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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Exercises 12 -15, decide whether the statement is correct or incorrect. Explain your reasoning in words or by drawing pictures. 12. 1/3 equal to 4/12 13. 4/6 equal to 2/3 14. 2/5 equal to 1/3 15. 2/5 equal to 5/10.
The correct statement:
1/3 equal to 4/12; 4/6 equal to 2/3; 2/5 equal to 5/10
incorrect statement: 2/5 equal to 1/3
What is Fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
a) 4/12
Writing into Simplest form
4/12 = 1/3
b) 4/6
Writing into Simplest form
4/6 = 2/3
c) 2/5 cannot be simplified to 1/5
d) 5/10
Writing into Simplest form
5/10= 1/2
Hence, The correct statement: 1/3 equal to 4/12; 4/6 equal to 2/3; 2/5 equal to 5/10 and incorrect statement: 2/5 equal to 1/3.
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I need help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The area of triangle using vertices is D) A = (1/2) [[tex](y_2-y_1)(x_3-x_1)[/tex]]
What is area of triangle using vertices ?
The length of a triangle's three sides must first be determined if the triangle's vertices are known. The distance formula can be used to determine the length. when the vertices in the coordinate plane are known, the process to determine the triangle's area. Consider the triangle PQR, whose coordinates P, Q, and R are [tex](x_1,y_1)(x_2,y_2)[/tex], and [tex](x_3,y_3)[/tex] respectively.
If the triangle's area is zero and its vertices are P[tex](x_1,y_1)[/tex] Q[tex](x_2,y_2)[/tex], and R[tex](x_3,y_3)[/tex] then (1/2) [[tex]x_1(y_2-y_3)[/tex] + [tex]x_2(y_3-y_1)[/tex]+ [tex]x_3(y_1-y_2)[/tex]] = 0 and its points are collinear.
Here the given vertices are, [tex](x_1,y_1),(x_1,y_2)[/tex] and [tex](x_3,y_3)[/tex] then the area of triangle is ,
=> A = (1/2) [[tex]x_1(y_2-y_3)[/tex] + [tex]x_2(y_3-y_1)[/tex]+ [tex]x_3(y_1-y_2)[/tex]]
=> A = (1/2) [[tex]x_1(y_2-y_3)[/tex] + [tex]x_1(y_3-y_1)[/tex]+ [tex]x_3(y_1-y_2)[/tex]]
=> A = (1/2)[ [tex]x_1y_2-x_1y_3+x_1y_3-x_1y_1+x_3y_1-x_3y_2[/tex]]
=> A = (1/2) [[tex]x_1y_2-x_1y_1+x_3y_1-x_3y_2[/tex]]
=> A = (1/2) [[tex]x_1(y_2-y_1)-x_3(y_2-y_1)[/tex]]
=> A = (1/2) [[tex](y_2-y_1)(x_3-x_1)[/tex]]
Hence the correct option is D) A = (1/2) [[tex](y_2-y_1)(x_3-x_1)[/tex]]
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Make Sense and Persevere
There are 5 players on a basketball team. In a game 4 players
scored 6 points each. The team scored a total of 34 points.
How many points did the other player score?
1. Tell how to make sense of the problem.
2. Tell the quantities you know. Then explain what you need
to find first to solve the problem.
3. Tell which operations you will use. Then solve the problem.
71,72×35,36 =2536.0192
give your answer to 2 decimal places
Answer:
the answer to 2dp is 2536.02
7 candy bars cost $6.65. At this rate, how much do 9 candy bars cost?
Answer: $8.55
because 6.65 divided by 7 is 0.95 and 0.95 multiplied by 9 is 8.55
so the answer is $8.55
what are her monthly payments
The interest she is pay total is $2340.822 when Angela's bank granted her a 6380 loan with a 3 year add-on interest period. 12.23% is the interest rate per year.
Given that,
For the purpose of buying new equipment for her business of antique restoration, Angela's bank granted her a 6380 loan with a 3 year add-on interest period. 12.23% is the interest rate per year.
We have to find will she pay interest at all.
We know that,
i=p×r×t
Here,
i is interest.
p is principal amount.
r is rate of interest
t is time.
So, p is $6380
r is 12.23%
t is 3 years
So,
i= 6380×0.1223×3
i= $2340.822
Therefore, the interest she is pay total is $2340.822 when Angela's bank granted her a 6380 loan with a 3 year add-on interest period. 12.23% is the interest rate per year.
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A notebook computer has a mass of 2.25 kilograms . about how many pounds does the notebook weigh
Answer:
5 pounds
Step-by-step explanation:
1 kg = 2.205 lbs.
2.25×2.205
⇒4.96125
Explain how to use Pascal's Triangle to expand the binomial (3x-4y)^11
The expansion of (3x-4y)¹¹ using Pascal's Triangle is:
177147x¹¹ - 2598156x¹⁰y - 17321040x⁹y² - 69284160x⁸y³ - 184757760x⁷y⁴ - 344881152x⁶y⁵ - 458941536x⁵y⁶ - 437944320 x⁴y⁷ - 291962880x³y⁸ - 129761280x²y⁹ + 34603008xy¹⁰ - 4194304y¹¹.
What is Pascal's Triangle?The triangle-shaped array of integers known as Pascal's triangle has one at the top and one on each of its two sides. Every new number has a value equal to the sum of the two numbers above it and is located between two other numbers and underneath them. Pascal's triangle is a triangular array of binomial coefficients that appears in algebra, combinatorics, and probability theory.In algebra, a triangle-shaped grouping of integers known as Pascal's triangle provides the coefficients for the expansion of any binomial formula, such as (x + y)ⁿ. Although it is much older, it bears the name of the French mathematician Blaise Pascal from the 17th century.So, the expression is:
(3x-4y)¹¹Now, use Pascal's Triangle to expand as follows:
(Refer table attached below for expansion)Therefore, the expansion of (3x-4y)¹¹ using Pascal's Triangle is:
177147x¹¹ - 2598156x¹⁰y - 17321040x⁹y² - 69284160x⁸y³ - 184757760x⁷y⁴ - 344881152x⁶y⁵ - 458941536x⁵y⁶ - 437944320 x⁴y⁷ - 291962880x³y⁸ - 129761280x²y⁹ + 34603008xy¹⁰ - 4194304y¹¹.
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kind of suck help please ? brianslest
Answer:
[tex]d=7[/tex]
[tex]a_9=59[/tex]
Step-by-step explanation:
If the first term of a sequence is [tex]3[/tex] and the second term is [tex]10[/tex], then each successive term in the sequence is [tex]7[/tex] more than the previous term. The common difference is [tex]7[/tex] ( [tex]d=7[/tex] ).
The formula representing the arithmetic sequence is:
[tex]a_n=7n-4[/tex]
Therefore, the ninth term in the sequence is:
[tex]a_9=7(9)-4[/tex]
[tex]a_9=63-4[/tex]
[tex]a_9=59[/tex]
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.
x2 + (y – 3)2 = 36
x2 + (y – 5)2 = 6
(x – 4)² + y² = 36
(x + 6)² + y² = 144
x2 + (y + 8)2 = 36
The equation that represents circles that have a diameter of 12 units and a center that lies on the y-axis is x²+ (y-3)² = 36
What is Equation of Circle?The location of a circle in the Cartesian plane is represented by a circle equation. We can write the equation for a circle if we know the location of the circle's center and how long its radius is. All of the points on the circle's circumference are represented by the circle equation.
The standard equation of a circle with center at
(a, b) and radius is r.
So, the standard equation circle is
(x -a)² + (y- b)² = r²
Given:
As, we know the standard form for equation of a circle is
(x-a)² + (y-b)² = b =r²
where (a, b) is the center of the circle and r is the radius of the circle.
We have
diameter = 12 units
radius = 12/2 = 6 units
So, the center will be at (0, 3)
Thus, the equation of circle
(x-0)² + (y-3)² = 6²
x²+ (y-3)² = 36
Hence, the Equation of Circle is x²+ (y-3)² = 36.
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Select all of the solutions for the linear inequality graphed below:
The solutions to the inequality whose graph is as represented in the attached image are;
A) (-4, 0)C) (0, 0)E) (-2,0)Graphical solution of inequalities.It follows from the task content that the graphical solutions for the inequality are represented on the graph and the points which are solutions for the inequality are to be identified.
Therefore, the points which are solutions for the inequality are points which are located in the shaded region of the graph.
Hence, such points include;
A) (-4, 0)C) (0, 0)E) (-2,0)The answer choices B, D and F represents points on the border line of the inequality graph and since the line is broken, they are not solutions to the inequality.
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what is the product of 9x-4 and 8x+5?
help plss? i dont know what this means so answer would be great.
Answer:
(e) b h a k
Step-by-step explanation:
You want the order of operations involved in the transformation ...
g(x) = a(bx -h) +k
Order of operationsThe Order of Operations tells you that multiplication takes precedence over addition, and expressions inside parentheses are evaluated first.
EvaluationWe note there is an expression in parentheses here: (bx -h). In that expression is a multiplication operation (bx) and an addition operation (_-h).
The multiplication is done first, so evaluating this expression in parentheses, we ...
multiply by bsubtract hOnce the parenthetical expression is evaluated, we proceed to the main event. Again, multiplication and addition are required. That means the next two steps are ...
multiply (the value of the parentheses) by aadd kIn summary, the operations we perform during evaluation of the transformation successively apply the parameters ...
b h a k
HELP!! which expression is equivalent to the given expression 2X^2 -11 X -6
Answer: C.
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Greta made $96.00 babysitting last week. If she worked 8 hours last week, which equation can be used to find h, her
hourly pay?
8h=96
h+8=96
h
= 96
h=96-8
To become a member at Anytime Fitness you must pay
an initiation fee of $49.99 when you sign up, $33.99 per
month for the membership.
How many months would you have been with Anytime
Fitness if you paid a total of $321.91 ?
It would take 8 months of membership for the total money paid of $321.91.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. A variable can either be dependent or independent. A dependent variable depend on other variable while an independent variable does not depend on other variables.
Let x be the number of months subscribed. Hence,
For Fitness :
Total payment = 33.99 x + 49.99
if you paid a total of $321.91 then the number of months subscribed will be;
321.91 = 33.99 x + 49.99
33.99 x = 321.91 - 49.99
33.99 x = 271.92
x = 271.92/33.99
x = 8
It would take 8 months of membership for the total money paid of $321.91.
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due tomorrow help please :)
Answer:
68°
Step-by-step explanation:
The angles are equal to each other. Set them equal and solve for x
5x + 18 = 8x - 12 Subtract 5x from both sides of the equation
18 = 3x - 12 Add 12 to both sides of the equation
30 = 3x Divide both sides by 3
10 = x
Now that you have found x plug is back into 5x + 18
5(10) + 18
50 + 18 = 68
Answer:
∠ FLJ = 68°
Step-by-step explanation:
∠ EKG and ∠ FLJ are alternate exterior angles and are congruent , then
8x - 12 = 5x + 18 ( subtract 5x from both sides )
3x - 12 = 18 ( add 12 to both sides )
3x = 30 ( divide both sides by 3 )
x = 10
Then
∠ FLJ = 5x + 18 = 5(10) + 18 = 50 + 18 = 68°
HELP PLEASE ASAP 30 POINTS PLUS BRAINLEST Find the sum of (8.7 x 10^6) and (5.5 x 10^5). Write the final answer in scientific notation.
14.2 x 10^11
1.42 x 10^10
9.25 x 10^6
9.25 x 10^5
Shown below is a "magic square"
Each column, row and diagonal has the same total.
Work out the missing fractions.
- 15
10
9
20
1
3
20
10
Answer:
123 423 21 34
Step-by-step explanation:
YOU WILL GET THE BRAINLIEST
The given graph of the function is increasing in the interval (-∞,-6),(-4,-1)(3,6), and (8,∞).
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and the independent variable. A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
Given that the graph of the function has increased and decreasing orders on the coordinate plane.
The interval in which the given graph of the function is increasing is,
(-∞,-6)
(-4,-1)
(3,6)
(8,∞)
Therefore, the given graph of the function is increasing in the interval (-∞,-6),(-4,-1)(3,6), and (8,∞).
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Simplify the variable expression by evaluating its numerical part, and enter
your answer below.
g- 16/4 +2
simplification of expression will be g - 2
Our expression is g - 16/4 + 2
16/4 = 4
so we c will write it as
g - 4 + 2
which can be further simplified to
g - 2
Therefore, our simplified expression comes out to be g - 2.
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Explain in detail the difference of a linear, quadratic, and geometric relationships between two variables.
The difference of a linear, quadratic reation.
What is quadratic equation?
it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation.
Trigonometric ratios describe these operations. The ide and trigonometric functions In the previous chapters, we discovered that the polynomial equation is the equation that results from equating a polynomial function to zero. A linear equation results from equating a function to zero if it is a linear polynomial. We get a quadratic equation if the function is a quadratic polynomial.
When we graph a linear equation, we get a straight line, however with a quadratic equation, we get a parabola.
Unlike the slope of a linear polynomial, the slope of a quadratic polynomial is constant.
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394.6/ 9 but use compatible numbers to estimate the quotient
The quotient estimated value of 394.6/9 is 43.84
What is quotient?A quotient is the number which is generated when we perform division operations on two numbers. Basically, it is the result of the division method. There are four main terminologies used in the arithmetic division such as divisor, dividend, quotient and remainder. For example, 15/3= 5 .The number that is being divided ( 15) is called the dividend, and the number that it is being divided by (3) is called the divisor. The result of the division(5) is the quotient.
Therefore the quotient of 394.6/9= 43.84
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(2h)
40°
(2h)
What is the value of h?
O h=20
O h=35
O h=55
O h=70
Answer:
I think it is 70Step-by-step explanation:
I looked it up(;-;)The measure of h from the triangle is h = 55
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the triangle be represented as ΔABC
And , the measure of ∠ABC = 40°
Now , Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
So , the measure of ∠ACB = ∠BAC = y° = 70°
And , 2h + y° = 180° ( angles on a straight line )
On simplifying , we get
2h + 70° = 180°
Subtracting 70 on both sides , we get
2h = 110
Divide by 2 on both sides , we get
h = 55
Hence , the measure of h = 55
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The complete question is attached below :
(2h)
40°
(2h)
What is the value of h of the triangle?
O h=20
O h=35
O h=55
O h=70
Question 1 (Multiple Choice Worth 5 points) (Graphing Proportional Relationships MC) The table shows a proportional relationship between x and y. x 4.3 9.2 3.4 y 17.2 36.8 13.6 Which of the following correctly describes the graph of the relationship? a.A line that goes through (0, 0) and (17.2, 4.3). b.A line that goes through (4.3, 17.2) and (36.8, 9.2). c.A line that goes through (17.2, 4.3) and (9.2, 36.8). d.A line that goes through (0, 0) and (4.3, 17.2).
The statement that correctly describes the graph of the relationship is (d) A line that goes through (0, 0) and (4.3, 17.2).
How to describe the graph?The table of values is given as
x 4.3 9.2 3.4
y 17.2 36.8 13.6
The table shows a proportional relationship
This means that the line of the graph must pass through the origin i.e. (0, 0)
From the table of values, we have the following point
(4.3, 17.2)
This means that the line of the graph goes through (0, 0) and (4.3, 17.2).
Hence, the true statement is (d)
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Answer:
No, it is not proportional because 9.2 over 18.4 does not equal 17.6 over 52.8.
Step-by-step explanation:
"What are the coordinates of your reflected triangle A’B’C’?"
Please help! Thank you!
A' - (-1,4)
B' - (-1,8)
C' - (-5,4)
hope this helps
Simplify to one trigonometric expression.
4 sin
()2 cos()
Answer:
Step-by-step explanation:
the answer is 4
If FG = 10x − 10, GH = x + 4, and FH = 16, what is FG?
If FG = 10x − 10, GH = x + 4, and FH = 16, FG is 10
How to determine FGinformation given in the question include
FG = 10x − 10
GH = x + 4
FH = 16
The problem is solved using substitution. this involves replacement of a variable with another that are same.
An instance of this a line FH having points FG and GH
FH contains FG and GH, hence adding both FG and GH gives FH
FH = FG + GH
plugging in the values
16 = 10x - 10 + x + 4
collecting like terms
16 = 11x - 6
16 + 6 = 11x
22 = 11x
rearranging the equation
11x = 22
x = 2
FG = 10x − 10
substituting the value of x
FG = 10 * 2 − 10
FG = 20 - 10
FG = 10
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In a study of helicopter usage and patient survival, among the 49,401 patients transported by helicopter, 244 of them left the treatment center against medical advice, and the other
49,157 did not leave against medical advice. If 40 of the subjects transported by helicopter are randomly selected without replacement, what is the probability that none of them left
the treatment center against medical advice?
The probability is
(Round to three decimal places as needed)
Answer:
40%
Step-by-step explanation:
Differentiate the function with respect to x.
Answer:
[tex]16x {}^{3} + 1[/tex]
Step-by-step explanation:
We need to differentiate the following function,
[tex]\longrightarrow f(x) = 4x^4 + x [/tex]
Let ,
[tex]\longrightarrow y = f(x) [/tex]
So that ,
[tex]\longrightarrow y = 4x^4+x [/tex]
Differentiating both sides wrt x ,
[tex]\longrightarrow \dfrac{dy}{dx}= \dfrac{d(4x^4+x)}{dx}\\[/tex]
[tex]\longrightarrow\dfrac{dy}{dx}= \dfrac{d(4x^4)}{dx}+\dfrac{dx}{dx}\\ [/tex]
[tex]\longrightarrow \dfrac{dy}{dx} = 4(4)x^{4-1} + 1 \\ [/tex]
[tex]\longrightarrow \underline{\underline{ \dfrac{dy}{dx}= 16x^3 +1}}[/tex]
