Answer: Let's call the width of the rectangular playing field "w" and the length "l". From the problem, we know that:
l = 3w + 4 (the length is 4 yards longer than triple the width)
We also know that the perimeter of a rectangle is the sum of the lengths of all four sides, so:
P = 2l + 2w
We are given that the perimeter is 416 yards, so we can substitute that into the perimeter equation:
416 = 2(3w + 4) + 2w
Simplifying and solving for w:
16 = 6w + 8
8 = 6w
w = 8/6 = 4/3
We can now substitute that back into the equation for the length:
l = 3w + 4
l = 3(4/3) + 4
l = 4 + 4
l = 8
So the dimensions of the rectangular playing field are 4/3 yards wide and 8 yards long.
Step-by-step explanation:
Dr. Leona Williams, a well-known plastic surgeon, has a reputation for being one of the best surgeons for reconstructive nose surgery. Dr. Williams enjoys a rather substantial degree of market power in this market. She has estimated demand for her work to be: Q = 480 – 0.2P where Q is the number of nose operations performed monthly and P is the price of a nose operation. What is the inverse demand function for Dr. Williams’ services? What is the marginal revenue function? The average variable cost function for reconstructive nose surgery is estimated to be:
AVC = 2Q2 – 15Q + 400
where AVC is the average variable cost (measured in dollars), and Q is the number of operations per month. The doctor’s fixed cost per month is $8,000. If the doctor wishes to maximize her profit, how many nose operations should she perform each month? What price should Dr. Williams charge to perform a nose operation? How much profit does she earn each month?
We can conclude that -
The inverse demand function for Dr. Williams’ services is -Q = 5(280 - P)
For maximum profit, she should perform 4 operations.What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is a story of Dr. Leona Williams who is a well-known plastic surgeon.
{ 1 } -
Dr. Williams estimated demand for her work is -
Q = 280 - 0.2P
Inverse of a function can be calculated by following the steps mentioned below -
Step 1 - Replace 'y' with 'x' and vice - versa.Step 2 - Rewrite the equation by solving for 'y'.Step 3 - Replace 'y' with f⁻¹(x).So, we can write -
P = 280 - 0.2Q
P - 280 = - 0.2Q
- (280 - P) = - 0.2Q
(280 - P) = 0.2Q
Q = (280 - P)/0.2
Q = 5(280 - P)
{ 2 } -
The average variable cost function for reconstructive nose surgery is -
AVC = 2Q² – 15Q + 400
Let AVC = A{Q}
For maximum profit -
d/dQ (A{Q}) = 0
d/dQ (2Q² – 15Q + 400) = 0
d/dQ (2Q²) - d/dQ (15Q) + d/dQ (400) = 0
4Q - 15 = 0
4Q = 15
4Q = 15
Q = 3.7
Q = 4 {approx.}
Therefore, we can conclude that -
The inverse demand function for Dr. Williams’ services is -Q = 5(280 - P)
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If Mario eats two cups of pretzels every night while he watches television how many cup dose he eat in one week
A manufacturer of cell phone screens has found that 5 percent of all screens produced have defects. Let pd represent the population proportion of all cell phone screens with a screen defect, therefore pd=0.05. For the sampling distribution of the sample proportion of cell phone screens from this manufacturer with a screen defect for sample size 400, μpˆd=0.05. Which of the following is the best interpretation of μpˆd=0.05 ?For a randomly selected cell phone screen from this population, the mean number of screen defects for the selected screen will be equal to 0.05.A For a randomly selected cell phone screen from this population, the mean number of screen defects for the selected screen will be equal to 0.05.B For every sample of size 400 from this population, the proportion of cell phone screens with a screen defect will be 0.05.C For every sample of size 400 from this population, the proportion of cell phone screens with a screen defect will be 0.05.D For all samples of size 400 from this population, the mean number of screen defects for the samples is 0.05.F For all samples of size 400 from this population, the mean number of screen defects for the samples is 0.05.G For all samples of size 400 from this population, the mean of all resulting sample proportions of cell phone screens with a screen defect is 0.05.H For all samples of size 400 from this population, the mean of all resulting sample proportions of cell phone screens with a screen defect is 0.05.I For all samples of size 400 from this population, the standard deviation of all resulting sample proportions of cell phone screens with a screen defect is 0.05.
Using the Central Limit Theorem, it is found that the correct option is: C
For all samples of size 400 from this population, the mean of all resulting sample proportions of cell phone screens with a screen defect is 0.05.
By the Central Limit Theorem, for a proportion p in a sample of size n, the mean of the sampling distribution of sample proportions is u=5, while the standard error is [tex]SE=\sqrt{\frac{p*(1-p)}{n} }[/tex]
In this problem, the mean of the sampling distribution of sample proportions is 0.05, that is, the mean proportion of all samples, hence, the correct option is C.
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Solve the problem by using addition, subtraction, multiplication, or division. First use front end rounding to estimate the answer. Then find the exact answer.
The foggiest place in a certain country is City A. It is foggy there an average of days each year. How many days is it not foggy each year? Find the estimated and the exact number of days.
The notion of an equation in algebra is a statistical statement that demonstrates the equality of two mathematical expressions.
For the stated question;
Use addition, subtraction, multiplication, or division to find the solution. To first estimate the response, use front end rounding. Find the precise response next. City A is located in the nation with the most haze. how many days a year are clear of fog.365 days are included in a year.
There are 256 days a year on average when it is foggy.
Determine the approximate number of clear days by using the formula:
We round the figures.
To the nearest tens, 365 days
= 370 days
The nearest tenth of 256 days
= 260 days
370 - 260 days, then
= 110 days
The precise number of days without fog is =
= 365 − 256
= 109
Thus, the precise number of days without fog is found as 109 days.
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The complete question is -
Solve the problem by using addition, subtraction, multiplication, or division. First use front end rounding to estimate the answer. Then find the exact answer. The foggiest place in a certain country is City A. It is foggy there an average of 256days each year. How many days is it not foggy each year? Find the estimated and the exact number of days.
Tarmu run 30 min and burned 170 calories. Write an equation that represents the number of calories,c, burned per min
c=170/30 is the equation that represents the number of calories,c, burned per min.
What is Division?A division is a process of splitting a specific amount into equal parts.
Given that Tarmu run 30 min and burned 170 calories
We need to find the equation that represents the number of calories, c, burned per min.
To find the calories burned in each minute we have to divide one hundred seventy by thirty.
c=170/30
c=5.66 cal/min
Hence, c=170/30 is the equation that represents the number of calories,c, burned per min.
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suppose that for a group of consumers the probability of eating pretzels is .75 and the probability of drinking coke in .65. further suppose that the probability of eating pretzels and drinking coke is about.55. determine if these two events are independent
7.) +9 – +16 = N
8.) +85 – +12 = N
9.) –6 –2 = N
10.) +13 – +12 = N SOMEONE PLEASE ANSWER
Answer:
here are the answers to the questions in order
Step-by-step explanation:
7. -7
8. 73
9. -8
10. 1
Add and Subtract Fractions with Unlike Denominators
Daniel decorated the backyard with 4 2/5 yards of pumpkin string lights and
6 3/4 yards of witch-hat string lights to spice up a Halloween party. How many yards
the two string lights did Daniel use?
Answer:11.15
Step-by-step explanation:
sry if its wrong :)
just add them
What number gives a result of −4
when 11
is subtracted from the quotient of the number and 5
?
The required number is 42 which gives a result of −4 when 11 is subtracted from the quotient of the number and 5.
What is the Quotient?A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient. The dividend contains the divisor a specific number of times.
Let n be the number in question; then, we can write the word problem as an equation like this:
⇒ (n/6) - 11 = -4
Add 11 on both sides of the equation,
⇒ (n/6) - 11 + 11 = 11 - 4
⇒ (n/6) = 7
Multiply by 6 on both sides of the above equation, and we get
⇒ n = 42
Hence, the number is 42.
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Which statement best describes a graph of paired points that form a proportional relationship? Responses A straight line can be drawn through all the points, and the line passes through the point (3, 0). A straight line can be drawn through all the points, and the line passes through the point , begin ordered pair 3 comma 0 end ordered pair, . A straight line can be drawn through all the points, and the line passes through the point (0, 3). A straight line can be drawn through all the points, and the line passes through the point , begin ordered pair 0 comma 3 end ordered pair, . A straight line can be drawn through all the points, and the line passes through the point (0, 0). A straight line can be drawn through all the points, and the line passes through the point , begin ordered pair 0 comma 0 end ordered pair, . A straight line cannot be drawn through all the points, but the line passes through the point (0, 0).
The proportional relationship is given by the equations -
y = mx or y = kx or y = mx + b or y = kx + b.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given are the statements describing proportional relationship.
Direct variation of {y} with {x} means that as {x} increases, the value of {y} increases uniformly with it. Mathematically →{K} = y/x = constant.
Scale factor {K} is a dimensionless value that indicates the constant ratio value indicating direct variation.The proportional relationship is given by the equation -y = mx or y = kx or y = mx + b or y = kx + b
Therefore, the proportional relationship is given by the equations -
y = mx or y = kx or y = mx + b or y = kx + b.
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-6z - 18z + 2z + 6z = 16
nvm don't answer
The value of z in the given linear equation in one variable is -1.
What is a single-variable linear equation?By equating it to zero, a linear polynomial over a field, from which the coefficients are extracted, can be converted into a linear equation.
The values that, when employed as stand-ins for the unknowns in such an equation, lead to the equality being true are the solutions.
When there is just one variable, there is just one solution. The term "linear equation" is generally understood to relate to this particular circumstance, when the variable is accurately referred to as the "unknown."
It is possible to interpret each solution as the Cartesian coordinates of a specific point on the Euclidean plane when there are only two variables.
-6z -18z + 2z +6z = 16
-16z = 16
z = -1
Hence, the value of z is -1
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Consider the equation 2x+7=5x−23
. Arrange the variable terms on the right side.
Enter your response in the box.
7=
−23
Answer:4x
Step-by-step explanation:
Determine the slope given graph
Answer:
slope = 4
Step-by-step explanation:
Which group cannot form 8 lines with an equal number of members in each line? A. 881 B. 440 C. 353 D. 224
Answer:
A. 881
C. 353
Step-by-step explanation:
In order to form 8 lines with each line having equal length, the total number of members has to be divisible by 8:
440/8 = 55, so 440 isn't the answer
224/8 = 28, so 224 isn't the answer
881/8 = 110.125. In addition, even numbers can't be divided evenly by odd numbers like 881, so A. 881 is the answer.
Same goes to 353 since 353 is also an odd number that can't evenly divide the even number 8. Hence, C. 353 is the answer as well.
Is this a polynomial?
Use the grouping method to factor x^3 + x^2 + 2x + 2.
A. (x + 1)(x + 2)
B. x(x + 2)(x + 1)
C. (x + 1)(x2 + 2)
D. (x^2 + 1)(x + 2)
use the given data to find the equation of the regression line. examine the scatterplot and identify a characteristic of the data that is ignored by the regression line. x y
The equation of the regression line is Y=2.83+0.52x .
What do you mean by regression line?Linear regression is the statistical technique that is most frequently used to simulate a relationship between two sets of variables. As a result, a data-applicable linear regression equation is produced.
Plotted your points and drew a linear regression line.
What is the formula to calculate the line regression?y = a + bₐₓx
bₐₓ = n∑xy-∑x-∑y
n∑x²- ∑x²
x = 8.81
y = 7.45
∑x² = 947
∑xy=770.95
bₐₓ = 0.52
a = 2.83
y=1.3082X + 3.3436.
Its equation is
y = 2.83+0.52x .
Therefore, the regression line in a scatter plot ignores non-linear properties, so the equation of the reggresion line will be y = 2.83+0.52x .
Your question is incomplete but most probably your full question was
Use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line.
x y
9 7.38
9 6.75
12 13.08
9 7.42
11 7.56
13 8.53
7 5.93
4 5.33
12 8.1
6 6.46
5 5.44
Required:
Create a scatterplot of the data.
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You and your family go to dinner at a local restaurant in Rexburg, Idaho and your online banking report shows that the total dinner bill (food, tax, and tip) was for $42. Suppose that you did not keep your receipt, but you remember you paid a 20% tip for the service.
What was your bill (food and tax) prior to calculating the tip? (tip was paid on the total of food and tax)
$
Number
(Round your answer to the nearest cent.)
Marty buys 12 ounces of granola what fraction of a pound of granola did Marty buy? Please help
The fraction of a pound of granola Marty buys is 3/4.
What is a fraction?A fraction is a part of a whole number, value, and variable.
There are proper and improper fractions, including complex fractions.
Proper fractions are those with the numerator less than the denominator. An improper fraction produces a whole number with a remainder when the denominator divides the numerator.
On the other hand, complex fractions are rational expressions that have some fractions in their numerators, denominators, or both.
1 pound = 16 ounces
The quantity of granola Marty buys = 12 ounces
The fraction of a pound of granola Marty buys = 3/4 (12/16)
Thus, we can conclude that Marty buys 3/4 or 75% of a pound of granola.
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which one shows a line with a slop of 2
The graph with the slope of 2 is the second graph.
How to find the slope of a line?The slope of a line is a measure of its steepness. The slope of a line is the change in dependent variable with respect to the change in the independent variable.
Therefore, let's find the slope of the graph to know the one with the slope of 2.
Hence,
slope = y₂ - y₁ / x₂ - x₁
Using the second graph,
(-1, -1)(0, 1)
slope = 1 + 1 / 0 + 1
slope = 2 / 1
slope = 2
Therefore, the graph with slope of 2 is the second graph.
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ow many ways can you select 7 cookies to buy from a bakery that sells cookies of 3 different flavors (oatmeal, chocolate chip, almond)? we assume that more than 7 cookies are displayed for each flavor. for example, one way is to choose 7 chocolate chip cookies
There are 2187 combinations to select 7 cookies from a bakery that sells cookies of 3 different flavors (oatmeal, chocolate chip, almond).
When selecting 7 cookies from a bakery that sells 3 different flavors, each cookie selected can be one of the 3 different flavors. This means that for the first cookie, there are 3 choices, for the second cookie, there are also 3 choices, and so on for the 7th cookie. This is known as the combinations formula and it can be represented as 3 x 3 x 3 x ... x 3 (3 being repeated 7 times).
Using the 3⁷ formula, we can calculate that there are 2187 ways to select 7 cookies from a bakery that sells cookies of 3 different flavors. This means that there are 2187 unique combinations of cookies that can be selected, assuming that more than 7 cookies are available for each flavor.
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Your question seems incomplete, but I assume the question was:
"How many ways can you select 7 cookies to buy from a bakery that sells cookies of 3 different flavors (oatmeal, chocolate chip, almond)? We assume that more than 7 cookies are displayed for each flavor. For example, one way is to choose 7 chocolate chip cookies."
find the area under the normal distribution curve whose mean is and whose standard deviation is using the given value for as a boundary.
The area under the normal curve with a mean of 20 and a standard deviation of 5 is 0.8413 when x = 25.
The area under the normal distribution curve is calculated using the z-score, which is the number of standard deviations a value is from the mean. To calculate the area under the normal curve for a given mean and standard deviation, one must use the formula:
Area = ½[1 + erf(z)]
Where erf is the Gaussian error function, and z is the z-score.
To calculate the area under the curve given a boundary x, the z-score must be calculated first. This is done using the formula:
z = (x - mean) / standard deviation
Substituting this into the formula above gives:
Area = ½[1 + erf((x - mean) / standard deviation)]
For example, if the mean is 20 and the standard deviation is 5, and the boundary value is x = 25, the area under the normal curve is calculated as follows:
z = (25 - 20) / 5 = 1
Area = ½[1 + erf(1)] = 0.8413
Therefore, the area under the normal curve with a mean of 20 and a standard deviation of 5 is 0.8413 when x = 25.
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Please help!!
Find the third, fourth, and tenth terms of the sequence described by the rule.
A(n) - 3+ (n-1)(5)
A(3)=
A(4)=
A(10)=
Answer:
A(3) = 13
A(4) = 18
A(10) = 48
Step-by-step explanation:
This seems like a plug and play.
Starting with A(3). Everywhere you see an n, you'll replace it with a 3, as follows;
3 + (3-1)(5) = ?
We'll solve it step by step. First is 3-1. That's 2, bringing it to
3 + (2)(5).
2 times 5 is 10, bringing it to
3 + 10.
3 + 10 = 13, which concludes
A(3) = 13.
Now doing it for the remaining 2.
3 + (4-1)(5)
3 + (3)(5)
3 + 15
A(4) = 18
Last one...
3 + (10-1)(5)
3 + (9)(5)
3 + 45
A(10) = 48
What is 11/12 = 3/4h?
h=
The value of h in the algebraic equation in fraction 11/12 = 3/4h is equal to 9/11
How to solve for the value of h in the algebraic equationWe shall first find the lowest common multiple LCM of the denominators to help us clear the fractions, before then simplifying further for the value of h as follows:
LCM of the denominators 12 and 4h is 12h
multiply both sides by the LCM
11/12 × 12h = 3/4h × 12h
11 × h = 3 × 3
11h = 9
divide both sides by the coefficient of h
11h/11 = 9/11
h = 9/11
Therefore, the value of h in the algebraic equation in fraction 11/12 = 3/4h is equal to 9/11.
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Let m = 3.
Enter >, <, or = to compare the expressions.
4m−145m−4
Answer:
=
Step-by-step explanation: Please mark brainliest
Substitute 3 in for m and solve
4m - 1 = 4(3) - 1 = 11
5m - 4 = 5(3) - 4 = 11
Answer:
Step-by-step explanation:
P&R3 model and solve
problems using linear
equations of the form:
ax = b *
x
a
= b, a ≠ 0*
ax + b = c *
x
a
+ b = c ,a ≠ 0*
a x( ) + b = c *
ax + b = cx + d *
* a bx ( ) + c = d ex ( ) + f
*where a, b, c, d, e, and f [C,
CN, PS, V]
1. Introduction to Solving Linear Equations (pg. 4-7)
• Model the solution of a given linear equation using concrete or
pictorial representations, and record the process.
Algebra stones and Algebra Tiles.
Solve x + 5 = 10 , x − 7 = 10 , 2x = 10 , x
3 = 10
2. Solving equations of the form ax+b=c and a/c +b=c (pg. 8-10)
• Solve a given linear equation symbolically.
• Solve a given problem using a linear equation and record the
process.
Solve. 4m+3=31 & 2
5
m − 5 = 3
3. Solving equations of the form a(x+b)=c and ax+b=cx+d(pg. 11-14)
• Determine, by substitution, whether a given rational number is a
solution to a given linear equation.
Solve. 4(m+3)=40 & 6m+3=2m+15
Is m=5 a solution to the equation 2(m + 2) = 14 ?
4. More practice with ax+b=cx+d (Pg. 15-18)
• Identify and correct an error in a given incorrect solution of a
linear equation
Solve. 2(m+1)+4m=4(m-2)+6.
5. Solve equation with fractions. (Pg. 19-23)
• Solve a given linear equation symbolically. Solve m
3 + 2m
5 − 1
2
= 2
6. Solve Linear equations without numbers. (Pg. 24-28)
• Solve a given linear equation symbolically.
Solve for m. )( =+ BnmA
P&R4 explain and illustrate
strategies to solve single
variable linear inequalities with
rational coefficients
within a problem-solving
context.
7. Introduction to linear inequalities (Pg. 29-33)
• Translate a given problem into a single variable linear inequality
using the symbols ≥, >, < , or ≤ .
• Determine if a given rational number is a possible solution of a
given linear inequality.
Write an expression to represent the following
statement: Melanie needs at least $280 for snow
boarding.
8. Inequalities that Include Addition and Subtraction (Pg. 34-37)
• Generalize and apply a rule for subtracting a positive or
negative number to determine the solution of a given inequality.
• Generalize and apply a rule for multiplying or dividing by a
positive or negative number to determine the solution of a given
inequality.
• Solve a given linear inequality algebraically and explain the
process orally or in written form.
• Verify the solution of a given linear inequality using
substitution for multiple elements in the solution.
Solve 2x + 5 < 25 and verify your solution.
True or False.
If −2x > −10 then x > 5 .
9. Solving Problems with Linear Inequalities (Pg. 38-41)
• Compare and explain the process for solving a given linear
equation to the process for solving a given linear inequality.
• Graph the solution of a given linear inequality on a number line.
• Compare and explain the solution of a given linear equation to
the solution of a given linear inequality.
• Solve a given problem involving a single variable linear
inequality and graph the solution.
Vertical Wireless charges $50/ month plus $0.25 for
all minutes above 400 minutes per month. Frue Gal has
decided that she does not want to pay more than $70
per month. Write an inequality to represent how many
minutes she can use per month without going over her
$70 limit. Approximate your solution on the number
line
10. Chapter Review and Practice Test
• Help students develop sound study habits.
• Many students will graduate high school saying they do not
know how to study for math tests.
11. Go over Practice Test
12. Unit Evaluation
the possible answers in the question mark are half or twice or eight times for both of the question marks. ASAP I NEED HELP
The size of each group will be half as big.
There will be twice as many groups.
How to divide fractions?We want to find out what is going to happen if we divide by 8/4 instead of 4/5.
The total of the tape diagram is 3¹/₅ = 16/5 and as such if we are going to divide by 4/5 we will have;
16/5 ÷ 4/5 = 4
However if we are dividing by 8/5, it means that the solution is;
16/5 ÷ 8/5 = 2
Thus, the solution will be half as big.
There will be twice as many groups.
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1. Match each equation with an equivalent equation. Some of the answer choices are
not used.
A. 3x + 6 = 4x+7
B. 3(x + 6) = 4x+7
C. 4x + 3x = 7-6
1.9x = 4x +7
2. 3x + 18 = 4x+7
3.3x = 4x + 7
4. 3x1 = 4x
5.7x = 1
Answer: Match each equation with an equivalent equation. Some of the answer choices are
not used.
A. 3x + 6 = 4x+7
B. 3(x + 6) = 4x+7
C. 4x + 3x = 7-6
1.9x = 4x +7
2. 3x + 18 = 4x+7
3.3x = 4x + 7
4. 3x1 = 4x
5.7x = 1
A. 3x + 6 = 4x+7 = 3
B. 3(x + 6) = 4x+7 = 2
C. 4x + 3x = 7-6 = 5
1.9x = 4x +7 = 3
3x + 18 = 4x+7 = 2
3.3x = 4x + 7 = 1
3x1 = 4x = not used
5.7x = 1 = not used
So,
3x + 6 = 4x+7 matches with 3
3(x + 6) = 4x+7 matches with 2
4x + 3x = 7-6 matches with 5
1.9x = 4x +7 matches with 3
3x + 18 = 4x+7 matches with 2
3x = 4x + 7 matches with 1
3x1 = 4x is not used
7x = 1 is not used
Step-by-step explanation:
What is 0.55 times 20.1?
(With work pls)
Answer:
0.55 times 20.1 is equal to 11.055
Step-by-step explanation:
To show work, we can simply multiply 0.55 by 20.1 using long multiplication.
0.55
20.1
0.55
+11.05
11.055
So 0.55 times 20.1 is equal to 11.055
Using the theory vectors, find all possible fourth corners to parallelograms that have vertices (1,1), (4,2), and (1,3)
So, the possible fourth corners are (4,4) and (-2,2).
Given the three vertices of a parallelogram (1,1), (4,2), and (1,3), we can use vector algebra to find the fourth corner. We know that opposite sides of a parallelogram are parallel, and therefore have the same vector direction. We can use this property to find the vector pointing from one corner to another and then use this vector to find the fourth corner.
One possible method is:
Find the vector pointing from (1,1) to (4,2) by subtracting the coordinates of the first point from the coordinates of the second point: (4,2) - (1,1) = (3,1)Find the fourth corner by adding this vector to the third point: (1,3) + (3,1) = (4,4)Another possible method is:
Find the vector pointing from (4,2) to (1,3) by subtracting the coordinates of the second point from the coordinates of the third point: (1,3) - (4,2) = (-3,1)Find the fourth corner by adding this vector to the first point: (1,1) + (-3,1) = (-2,2)So, the possible fourth corners are (4,4) and (-2,2).
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Identify the kind of sample that is described.
A football coach randomly selected the varsity or junior varsity team and then asks all players from that team their opinion on a new logo.
A. Stratified
B. Simple Random
C. Voluntary Response
D. Cluster
E. Systematic
The given sample of the randomly selected players from the teams as described is a stratified sample. Hence, the right answer is option A.
In a stratified sample, the population is divided into groups (or strata) based on some characteristic, and a random sample is selected from each group. In this case, the population is the football players, and the groups are the varsity and junior varsity teams. The coach randomly selects one of these teams and then asks all players from that team their opinion on a new logo.
This type of sampling is used when the population is divided into subgroups that are different in some way, and the researcher wants to ensure that these subgroups are represented in the sample. In this case, the coach wants to ensure that both varsity and junior varsity players are represented in the sample, as they may have different opinions on the new logo.
It's not a simple random sample because he selected the team first and then the players. Also, it's not a voluntary response sample because the coach is selecting the players.
It's not a cluster sample because the coach is not selecting the players based on location or geographic proximity, and it's not a systematic sample because he is not selecting the players based on the order in which they appear in a list or a database.
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