Similarly, CF is the altitude of the triangle ACD, and it is perpendicular to the base AD.
Let's use the properties of parallelograms and triangles to solve for the area and length of CF.
Since ABCD is a parallelogram, we know that opposite sides are parallel and equal in length. Therefore, BC = AD = 6 cm.
To find the area of the parallelogram, we can use the formula:
ar(ABCD) = base × height
We can choose any base and height, as long as they form a right angle. Since we know AE is the altitude of the parallelogram, we can use it as the height. Let's choose base AB, which is perpendicular to AE. Therefore,
ar(ABCD) = AB × AE = 12 cm × 7.5 cm = 90 cm²
So, the area of the parallelogram ABCD is 90 cm².
Now, let's find the length of CF. Since CF is the altitude of the triangle ACD, we can use the formula for the area of a triangle:
ar(ACD) = 1/2 × base × height
where the base is AD and the height is CF. We know the area of the triangle ACD is half the area of the parallelogram ABCD, which is 90/2 = 45 cm². Therefore,
45 cm² = 1/2 × 6 cm × CF
Simplifying this equation, we get:
CF = (45 cm² × 2) / (6 cm) = 15 cm
So, the length of CF is 15 cm.
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Gordon currently brings in an annual salary of $92,338 and anticipates a raise of 5% every
year. What will his salary be in 3 years?
If necessary, round your answer to the nearest cent.
Answer:
Gordon will have $106892.8 in three years
Step-by-step explanation:
92338 (0.05 + 1)³=
92338(1.05)³=
92338 x 1.16 =
106892.8
Select all the equations that are equivalent. 52 = 8n + 4 4(2n + 1) = 52 4 = 52 – 8n 4n = 48 n = 6
Answer:
all of these equations except 4n = 48
Step-by-step explanation:
your equations are
52 = 8n+4
4(2n+1) = 52
4 = 52-8n
4n = 48
n = 6
let's solve these equations!
52 = 8n + 4
48 = 8n
n = 6
4(2n+1) = 52
8n + 4 = 52
8n = 48
n = 6
4 = 52-8n
-48 = -8n
n=6
4n = 48
n = 12
all of these equations simplify to n = 6 except for 4n = 48, so they're all equivalent
EFGHI~ WVUTS. Find EI and ST.
I
E 16
16
H
Submit
24
24
G
T
S
U
Write your answers as decimals or whole numbers.
EI =
ST=
18
W
18
The side lengths on the similar polygons are given as follows:
EI = 16.ST = 27.What are similar polygons?Similar polygons are polygons that share these two features presented as follows:
Congruent angle measures.Proportional side lengths.Considering the equivalent side lengths, the proportional relationship for the side lengths in this problem is given as follows:
18/16 = 18/EI = ST/24.
Hence the length of EI is given as follows:
EI = 16.
The length of ST is obtained as follows:
18/16 = ST/24
16ST = 18 x 24
ST = 18 x 24/16
ST = 27.
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Measure & T The optimal tilt for Keenan's solar panelis between 58° and 60° to the horizontal. Has Keenan placed his solar panel at an optimal angle?
Keenan has placed his solar panel at an optimal angle.
How determine if Keenan has placed his solar panel at an optimal angle?The cosine law is a mathematical relationship between the sides and angles of a triangle. The cosine law states that:
cos(C) = (a² + b² - c²) / 2ab
where a, b, and c are the lengths of the sides of the triangle and C is the measure of one of the angles. This law can be used to find unknown side lengths or angle measures in a triangle when given the other values.
Check the attached image for labelling.
The angle we are trying to calculate is labelled C.
cos (C) = (20² + 18² - 19²) / (2*20*18)
cos (C) = 363/720
C = cos⁻¹(363/720)
C = 59.72°
Since the angle obtained is between 58° and 60°. Thus, Keenan has placed his solar panel at an optimal angle.
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Complete Question
Check the attached image for complete question
A triangle has a perimeter of 9x 6. the first side of the triangle has a length of 5x, and the second side has a length of 3x − 7. what is the length of the third side of the triangle? x 13 x − 1 8x − 7 17x − 1
The length of the third side of a triangle with perimeter 9x + 6 and measures of other two sides of the triangle is equal to option a. x + 13.
Perimeter of the triangle is equal to
= 9x + 6
First side of the triangle = 5x
Second side of the triangle = 3x - 7
Let 'n' be the third side of the triangle
perimeter of the triangle = 9x + 6
⇒ 5x + 3x - 7 + n = 9x + 6
⇒ n + 8x - 7 = 9x + 6
⇒ n = 9x -8x + 6 + 7
⇒ n = x + 13
Therefore, the third side of the triangle with given perimeter of the triangle is equal to option a. x + 13.
The above question is incomplete , the complete question is :
A triangle has a perimeter of 9x + 6. the first side of the triangle has a length of 5x, and the second side has a length of 3x − 7. what is the length of the third side of the triangle?
a. x + 13 b. x − 1 c. 8x − 7 d. 17x − 1
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NEED THIS ASAP
Find m/EFG.
m/EFG
Answer: 41 degrees
Step-by-step explanation:
121-39=82
82/2=41
Use Evcel fo find the probabinty that in 112 trials with probabinty0.42of success that there are 30 or fewer suce ses. Round to 6 decimaiplaces Type your answer hern
The probability that there are 30 or fewer successes in 112 trials with a probability of 0.42 of success is 0.874763 rounding to 6 decimaiplaces.
To use the Excel spreadsheet programme to calculate the likelihood that 30 or fewer successes occur in 112 trials with a success probability of 0.42, follow these steps:
In Excel, create a new spreadsheet with the first column labelled "Number of Successes" and the second column labelled "Probability."
Enter "0" in the first row of the "Number of Successes" column.
Enter "1" in the second row of the "Number of Successes" column.
Continue to input numbers in the "Number of Successes" column in ascending order until you reach 30.
Enter the following formula in the field next to the "0" in the "Probability" column: =BINOM.DIST (0,112,0.42,TRUE)
Enter the following formula: =SUM (B1:B31)
The result in the cell where you input the formula in step 8 will be the chance of 30 or fewer successes in 112 trials with a success rate of 0.42.
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Which equation represents the relationship shown in the table?
Answer:
Diatance biked = rate • time
compatible numbers are used to estimate this sum. 181 204 which estimate is the most accurate? responses 350 350 375 375 425 425 450
The most accurate estimated sum of 181 and 204 is 380
The given numbers are 181 and 204
The compatible numbers are defined as the numbers that are easy to do the arithmetic operations. The arithmetic operations are addition, subtraction, division and multiplication etc.
To find the sum of the compatible numbers first we have to round the given numbers to the nearest tens or hundreds and do the the arithmetic operation
Round 181 to the nearest tens = 180
Round 204 to the nearest tens = 200
Then the sum of compatible numbers will be
180 + 200 = 380
Therefore, the most accurate estimation is 380
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a factor of 24 is chosen at random what is the probalility as a decimal that its a 2 digit numbers
Answer:
1/4 as fraction
0.25 as decimal
= 0.25
Step-by-step explanation:
Factors of 24 starting at 1 are:
1 x 24 = 24
2 x 12 = 24
3 x 8 = 24
4 x 6 = 24
Then the pattern repeats in decreasing orders of products of numbers . 6 x 4, 8,x 3 etc which are duplicates of the ones shown above
Factors of 24 are:
1, 2, 3, 4, 6, 8, 12, 24
There are 8 factors
Out of the 8 factors, only two - 12 and 24 are two digit numbers
P(factor is a 2 digit number = # two-digit numbers/Total # factors
= 2/8
= 1/4
= 0.25
Answer:
1/4 as a fraction
0.25 as decimal
0.25
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I NEED HELP!!!!!!
Workers install 840 chairs at a constant rate. After 5 days, the workers still have to install 240 chairs. How much time does it take to install the chairs from start to finish?
Let's call the time it takes to install all the chairs from start to finish "t". The workers install 840 chairs per day, so in "t" days they will have installed 840 * t chairs.
At the end of 5 days, they still have 240 chairs to install, so they have installed 840 * 5 chairs so far. We can use this information to write an equation:
840 * t - 840 * 5 = 240
Expanding and simplifying the equation gives us:
840t - 4200 = 240
Adding 4200 to both sides gives us:
840t = 4440
Finally, dividing both sides by 840 gives us:
t = 5.2857142857...
So it takes approximately 5.29 days to install all the chairs from start to finish.
What is the formula used to calculate the surface area for a square pyramid?
The formula used to calculate the surface area of a square pyramid is A = a^2 + 2a[tex]\sqrt{\frac{a^2}{4}+h^2 }[/tex]
The square pyramid is the geometric shape that has a square base and 4 lateral face. The total number of faces will be five. The base shape is square and the side shape will be triangle. Number of edges in the square pyramid is eight
The surface area is the amount space covered by the surface of the object
Here the surface area of the square pyramid is
A = a^2 + 2a[tex]\sqrt{\frac{a^2}{4}+h^2 }[/tex]
Where A is the surface area of the square pyramid
a is the base edge
h is the height of the square pyramid
Therefore, the surface area is A = a^2 + 2a[tex]\sqrt{\frac{a^2}{4}+h^2 }[/tex]
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Maggie made 4 valentines in 6 hours.
What is the RATE of valentines made PER hour?
x + y = -5 is it a solution
Answer: The equation X + y = -5 represents a straight line in a two-dimensional plane. To determine whether a specific point (X, y) is a solution of the equation, you can substitute the values of X and y into the equation and see if it holds true. If the equation is satisfied, then the point (X, y) is a solution. If the equation is not satisfied, then the point (X, y) is not a solution.
For example, if X = 2 and y = -7, then the equation becomes:
2 + (-7) = -5
-5 = -5
Since the equation holds true, the point (2, -7) is a solution of the equation X + y = -5.
Step-by-step explanation:
Which choice names a chord of circle F?
FE
BA
A and F
FD
A certain number is multiplied by 4 and the results equals 8 less than 8 times of the number. Find the number
The number is 2. To find the unknown number that satisfies the equation "4x = 8x - 8," we can simplify and solve for x, which gives us the answer x = 2.
Let's call the unknown number "x".
According to the problem statement, "A certain number is multiplied by 4 and the result equals 8 less than 8 times of the number" can be translated into the following equation:
4x = 8x - 8
Simplifying this equation, we can move 4x to the right side of the equation:
4x - 8x = -8
Simplifying further, we get:
-4x = -8
Dividing both sides by -4, we find:
x = 2
Therefore, the number is 2.
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PLEASE HELP!!! ITS DUE SOON!
The solutions to the system of linear equation (x, y) are 1 and 4/3 respectively
What is system of linear equationA system of linear equations is a collection of two or more linear equations with the same variables. The goal of solving a system of linear equations is to find the values of the variables that simultaneously satisfy all the equations in the system.
From the question given;
-x + 6y = 7 ...eq(i)
6x - 30y = -34 ...eq(ii)
From eq (i)
x = 6y - 7 ..eq (iii)
Put eq (iii) into eq (ii)
6(6y - 7) - 30y = -34
36y - 42 - 30y = -34
6y - 42 = -34
6y = -34 + 42
6y = 8
y = 4/3
Put y = 4/3 into eq (i)
-x + 6(4/3) = 7
-x + 24 / 3 = 7
x = 24/3 - 7
x = 1
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HELP ASAP, WILL GIVE BRAINLIEST
Where is the above note played on the guitar?
Open second string
Open third string
Second string, first fret
Third string, second fret
Answer:
Second string, first fret.
Step-by-step explanation:
in a magnetometry experiment, after a minute of collecting data the statistical noise was reduced to 1 picotesla. for how many more minutes should data be collected in order to reduce the random error by a factor of 10
In a magnetometry experiment, It will take 1 more minute for data be collected in order to reduce error the statistical noise by a factor of 10.
To reduce the random error by a factor of 10, we need to reduce the statistical noise to 1/10 picotesla. Since the statistical noise was initially 1 picotesla, this means we need to reduce it by a factor of 10.
We can use the following formula to calculate the time needed to reduce the statistical noise by a certain factor:
t = (log (final noise / initial noise)) / (log (reduction factor))
Here, the final noise is 1/10 picotesla, the initial noise is 1 picotesla, and the reduction factor is 10.
Plugging in these values, we get:
t = (log (1/10 / 1)) / (log (10))
t = (log (1/10)) / (log (10))
t = -1 / 1
t = -1
The negative value of t doesn't make sense in this context, so we need to take the absolute value:
t = |-1|
t = 1
Therefore, it will take 1 more minute to reduce the statistical noise by a factor of 10.
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____The given question is incomplete, the complete question is given below:
Reduction of the standard error
In a magnetometry experiment, after a minute of collecting
data the statistical noise was reduced to 1 picotesla.
For how much longer should data be collected in order
to reduce the random error by a factor of 10?
Determine which differential equation corresponds to each phase line. You should be able to state briefly how you know your choices are correct. ? 1. ? 2. ? 3. ? 4. ? 5. ? 6. ? 7. ? 8
The differential equations given correspond to phase lines with slopes that depend on the power of the x term in the equation.
1. y' = x: This differential equation corresponds to a phase line with a slope of 1, since the y' term is equal to the x term.
2. y' = -x: This differential equation corresponds to a phase line with a slope of -1, since the y' term is equal to the negative of the x term.
3. y' = [tex]x^2[/tex]: This differential equation corresponds to a phase line with a slope of 2x, since the y' term is equal to the x squared term.
4. y' = [tex]-x^2[/tex]: This differential equation corresponds to a phase line with a slope of -2x, since the y' term is equal to the negative of the x squared term.
5. y' =[tex]x^3[/tex]: This differential equation corresponds to a phase line with a slope of [tex]3x^2[/tex], since the y' term is equal to the x cubed term.
6. y' = [tex]-x^3[/tex]: This differential equation corresponds to a phase line with a slope of [tex]-3x^2[/tex], since the y' term is equal to the negative of the x cubed term.
7. y' = [tex]x^n[/tex]: This differential equation corresponds to a phase line with a slope of [tex]nx^(n-1)[/tex], since the y' term is equal to the x to the power of n term.
8. y' = -[tex]x^n[/tex]: This differential equation corresponds to a phase line with a slope of [tex]-nx^(n-1),[/tex] since the y' term is equal to the negative of the x to the power of n term.
In summary, the differential equations given correspond to phase lines with slopes that depend on the power of the x term in the equation.
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Complete question:
Determine which differential equation corresponds to each phase line. You should be able to state briefly how you know your choices are correct. ?
1. y' = x
2. y' = -x
3. y' = [tex]x^2[/tex]
4. y' = [tex]-x^2[/tex]
5.y' =[tex]x^3[/tex]
6.y' = [tex]-x^3[/tex]
7. y' = [tex]x^n[/tex]
8. y' = -[tex]x^n[/tex]
Sarah used an equation to solve the problem below. Justify each step of her work. About 11% of people are left handed. How many people would you expect to be left handed in a class of 30 students?
Answer:
To solve the problem, Sarah used the equation:
Left-handed people = (11/100) * Total people
Step 1: Plug in the total number of people (30) into the equation.
Left-handed people = (11/100) * 30
Step 2: Simplify the right side of the equation.
Left-handed people = (11/100) * 30
Left-handed people = 3.3
Step 3: Round the answer to the nearest whole number.
Left-handed people = 3
So, Sarah expects 3 people in a class of 30 to be left-handed. Each step of Sarah's work is justified because she used the percentage formula to find the number of left-handed people in a class and rounded the answer to the nearest whole number.
a student committee has 6 membersâ€""4 undergraduate and 2 graduate students. a subcommittee of 3 members is to be chosen randomly so that each possible combination of 3 of the 6 students is equally likely to be selected. what is the probability that there will be no graduate students on the subcommittee?
The probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.
The number of possible subcommittees that contain only undergraduate students can be calculated by choosing 3 members from the 4 undergraduate students. This can be done in
(4 choose 3) = 4 ways.
The total number of possible subcommittees of three students that can be formed from the 6 members of the committee can be calculated by choosing 3 members from the 6 students. This can be done in
(6 choose 3) = 20 ways.
Therefore, the probability that there will be no graduate students on the subcommittee is:
Number of subcommittees with only undergraduate students / Total number of possible subcommittees
= 4 / 20
= 1/5
= 0.2
So, the probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.
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an online coupon service has offers for free samples. part: 0 / 20 of 2 parts complete part 1 of 2 (a) how many different requests are possible if a customer must request exactly free samples? the number of different requests is .
The number of possible requests for free samples is 5^1 = 5. This means that the customer has 5 different requests that they can make for free samples.
The number of possible requests for free samples can be calculated using the combination formula. The combination formula is used to calculate the number of combinations with repetitions of size “n” taken from a set of “r” elements . The formula is: [tex]C(n,r) = n^r[/tex] In this case, n = number of requests (1 request) and r = number of free samples offered (let’s say, 5). Therefore, the number of possible requests for free samples is[tex]5^1 = 5.[/tex]This means that the customer has 5 different requests that they can make for free samples.
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4 Statistic Homework Questions! Will Give Brainliest!
-11x-11 ≥ −6+13x
X <
An online furniture store sells chairs for $100 each and tables for $450 each. Every
day, the store can ship at most 16 pieces of furniture and must sell at least $3000
worth of chairs and tables. If 9 chairs were sold, determine the minimum number of
tables that the store must sell in order to meet the requirements.
The minimum number of tables the store must sell is 5.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Using t and c as variables, we get
100c + 400t ≥ 3000
c+t≤16
The online furniture store must sell at least $3000 worth of chairs and tables each day, and can ship at most 16 pieces of furniture.
If the store sells 9 chairs for a total of $900, it needs to sell at least 5 tables to reach a total revenue of $3000.
Since the total number of pieces of furniture sold is 14 (9 chairs + 5 tables), which is less than the maximum of 16, the store meets the daily shipping requirement.
Therefore, the minimum number of tables the store must sell is 5.
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The function P(n) = 108 + 10 log(n) gives the
total sound power in decibels when n drill presses are operating in a factory. What is the total sound power, to the nearest decibel, when three drill presses are operating?
112.8 is the the total sound power, when three drill presses are operating
What is a function?A relation is a function if it has only One y-value for each x-value.
Given that a function P(n) = 108 + 10 log(n) gives the total sound power in decibels when n drill presses are operating in a factory.
We need to find the total sound power, to the nearest decibel, when three drill presses are operating
We have to consider n as 3
P(3) = 108 + 10 log(3)
=108+10×0.477
=108+4.77
=112.77
Hence, 112.8 is the the total sound power when three drill presses are operating
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If 70% of a number is 224 and 95% of the same number is 304, find 25% of that number.
Using the information given in the problem to set up two equations and by solving them
25% of the number is 80.
What is an equation?An equation is a mathematical statement that expresses the equality of two expressions. It typically consists of two parts: the left-hand side and the right-hand side, separated by an equal sign (=). The left-hand side and right-hand side can contain variables, numbers, and mathematical operations such as addition, subtraction, multiplication, and division.
According to the given informationLet's call the number we're looking for "x". We can use the information given in the problem to set up two equations:
0.7x = 224 (equation 1)
0.95x = 304 (equation 2)
We want to find 25% of the same number, which can be written as 0.25x. We can solve for x using either equation 1 or equation 2 and then plug that value into 0.25x to find the answer.
Let's solve for x using equation 2:
0.95x = 304
x = 304/0.95
x = 320
Now that we know x is 320, we can find 25% of that number:
0.25x = 0.25(320) = 80
So 25% of the number we were looking for is 80.
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Write an explicit formula for a_na n , the n^{\text{th}}n th term of the sequence 3, -15, 75, ...3,−15,75,....
The explicit formula for the geometric series is [tex]a_n = 3(5)^{n-1}[/tex].
What is geometric progression?A geometric series is one in which there is a constant separating the two succeeding numbers. In other words, to create a geometric progression, each succeeding term is multiplied by the constant term.
Given that the geometric sequence is,
3, 15, 75......
The common ratio of the series is calculated as the ratio of the second term to the first term,
r = 15 / 3
r = 5
The explicit formula can be written as:-
[tex]a_n = a_1(r)^{n-1}[/tex]
[tex]a_n = 3(5)^{n-1}[/tex]
Therefore, the formula is [tex]a_n = 3(5)^{n-1}[/tex].
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the answer is 120 I need two possible number sentences using division pls
Answer:
240/2, 360/3
Step-by-step explanation:
240/2 and 360/3 both involve division and both of their answers are equal to 120, assuming these count as number sentences.
