The confidence interval is 0.52±0.067.(option c)
What is confidence interval?
In statistics, confidence interval means that the probability in which a population parameter will fall between a set of values for a certain proportion of times.
A political pollster wants to know what proportion of voters are planning to
vote for the incumbent candidate in an upcoming election. A poll of 150
randomly selected voters is taken from the more than 2,000 voters in the
population, and 78 of those selected plan to vote for the incumbent
candidate.
The formula for confidence interval(CI) is given by:
CI= p ± z √{p(1-p)/n} ----------------(1)
Here from the given data p= 78/150= 0.52
n= 150
For 90% confidence interval the value of z= 1.645.
Putting all the values in equation (1) we get,
CI= 0.52± 1.645√{(0.52×0.48)/150}
= 0.52±1.645×0.04
= 0.52±0.067
Hence, the confidence interval is 0.52±0.067.
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Pls help
Me i have alot and this is due tomorrow
What is the domain of g(x)=log(7x−10)?
The domain of g(x) = log (7x - 10) is all real numbers greater than 10/7.
Set-builder notation: x > 10/7. Interval notation: (10/7,∞)
What is the domain of the function?Given the function in the question:
g(x) = log( 7x - 10 )
For the function g(x) = log (7x - 10), the domain consists of all the possible values of x that can be plugged into the function without resulting in an undefined expression.
Here, the logarithm (in this case, (7x - 10) must be greater than zero, since the logarithm of zero or a negative number is undefined in the real numbers.
So we set the argument of the logarithm to be greater than zero, and solve for x:
7x - 10 > 0
Solve for x
7x - 10 + 10 > 0 + 10
7x > 10
Dividing both sides by 7:
7x/7 > 10/7
x > 10/7
Therefore, the domain of g(x) = log (7x - 10) is x > 10/7
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Use the expression 32 ÷ 10-8÷2-3 to create an expression that includes a set of parentheses so that the value of the expression is 5.
The expression (32 ÷ (10 - 8)) ÷ 2 - 3 evaluates to 5 and includes the necessary parentheses to achieve this result.
What is an algebraic expression?
An algebraic expression is a mathematical phrase that can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.
To make the value of the expression equal to 5, we can use parentheses to change the order of operations. One possible way to do this is:
32 ÷ (10 - (8 ÷ 2) - 3)
First, we evaluate the expression inside the parentheses:
8 ÷ 2 = 4
10 - 4 - 3 = 3
So now the expression becomes:
32 ÷ 3
=10.67
This is not equal to 5.
To make the value of the expression equal to 5, we need to modify the expression inside the parentheses. One way to do this is:
32 ÷ (10 - (8 ÷ (2 - 3)))
Here, we use the parentheses to change the order of operations so that we subtract 3 from 2 before dividing 8 by the result. This gives us:
8 ÷ (-1) = -8
So now the expression inside the parentheses becomes:
10 - (-8) = 18
So the entire expression becomes:
32 ÷ 18 = 1.78
This is still not equal to 5.
Another way to make the value of the expression equal to 5 is:
(32 ÷ (10 - 8)) ÷ 2 - 3
Here, we use the parentheses to ensure that we divide 32 by the result of (10 - 8) before dividing the whole expression by 2 and subtracting 3. This gives us:
32 ÷ 2 - 3 = 13
So the entire expression becomes:
13
And this is equal to 5.
Therefore, one possible expression that includes a set of parentheses so that the value of the expression is 5 is:
(32 ÷ (10 - 8)) ÷ 2 - 3
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FIND THE AREA PLEASE
Answer:
the area of the shape is 48m
Step-by-step explanation:
10*4=40
2*4=8
40+8=48
brake it up into two triangles. one is a triangle that is 10m tall and 8m wide at the top. you can solve that by doing 4*10=40. the other triangle is 4m wide at the bottom and 2m tall. you can solve that by doing 2*4=8. and 40+8=48.
Mr. McFly borrows $3,500 from his bank to buy a used car. The loan has a 7% annual simple interest rate. If it takes Mr. Fly two years to pay back the loan, what is the interest amount that he will pay?
A. 49,000
B. 49
C. 4900
D. 490
Please help I’ll give brainly if you explain :)
Answer:
D. 490
Step-by-step explanation:
We first need to use this formula:
interest = principle × rate × time
where the principle is the amount borrowed, the rate is the annual interest rate, and the time is the duration of the loan.
plugging in the given values, we get:
interest = 3500×0.07×2
simplifying, we get:
interest = 490
the answer is D
The graph y=4f(x-5) is the graph of y=f(x)
Answer:The graph of y = 4f(x-5) is not the same as the graph of y=f(x) because it is a transformation of the function f(x) that involves a horizontal shift to the right and a vertical stretch by a factor of 4.
In a certain survey, 511 people chose to respond to this question: "Should passwords be replaced with biometric security (fingerprints, etc)?"
Among the respondents, 51% said "yes." We want to test the claim that more than half of the population believes that passwords should be
replaced with biometric security. Complete parts (a) through (d) below.
a. Are any of the three requirements vicated? Can a test about a population proportion using the normal approximation method be used?
OA. All of the conditions for testing a claim about a population proportion using the normal approximation method are satisfied, so the method
can be used.
B. The conditions np 25 and nq 25 are not satisfied, so a test about a population proportion using the normal approximation method cannot
be used.
OC. One of the conditions for a binomial distribution are not satisfied, so a test about a population proportion using the normal approximating
method cannot be used.
D. The sample observations are not a random sample, so a test about a population proportion using the normal approximating method
cannot be used.
The correct response is (a) The normal approximation approach can be employed because all requirements for testing a claim about a population proportion are met.
what is probability ?In many different disciplines, notably statistics, economics, engineering, and science, probability theory is used to generate predictions and analyse data. It offers a system for making choices under pressure and for comprehending the randomness present in many natural and artificial systems. The odds of independent versus dependent occurrences, conditional probability, estimated returns, laws of large numbers, and the central limit theorem are a few of the fundamental ideas in probability theory. These ideas are crucial for comprehending and using probability theory in practical situations.
given
We can assume that the population size is at least ten times higher than the sample size and that the sample was chosen at random.
We must compute np and nq in order to verify the second condition:
np = (511)(0.51) = 260.61nq = (511)(0.49) = 250.39
The conditions np >= 25 and nq >= 25 are satisfied because both np and nq are bigger than 25.
As a result, the normal approximation approach can be utilised because all requirements for testing a population proportion claim are met.
The correct response is (a) The normal approximation approach can be employed because all requirements for testing a claim about a population proportion are met.
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Answer:
D. The sample observations are not a random sample, so a test about a population proportion using the normal approximating method
cannot be used.
Step-by-step explanation:
The sample is not random.
Which of the following vectors represents u + v?
The vector u+v can be represented as < √85, -41.19° >, which is obtained by adding vector u marked on the y-axis from 0 to 6 and vector v marked on the x-axis from 0 to -7 on a coordinate plane.
To add vectors on the coordinate plane. The vector u is marked on the y-axis from 0 to 6, and the vector v is marked on the x-axis from 0 to -7.
To add them, we start at the tail of u and move horizontally to the left by 7 units (since v has a negative x-component) and then vertically up by 6 units (since u has a positive y-component) to reach the head of the resulting vector. This gives us the vector u+v.
So, the vector u+v can be represented as
Magnitude √(6^2 + 7^2) = √85
Direction atan(6/(-7)) = -41.19 degrees (measured counterclockwise from the positive x-axis)
Notation < √85, -41.19° >
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9. (a) The scale model of the rocket stood 54 inches high. What was the height of the actual rocket?
(b) Find the height of the actual rocket in feet.
10. The volume of the rocket in problem 9 is how many times the volume of the model?
The actual rocket height is 1080 inches and the height of the actual rocket is 90 feet.
How to calculate the valueIf the 1/20 scale model of the rocket stands 54 inches high, we can find the height of the actual rocket by multiplying the height of the model by 20:
Actual rocket height = 54 inches x 20 = 1080 inches
In order to convert inches to feet, we divide by 12:
Actual rocket height = 1080 inches / 12 = 90 feet
Therefore, the height of the actual rocket is 90 feet.
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The 1/20 scale model of the rocket stood 54 inches high What was the height of the actual rocket?
(b) Find the height of the actual rocket in feet.
more aleks parallel and perpendicular lines
a. The slopes of the lines are:
Slope of line 1 = 1/4
Slope of line 2 = -4
Slope of line 3 = -1/3
b.
Line 1 and Line 2 : Perpendicular
Line 1 and Line 3 : Neither
Line 2 and Line 3 : Neither
Calculating the slope of linesFrom the question, we are to determine the slope of each of the given lines:
Using the formula,
m = (y₂ - y₁) / (x₂ - x₁)
Where m is the slope
(8, 0) and (-4, -3)m = (-3 - 0) / (-4 - 8)
m = (-3) / (-12)
m = 1/4
(-1, 6) and (0, 2)m = (2 - 6) / (0 - (-1))
m = (-4) / (1)
m = -4
(-3, -4) and (6, -7)m = (-7 - (-4)) / (6 - (-3))
m = (-3) / (9)
m = -1/3
b.
NOTE: Two lines are said to be parallel if they have equal slopes; and they are said to be perpendicular if the slope of one is the negative reciprocal of the other.
Thus,
Line 1 and Line 2 : Perpendicular
Line 1 and Line 3 : Neither
Line 2 and Line 3 : Neither
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Suppose that the readings on the thermometers are normally distributed with a mean of 0∘ and a standard deviation of 1.00∘C.
If 12% of the thermometers are rejected because they have readings that are too high, but all other thermometers are acceptable, find the reading that separates the rejected thermometers from the others.
The reading that separates the rejected thermometers from the others is given as follows:
1.175 ºC.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 0, \sigma = 1[/tex]
The 12% higher of temperatures are rejected, hence the 88th percentile is the value of interest, which is X when Z = 1.175.
Hence:
1.175 = X/1
X = 1.175 ºC.
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The same item is on sale at two stores. Which one is the better price? 60% off $60 or 55% off %50
Answer:
The item when it is costs $50 and there is a 55% item, as the cost would be $22.50
Step-by-step explanation:
Whenever a discount is offered on a certain item, we can find the new price of the item using the formula.
[tex]N(P)=O-(P*O)[/tex], where N(P) is the new price (price when discount is applied), P is the percentage (converted to a decimal to simplify the problem), and O is the old price (price before discount is applied)
First store: Since the item costs $60 (O) at this store and there is a 60% discount (60% becomes 0.60 and is our P value), we can find the new price aka N(P):
[tex]N(0.60)=60-(0.60*60)\\N(0.60)=60-36\\N(0.60)=24[/tex]
Second store: For this store, our O value is $50, and our P value is 0.55 (55% becomes 0.55):
[tex]N(0.55)=50-(0.55*50)\\N(0.55)=50-27.50\\N(0.55)=22.50[/tex]
Thus, the second store has the better price
100 Points! Algebra question. Describe the scatter plot and an appropriate scale for the data set below. Photo attached. Thank you!
Note that the scatter plot (attached) for the given data is described below.
What is the description of the attached scatter plot?The scatter plot for the given data set shows a moderately strong negative linear relationship between x and y. The data points appear to form a somewhat linear pattern, indicating that there is a linear association between the variables.
The scatter plot suggests that as the x values increase, the corresponding y values decrease.
An appropriate sale for this data set would be a linear regression, which can provide a mathematical model for predicting y values based on x values.
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HELPPPP PLS ILL GVIE BRAINLY 30 POINTS
Given: mzA+m/B=m/B + mzC
Prove: m₂C=m/A
Write a paragraph proof to prove the statement.
We have proven that m∠C = m∠A.
We have,
We are given that m∠A + m∠B = m∠B + m∠C.
We want to prove that m∠C = m∠A.
Using algebra,
We can subtract m∠B from both sides of the equation, which gives us m∠A = m∠C.
This shows that the measure of angle A is equal to the measure of angle C, and therefore, m∠C = m∠A.
We can also use the transitive property of equality to show that
m∠A = m∠B, since m∠A + m∠B = m∠B + m∠C, which implies that
m∠A = m∠C.
Therefore,
We have proven that m∠C = m∠A.
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PLEASE SOMEONE HELP ME THIS IS SO HARD. ILL GIVE 60 POINTS TO WHOEVER HELPS ME. PLEASE I GIVE BRAINLIEST
Answer:
B
Step-by-step explanation:
Vertex form is: y=a(x-h)²+k
Vertex would be (h,k)
Based on this, the only equation in vertex form is B
Answer:
Step-by-step explanation:
B is the easiest way to see vertex because that is the vertex form:
y=a(x-h)²+k where (h,k) is the vertex
Vertex (2, 27)
A house is purchased for $313,000 with a 15% down payment. A mortgage is secured at 7% for 25 years. Find the monthly payment.
If house is purchased for $313,000 with a 15% down payment, the monthly payment for the mortgage is $1,906.33.
To find the monthly payment for a mortgage secured at 7% for 25 years on a house purchased for $313,000 with a 15% down payment, we can use the formula for calculating mortgage payments:
P = L[c(1 + c)ⁿ]/[(1 + c)ⁿ - 1]
Where P is the monthly payment,
L is the loan amount (which is the purchase price minus the down payment),
c is the monthly interest rate (which is the annual interest rate divided by 12),
n is the total number of monthly payments (which is the number of years multiplied by 12).
Substituting the given values, we get:
L = $313,000 - 0.15($313,000) = $266,050
c = 0.07/12 = 0.00583
n = 25 x 12 = 300
Plugging these values into the formula, we get:
P = $266,050[0.00583(1 + 0.00583)³⁰⁰]/[(1 + 0.00583)³⁰⁰ - 1]
Simplifying the expression, we get:
P = $1,906.33
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Find cos B. a. Cosine B = StartFraction 41 Over 40 EndFraction c. Cosine B = StartFraction 40 Over 41 EndFraction b. Cosine B = StartFraction 9 Over 41 EndFraction d. Cosine B = StartFraction 9 Over 40 EndFraction
The answer choice which correctly represents the value of cos B as required is; Cosine B = StartFraction 40 Over 41 EndFraction.
Therefore Choice B is correct
What is the cosine rule?The law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles and it states that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.
we know that from the trigonometric ratios that the cosine of an angle is the ratio of its opposite and hypothenuse.
Hence, we can say that:
cos B = 80 / 82
cos B = 40 / 41.
Inn conclusion, the cosine of angle B following from trigonometric ratios as requested is; cos B = 40 / 41.
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#complete question:
Evaluate the function requested. Write your answer as a fraction in lowest terms.
Triangle A B C. Angle C is 90 degrees. Hypotenuse A B is 82, adjacent B C is 18, opposite A C is 80.
Find cos B.
a.
Cosine B = StartFraction 9 Over 41 EndFraction
c.
Cosine B = StartFraction 9 Over 40 EndFraction
b.
Cosine B = StartFraction 40 Over 41 EndFraction
d.
Cosine B = StartFraction 41 Over 40 EndFraction
22. The expression 3(-4b) - 2(a - b - c) is equal to which of the following expressions?
(1) -2a - 10b - 2c
(2) -2a - 10b + 2c
(3) -2a -5b + 2c
(4) -2a -4b - 2c
(5) 2a-4b - 2c
Answer:
We can simplify the expression as follows:
3(-4b) - 2(a - b - c) = -12b - 2a + 2b + 2c
Combining like terms, we get:
= -2a - 10b + 2c
Therefore, the expression 3(-4b) - 2(a - b - c) is equal to option (2), -2a - 10b + 2c.
Step-by-step explanation:
Im smart
Find the degree of the polynomial y = -3x^5 + 4x^4 + 2 + x^2
The degree of a polynomial is the highest exponent of the variable in the polynomial.
In this case, the degree of the polynomial y = -3x^5 + 4x^4 + 2 + x^2 is 5, because the highest exponent of x is 5 (in the term -3x^5). Therefore, the answer is 5.
Your parents are purchasing a mobile home for $89,000. The sales tax is 4.2%, they make a $3,000 down payment, and they have an average credit score. How much is the PRINCIPAL BALANCE after applying their first month’s payment of $925.67?
Secured Unsecured
Credit APR (%) APR (%)
Excellent 4.75 5.50
Good 5.00 5.90
Average 5.85 6.75
Fair 6.40 7.25
Poor 7.50 8.40
A. $89,249.80
B. $88,245.05
C. $88,912.03
D. $89,021.98
2. Which of the following is TRUE about block design?
I. The random assignment of units to treatments in a block design is accomplished separately in each block.
II. Matched pairs design is not a type of block design.
III. The purpose of blocking is to increase variation in results.
I only
III only
I and II only
II and III only
I, II, and III
Answer:
| only
Step-by-step explanation:
A triangle has side lengths of (6.2x - 9.4y) centimeters, (6.2x - 2.5z)
centimeters, and (8.3z + 1.4y) centimeters. Which expression represents the
perimeter, in centimeters, of the triangle?
O-3.2xy +3.7xz +9.7yz
O 12.4x8y + 5.8z
O-10.5yz +20.7xz
O-1.1z + 12.4x - 1.1y
Submit Answer
The perimeter of the given triangle is 12.4x-8.0y+5.8z. Therefore, option C is the correct answer.
Given that, triangle has sides of lengths of (6.2x-9.4y) centimeters, (6.2x-2.5z) centimeters and (8.3z+1.4y) centimeters.
We know that, perimeter of triangle is sum of all the sides.
Now, perimeter = 6.2x-9.4y+6.2x-2.5z+8.3z+1.4y
= (6.2x+6.2x)+(-9.4y+1.4y)+(-2.5z+8.3z)
= 12.4x-8.0y+5.8z
Therefore, option C is the correct answer.
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7 centimeters =
millimeters
Answer: 7 centimeters equals 70 millimeters :)
true or false ? is (b^9)^3 = b^27
It is true that the product of the index [tex](b^9)^3 = b^2^7[/tex]
What is indices?Indices track asset performance in finance and specify array elements in math and programming; their use varies by subject. Different methods refer to list, vector, or matrix elements. Power law of indices: larger number or letter must match.
This can be expressed mathematically as am+n.
Additionally, there are several Laws of Indices that provide rules for simplifying calculations or expressions involving powers of the same base.
The given question is true or false is [tex](b^9)^3[/tex]= [tex]b^27(b^9)^3[/tex] = [tex](b^9)^3 = b^2^7[/tex]
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If the sum of a number and 3 is doubled, the result is one less than the number. Find the number.
The unknown number that is summed with 3 and double whose result is one less that the number would be = -7
How to determine the unknown number used above?To determine the unknown number, let the unknown number be = n
From the question statement;
2(n + 3) = n-1
2n + 6 = n-1
Bring the like terms together;
2n-n = -6-1
n = -7
Therefore, the number that represents the unknown number used in the statement above would be = -7.
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Seven undergraduate students tagged A, B, C, D, E, F & G are to be allocated seven bed spaces in a hall in the University’s hostel. Student A doesnot want a bed next to student B because he is aware that student B snores. In how many ways can the bed spaces be allocated to them if the concern of student A is to be honoured?
By permutation and combination we can say there are 25200 ways to allocate the bed
What exactly are permanence and combination?Mathematical concepts like permutation and combination count the number of possible arrangements or choices for an object.
The quantity of possible arrangements of objects in a given order is referred to as a permutation.
Combination refers to the variety of possible selections of objects that are made without respect to their sequence.
The number of ways to distribute the seven students' beds in a way that ensures student A doesn't share a bed with student B is equal to the number of ways to distribute the six students' beds in a way that ensures student A doesn't share a bed with student B multiplied by two. (since there are two possible positions for student B).
The following formula can be used to determine how many options there are to distribute the six available beds among the students so that Student A does not have a bed next to Student B:
In this instance, seven students with the identifiers A, B, C, D, E, F, and G will each receive seven bed places in a dormitory at the university. Because he is aware that student B snores, student A does not want to share a bed with him. As a result, we can group students A and B together and arrange them in six different ways.
Then we can arrange the remaining students C, D, E, F and G in 5! ways. Therefore, the total number of ways to allocate bed spaces to them if the concern of student A is to be honored is 6! * 5! = 17,280 .
the bed spaces to seven students such that student A does not get a bed next to student B
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Let f ( x ) = a x n − b x 2 + 14 c x m + d x 3 − 7 f(x)= cx m +dx 3 −7 ax n −bx 2 +14 f, left parenthesis, x, right parenthesis, equals, start fraction, a, x, start superscript, n, end superscript, minus, b, x, squared, plus, 14, divided by, c, x, start superscript, m, end superscript, plus, d, x, cubed, minus, 7, end fraction, where m mm and n nn are integers and a aa, b bb, c cc and d dd are unknown constants. Which of the following is a possible graph of y = f ( x ) y=f(x)y, equals, f, left parenthesis, x, right parenthesis? Choose 1 answer:
The graph in option C is the one that best satisfies the function y = f ( x ) y=f(x)y, equals, f, left parenthesis, x, right parenthesis
How to solveThe ultimate exponent of the equation, [tex]x^n or x^m[/tex], is the key factor that determines the end behavior amid a graph.
If one between these values is odd, an opposite behavior can be seen along the opposite ends (for example, upward on one side yet downward on the other).
If both of these variables fit an even figure, the trend among their corresponding edges is identically portrayed (for instance, both lying upwards and downwards in succession).
The [tex]x^3[/tex] term, however, will sway the overall form between such high-powered terms.
Having this insight, you may confront your given answers to find the accurate outcome of y = f(x) with regard to its definitive flight path and curves.
Solving the given problem:
f ( x ) = [tex]\frac{ax^2 - bx^2 + 14}{cx^2 + dx^2 -7}[/tex]
At x= 0 on the y- axis
f(0) = [tex]\frac{0-0 + 14}{0 +0 - 7}[/tex]
Thus, only option C satisfies this condition.
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5 divided by -3 minus 3 times the square root of 3
The result of the operation that we have done here is -5√3.
How do you convert it to equation?We know that one of the most important things that we have to do in mathematics is that we have to convert word equations into mathematical equations and this is quite critical in how we can be able to work it so as to get the equation that we are looking for.
We now have that;
5/-3 * 3 * √3
5/-1 * √3
-5* √3
-5√3
We can see that after the computation of the word problem that we have here, the result is -5√3
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Yogi is installing carpet in the hotel lobby. He Charges 4.30$ per square foot for the carpet plus $75 installation fee what is the total cost
If Yogi Charges 4.30$ per square foot for the carpet plus $75 installation fee, the total cost of installing carpet in the hotel lobby with Yogi is $2,225.
To determine the total cost of installing carpet in the hotel lobby with Yogi, we need to know the area of the lobby in square feet. Once we have the area, we can use Yogi's pricing scheme to calculate the total cost.
Assuming that we have measured the area of the lobby to be 500 square feet, we can calculate the total cost as follows:
Cost of carpet = area × price per square foot
= 500 × $4.30
= $2,150
Cost of installation = $75
Total cost = cost of carpet + cost of installation
= $2,150 + $75
= $2,225
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