a) The confidence interval is given as follows: (71.43, 77.17).
b) The manufacturer's claim is not correct, as 78 is not a part of the interval.
c) A sample of 55 employees is needed to achieve the desired margin of error.
What is a t-distribution confidence interval?The bounds of the t-distribution confidence interval, used when only the standard deviation for the sample is known, are given by the equation presented as follows:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
The variables of the equation are presented as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, considering the 95% confidence level and 12 - 1 = 11 df, is of:
t = 2.201.
The remaining parameters, namely sample mean, sample standard deviation and sample size are given as follows:
[tex]\overline{x} = 74.3, s = 4.52, n = 12[/tex]
(obtained using a calculator from the sample given in this problem).
The bounds of the interval are given as follows:
Lower bound: 74.3 - 2.201 x 4.52/sqrt(12) = 71.43.Upper bound: 74.3 + 2.201 x 4.52/sqrt(12) = 77.17.The interval does not contain the number 78, hence it is not a good estimate for the mean amount.
For item c, the z-distribution is used, as the population standard deviation is used, hence the minimum sample size is obtained as follows:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]1.04 = 1.96\frac{3.91}{\sqrt{n}}[/tex]
[tex]1.04\sqrt{n} = 1.96 \times 3.91[/tex]
[tex]\sqrt{n} = \frac{1.96 \times 3.91}{1.04}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96 \times 3.91}{1.04}\right)^2[/tex]
n = 55. (rounded up, as a sample size of 54 would mean that the margin of error would be slightly above 1.04).
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In an election for a corporation seat, there were two candidates. A total of 9,791 votes were polled. 116 votes were declared invalid. The successul candidate got 5 votes for every 4 votes his opponent had. By margin did the successful candidate win?
Margin did the successful candidate win is 5375 - 4300 = 1075.
Given:
In an election for a corporation seat, there were two candidates. A total of 9,791 votes were polled.
116 votes were declared invalid. The successful candidate got 5 votes for every 4 votes his opponent had.
Number of valid votes = 9791 - 116 = 9675.
Let the number of votes of successful candidate = 5x
Let the number of votes of opponent = 4x
5x + 4x = 9675
9x = 9675
divide by 9 on both sides
x = 9675/9
x = 1075
Hence the votes for successful candidate = 5*1075 = 5375.
votes for opponent = 4*1075 = 4300.
Margin by which the successful candidate wins = 5375 - 4300 = 1075.
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How to find x here if the perimeter, diagonal, and length is given?
Answer:
see explanation
Step-by-step explanation:
(a)
perimeter (P) is calculated as
P = 2(l + b) ← l is the length and b the breadth
given l = x and P = 20 , then
2(x + b) = 20 ( divide both sides by 2 )
x + b = 10 ( subtract x from both sides )
b = 10 - x
Using Pythagoras' identity in the right triangle
x² + (10 - x)² = 8²
x² + 100 - 20x + x² = 64 ( subtract 64 from both sides )
2x² - 20x + 36 = 0 ( divide through by 2 )
x² - 10x + 18 = 0 ← as required
(b)
solve using the method of completing the square
x² - 10x + 18 = 0 ( subtract 18 from both sides )
x² - 10x = - 18
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 5)x + 25 = - 18 + 25
(x - 5)² = 7 ( take square root of both sides )
x - 5 = ± [tex]\sqrt{7}[/tex] ( add 5 to both sides )
x = 5 ± [tex]\sqrt{7}[/tex]
Then
x = 5 - [tex]\sqrt{7}[/tex] ≈ 2.35 ( to 3 significant figures )
x = 5 + [tex]\sqrt{7}[/tex] ≈ 7.65 ( to 3 significant figures )
The owner buys jackets for $45 and sells them how many jackets must the owner buy for the total jacket sales to be at least $390
What is the last digit of the number 4^2016?
Answer:
The last number is 4
Step-by-step explanation:
wats the slope?ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ
Hiroshi spends 30 minutes on history homework, 60 minutes on English homework, and x minutes on math homework. One fourth of his total homework time is spent on math. Which equation can be used to find the amount of time Hiroshi spends on his math homework?
StartFraction one-fourth EndFraction left-parenthesis x plus 30 plus 60 right-parenthesis equals x.(x + 30 + 60) = x
StartFraction one-fourth EndFraction left-parenthesis x right-parenthesis equals x left-parenthesis 30 plus 60 right-parenthesis.(x) = x(30 + 60)
StartFraction one-fourth EndFraction x left-parenthesis 30 plus 60 right-parenthesis equals x.x(30 + 60) = x
StartFraction one-fourth EndFraction left-parenthesis x right-parenthesis equals left-parenthesis 30 plus 60 right-parenthesis.(x) = (30 + 60)
An equation that can be used to find the amount of time Hiroshi spends on his math homework would be 1/4(30 + 60 + x) = x
In this question, Hiroshi spends 30 minutes on history homework, 60 minutes on English homework, and x minutes on math homework.
So, his total homework time would be,
(30 + 60 + x)minutes
Also, we have been given One fourth of his total homework time is spent on math.
We need to find an equation that can be used to find the amount of time Hiroshi spends on his math homework.
So, we get an equation,
1/4(30 + 60 + x) = x
Therefore, an equation that can be used to find the amount of time Hiroshi spends on his math homework would be 1/4(30 + 60 + x) = x
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Answer:
c
Step-by-step explanation:
Which option shows an expression meaning 4 less than 5 times
a number?
You can earn 5 coins
4n-5
5n+ 4
5n-4
4n+5
Submit
Answer: 5n - 4
Step-by-step explanation:
n is the number, 5 times the number is 5n. 4 less means subtract 4. So the correct expression is 5n - 4
(-7 + 3) x 3² + ⅖ x (-1.1 - 3.9)
Solution to the fraction (-7 + 3) x 3² + ⅖ x (-1.1 - 3.9) = -38
How to solve fraction?Fractions are expressed in mathematics as a number value that defines a part of a whole or group of objects
To simplify the fraction into a simple form the following steps are followed;
Evaluate (-7 + 3) x 3² + ⅖ x (-1.1 - 3.9)
(-7 + 3) x 9 + ⅖ x (-1.1 - 3.9)
Add the numbers
(-4) x 9 + ⅖ x (-1.1 - 3.9)
Evaluate the exponent
(-4) x 9 + ⅖ x (-5)
Multiply the number
-36 + ⅖ x (-5)
-36 -10/5
Subtract the number from each other
-36 -10/5
=-36-2
Answer = -38
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HELPPPPP pleaseeeeeeeeeeeeeeeeeeeee
hi some 1 help me out
Answer:
3(3+4) IS NOT EQUAL TO 3^3
Step-by-step explanation:
3(3+4)
Expand brackets to get 21 (3x3 = 9, 3x4 = 12, 9 + 12 = 21)
3^3 = 3 x 3 x 3
3x3 = 9
9 x 3 = 27
21 < 27
what is the total cost of cake option 1
Answer:
give me the question dude......
Step-by-step explanation:
Directions
Read the instructions for this self-checked activity. Type in your response to each question, and check your answers. At the end of the activity, write a
brief evaluation of your work.
Activity
In the first Lesson Activity, you derived an equation to model a car wash. The equation is y = 5x - 75. In this activity, you will graph this equation.
Question 1
Is it possible to graph the line that represents this equation by using two points found in the previous Lesson Activity, (15, 0) and (0, -75)? Explain
your answer.
Yes, the graph goes through those two points.
What is Graph?
In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.
The points on the graph often represent the relationship between two or more things.
What is linear equation?
A linear equation is an algebraic equation of the form y=mx + b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.
Explanation for the answer:
The equation can be graphed by plotting the two given points and drawing a line through them. Such a graph is shown in the attachment.
You can graph a line for any linear equation from any two points that fit the equation. So you can use the points (0, -75) and (15, 0) to graph the line representing the situation.
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What is the equation of this graphed line?
Answer:
y = 2x + 2
Step-by-step explanation:
(y-y1)/(y2-y1)=(x-x1)/(x2-x1)
(y-6)/(-6-6)= (x-2)/(-4-2)
(y-6)/-12 = (x-2)/-6
y-6 = 2x-4
y = 2x -4 + 6
y = 2x + 2
A standard toilet uses 1.6 gallons per flush. If a toilet is flushed two times per day, how much water will be used in a week (7 days)?
Total Water Used by a standard flush in a week i.e. 7 days is 22.4 gallons.
What is Multiplication?
In mathematics, multiplying implies adding equal groups. The number of items in the group grows as we multiply.
Solution:
Given that,
The standard toilet uses 1.6 gallons of water per flush
Also, it is flushed twice a day
To Find, Total water used in a week i.e. 7 days
Since, flush uses 1.6 gallons water per flush
Total water used in a day is 2*1.6 = 3.2 gallons
This implies,
Total water used in 7 days = 7 * 3.2 = 22.4 gallons
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A student earned the scores in the data set in one course.
{88, 72, 68, 78, 94}
What is the mean of the scores?
Answer:
80
Step-by-step explanation:
the mean of a data set is calculated as
mean = [tex]\frac{sum}{count}[/tex] = [tex]\frac{88+72+68+78+94}{5}[/tex] = [tex]\frac{400}{5}[/tex] = 80
The ratio of teachers to students is 1 to 26. Find an equivalent ratio
Answer:
2:52
Step-by-step explanation:
Multiply by 2
-
Which graph represents the function f(x) = |x] – 4?
Graph for the modulus function is as follows.
What is modulus function?
A modulus function is a function that determines a number or variable's absolute value.
Main body:
Given that,
Which graph represents the function f(x) = 4⌈x⌉?
Now,
to represent the graph of Y = IxI-4 .
So,
Taking x = 0, we get
Y = IxI -4
Y = I0I -4
Y = -4
Taking x = 1, we get
Y = IxI - 4
Y = I1I -4
Y = -3
Taking x = 2, we get
Y = IxI - 4
Y = I2I - 4
Y = -2.
Taking x = -1, we get
Y = IxI - 4
Y = I-1I - 4
Y = 1 -4
Y = -3
Taking x = -2, we get
Y = IxI - 4
Y = I-2I - 4
Y = -2
Hence the graph for the function is as follows.
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Q1) Reggie's annual salary increased from $43,400 to
$46,300 this year and his colleague Gerald's annual
salary increased from $39,970 to $43,720. Who received
a higher rate of increase this year?
Answer:
Gerald received the higher rate of increase
Step-by-step explanation:
7 The profit function, p(x), for a company is the
cost function, c(x), subtracted from the revenue
function, (x). The profit function for the
Acme Corporation is p(x) = -0.5x² + 250x - 300
and the revenue function is r(x) = -0.3x² + 150x.
The cost function for the Acme Corporation is
1) c(x) = 0.2x² - 100x + 300
2) c(x) = 0.2x² + 100x + 300
3) c(x) = -0.2x² + 100x - 300
4) c(x) = -0.8x² + 400x - 300
The cost function for the Acme Corporation is -0.2x² + 100x - 300. a cost function, transfers an event or the values of one or more variables onto a real number that signifies the event's "cost" in real terms.
How to find cost function ?A loss function, also known as a cost function, is a function used in mathematical optimization and decision theory that transfers an event or the values of one or more variables onto a real number that intuitively represents some "cost" connected to the occurrence. A loss function is the goal of an optimization problem.
The event in question is some function of the difference between the estimated and true values for a particular instance of data, and in statistics, parameter estimation is typically done using a loss function.
Given that the profit function is
p(x) = 0.5x^2 + 250x+300
also given that the revenue is given as
r(x) = 0.3x^2 + 150x
we know that profit= revenue - cost
hence cost = revenue-profit
cost = r(x) -p(x)
cost= 0.3x^2 + 150x-(0.5x^2 + 250x+300)
cost= 0.3x^2 + 150x-0.5x^2 - 250x-300
collect like terms
cost=0.3x^2-0.5^2+150x-250x-300
The cost function for the Acme Corporation = -0.2x^2-100x-300
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ANSWER PLEASE!
Armando lost 975 coins playing his
favorite video game. He lost the same number of coins in each of the 15 levels he played. What was the change in Armando's coins at the end of each level of the game?
Answer: 81.25
Step-by-step explanation:
Answer:
Armando lost 65 coins each level.
Step-by-step explanation:
Given information,
→ Armando lost 975 coins playing his favorite video game.
→ He lost the same number of coins in each of the 15 levels he played.
Forming the equation,
→ 15x = 975
Now required value of x will be,
→ 15x = 975
→ x = 975/15
→ [ x = 65 ]
Hence, he lost 65 coins each level.
Please help me with these sorry for how many there are
Answer: 19.2, 1.7, 15.93, 0.0512
Step-by-step explanation:
We can multiply these straight across but the trick with decimals is that your answer needs to have the same decimal place distance as what you are multiplying. In the first question, we go one decimal place. In the second, we go two decimal places. In the fourth, we go four decimal places.
Isabelle wanted to arrange her baseball cards in pairs but was one card short . she tried to arrange them by fives and was still one card short. she finally arranged her cards by sevens. what is the least number of cards she could have had?
The Least number of baseball cards Isabella could have is 49
How to determine the least number of cardsTo solve the problem, the multiples of seven will be necessary to ascertain the one that will:
have remainder 1 when divided by 2 remainder 4 or fall short by 1 when divided by 5multiples of 7: 7 , 14 , 21 , 28 , 35 , 42 , 49 , 56 , 63....
14 is short of 1 when divided by 5 but it is divisible by 2 without remainder
49 is the least number that fall short of 1 card to make it a multiple of 5 and have a remainder one when divided by 2
Hence the answer is 49
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Help with question pleaae
The length of triangle AB is 22.5.
Triangle A = 7.5
Triangle B = 15
Whole = 22.5
As per the given question
Figure is made of 2 triangles.
Triangle A
Triangle B
9
7
As it is 2 triangles so
So A = 7.5
B = 15
The whole is = 15 + 7.5
=22.5
Each part is 7.5 and 15 respectively and whole is 22.5 per square unit.
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2x−4y=6
Step 2 of 2 : Determine the missing coordinate in the ordered pair (?,5) so that it will satisfy the given equation.
(8/10)=(9/n)
Solve for n
Answer:
n=90/80
Step-by-step explanation:
you make n the subject of the formular
A firm manufactured 1000 Tv sets during its first year.the total firms production during the 10 year of operationis 29035 sets .
For each the level of output for 15th year using per year constant increase in production .
Answer:
6922 TV sets
Step-by-step explanation:
You want the production in the 15th year if production in the first year is 1000 and it increases yearly by a constant amount. The total production in the first 10 years is 29035.
Arithmetic seriesAn arithmetic series is one that has a constant difference from one term to the next. If a1 is the first term of the series, and d is the common difference between terms, the n-th term is ...
an = a1 +d(n -1)
And the sum of n terms is ...
Sn = (2a1 +d(n-1))(n/2)
ApplicationTo find the 15th term, we can make use of the given values to find the common difference, then use the formula for the n-th term.
S10 = (2(1000) +d(10 -1))(10/2) . . . . . sum formula with a1=1000
29035 = 10000 +45d . . . . . . . . . . . simplified
d = (29035 -10000)/45 = 423 . . . . the increase in production each year
Production in the 15th year is ...
a15 = 1000 +423(15 -1) = 1000 + 5922 = 6922
The output in the 15th year was 6922 TV sets.
Pls help me need by today
The measure of the line AC is 15√3/2
The measure of the line BC is 15/2
What is a Triangle?Triangle ABC is the display style for a triangle with vertices A, B, and C.
In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane (i.e. a two-dimensional Euclidean space). All triangles are enclosed in a single plane if all of geometry is the Euclidean plane, however this is no longer true in higher-dimensional Euclidean spaces.
One of the internal angles of a right triangle (also known as a right-angled triangle) measures 90 degrees (a right angle). The hypotenuse, the triangle's longest side, is the side that faces the right angle. The triangle's other two sides are referred to as its legs, Right triangles follow the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs of a right triangle (a2 + b2 = c2). Special right triangles have extra characteristics that simplify computations involving them. The 3-4-5 right triangle is one of the two most well-known.
Sin 60⁰=x/15
√3/2=x/15
x=15√3/2
The measure of the line AC is 15√3/2
Cos 60⁰= y/15
1/2=y/15
y=15/2
The measure of the line BC is 15/2
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The revenue function is given by R(x)=x⋅p(x) dollars where x is the number of units sold and p(x) is the unit price. If p(x)=26(4)−x5, find the revenue if 15 units are sold. Round to two decimal places.
If price p(x) =26(4)^{-x/5}, the revenue when 15 units are sold is equal to $6.09.
How to calculate the amount of revenue at p(15)?From the information provided, the amount of revenue with respect to price that's being generated in this scenario can be calculated by using the following function (expression):
R(x) = x × P(x)
Where:
x represents the number of units sold.p(x) represents the unit price.Since the revenue function, we would simply substitute the value of the unit price and evaluate as follows:
Revenue, R(x) = x × 26(4)^{-x/5}
Substituting the given parameters into the formula, we have;
Revenue, R(x) = 15 × 26(4)^{-15/5}
Revenue, R(x) = 15 × 26(4)^{-3} or (15 × 26)/4³
Revenue, R(x) = 15 × 26(0.015625) or 390/64
Revenue, R(x) = 6.09375 ≈ $6.09.
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Complete Question:
The revenue function is given by R(x)=x⋅p(x) dollars where x is the number of units sold and p(x) is the unit price. If p(x)=26(4)^{-x/5}, find the revenue if 15 units are sold. Round to two decimal places.
6x-5=6x+5 pls help me fast
Answer:
No solution
Step-by-step explanation:
6x - 5 = 6x + 5
6x = 6x + 10
0 = 10
0 cannot be equal to 10 at anytime, so this equation has no solution
Answer: No solution.
Step-by-step explanation:
Given:
6x - 5 = 6x + 5
Add 5 to both sides of the equation:
6x = 6x + 10
Subtract 6x from both sides of the equation
0 ≠ 10
Since 0 does not equal 10, there is no solution to this equation.
8x + 16x - 12 = 24x- 12
Does the equation have one,
none, or infinite solutions?
Explain why.
Answer:
Infinite solutions
Step-by-step explanation:
The equation is,
→ 8x + 16x - 12 = 24x - 12
Let's solve for the value of x,
→ 8x + 16x - 12 = 24x - 12
→ 24x - 24x = -12 + 12
→ [ 0 = 0 ]
Hence, it has infinite solution. Because, all the real numbers are suitable.
Answer:
infinite number.
Step-by-step explanation:
Comment
There is only the same letter (x) on both sides of the equation. None of the xs are raised to any power. The power is 1 for all of them. That being so, there is only ONE solution.
x^2 + 5x + 6 would give 2 solutions because the x is raised to the second power.
x^3 + x^2 + 4x + 9 would give 3 solutions.
Solution
8x + 16x - 12 = 24x - 12 This equation is a little different. Both sides are exactly the same -- 24x - 12. That means that there is an infinite number of solutions.
For example let x = 10
The right side = 240 - 12 = 228
The left side = 8*10 + 16*10 - 12 = 228
You can't come up with a number that will make the left side unequal to the right side.