Answer:
a) t-statistic t = 0.9532
b) The standard error S.E = 1.2
c) The new t-statistic = 1.95
d) The new estimated standard error =0.666
Step-by-step explanation:
Step(i):-
Given that the mean of the Population = 16
The sample size n=27
The mean of the sample = 17.1
Given that the variance of the sample (S²) = 36.0
The standard deviation of the sample (S) = √36 = 6
Test statistic
[tex]t = \frac{x^{-} -mean}{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]t = \frac{17.1 -16}{\frac{6}{\sqrt{27} } }[/tex]
t = 0.9532
b)
The standard error is defined by
[tex]S.E = \frac{S.D}{\sqrt{n} } = \frac{6}{\sqrt{27} } =1.154[/tex]
Step(ii):-
c) given that the sample size n = 81
Test statistic
[tex]t = \frac{x^{-} -mean}{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]t = \frac{17.1 -16}{\frac{6}{\sqrt{81} } }[/tex]
t = 1.65
d)
The new standard error is defined by
[tex]S.E = \frac{S.D}{\sqrt{n} } = \frac{6}{\sqrt{81} } = 0.66[/tex]
Find the missing length indicated. need help
The missing length of given right triangle is equal to 25.
RIGHT TRIANGLE
A triangle is classified as a right triangle when it presents one of your angles equal to 90º. The greatest side of a right triangle is called hypotenuse. And, the other two sides are called cathetus or legs.
The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.
The Pythagorean Theorem says: (hypotenuse)²=(leg1)²+(leg2)² . And the main trigonometric ratios are: sin (x), cos (x) and tan (x) , where:
[tex]sin(x)=\frac{opposite\ leg}{hypotenuse} \\ \\ cos(x)=\frac{adjacent\ leg}{hypotenuse} \\ \\ tan(x)=\frac{opposite\ leg}{adjacent\ leg}[/tex]
There is another important property, where h²=m*n. See the attached image.
From the previous informations presented, you can solve the given question.
From Pythagorean Theorem you can find h (heigth). Thus,
15²=9²+h²
h²=225-81
h²=144
h=12
If h=12 and m=9, from h²=m*n you can find n.
h²=m*n
12²=9*n
144=9n
n=144/9
n=16
Therefore, x= m+ n= 9+16=25.
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Suppose a line has a slope of −5.
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
The slope of a line parallel to this line is -5 and the slope of a line perpendicular to this line is 1/5
How to determine the slopes?The slope is given as:
m = -5
Parallel line have the same slope.
So, the slope of a line parallel to this line is -5
However, perpendicular lines have their slopes to be opposite reciprocal
This means that:
Perpendicular slope = -1/-5Perpendicular slope = 1/5The slope of a line perpendicular to this line is 1/5
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Question 4 of 10
What should you substitute for y in the second equation (bottom equation) in
order to solve the system by the substitution method?
5x+y=10
3x-2y =6
A. -0.2y+2
B. -5x+10
C. 5x-10
D. 1.5x+3
Answer:
B
Step-by-step explanation:
5x+y=10
-5x -5x
y= -5x+10
which of the following functions is graphed below?
The function that's illustrated in the graph is function D.
How to explain the function?First, you look at the left side of the graph. You can tell by the shape that it is an x³ function.
Also, the filled-in circle means inclusive. so we know that when x is less than or equal to a number.
The answer that illustrates the information explained is D.
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Answer:
B.
Step-by-step explanation:
An open circle means to exclude the point.
A closed circle means to include the point.
In this graph we see a part of a parabola with an open circle above. The parabola starts at x = 1, but does not include x = 1, and the x values of the parabola increase.
A parabola has an x squared in the equation.
The solution has to have an equation with an x² as its greatest exponent, and also must include x > 1.
The lower part of the graph is a third degree polynomial, so it must have an x cube term, x³. Also, the greatest x value for the x³ function is x = 1, but x = 1 is included. Then all x values tot he left of x = 1 are also included, so for the cubic polynomial, the domain (x values) must be x ≤ 1.
The answer is B.
Charlotte owns two entertainment websites. Here are some details about those
websites for one entire month:
Number of writers
Number of posts posted
Average number of words of post
Average likes per post
Average comments per post
Number of new subscribers
Revenue
Expenses
Profit (Revenue-Expenses)
Website A Website B
5
11
110
200
100
170
3500
450
20,000
$75,000
$47,000
$28,000
3500
500
9000
$30,000
$20,000
$10,000
Charlotte wants to know which website produces a larger amount of content per a
single writer.
1) Charlotte thought of two different ways to define this quantity, Identify these two
definitions among the following options.
4 of 4
In order to define the quantity of which of the two website produces a larger amount of content per single writer, Charlotte thought of:
A Average number of posts per writer C Average number of words per writerHow can Charlotte define the quantity?Charlotte wants to know which website has more content per writer which means that she wants to know which website is more productive with writing.
One way she can do this is to check the average number of posts per writer per website. This would show her which website has a writer that writes more content on average.
Charlotte could also use average number of words per writer. This shows just how much writing the writers in each websites are doing, in terms of words. The website with the higher average words per writer is therefore providing more content.
Options for this question include:
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Consider the following 8 numbers, where one labelled
x
is unknown.
34
,
31
,
15
,
x
,
17
,
4
,
20
,
25
Given that the range of the numbers is 69, work out 2 values of
x
.
x
=
x
=
Answer:
x = 73
x = -35
Step-by-step explanation:
Here are the 8 numbers:
34, 31, 15, x, 17, 4, 20, 25
Here are the 8 numbers in ascending order with x as the greatest number:
4, 15, 17, 20, 25, 31, 34, x
x - 4 = 69
x = 73
Here are the 8 numbers in ascending order with x as the smallest number:
x, 4, 15, 17, 20, 25, 31, 34
34 - x = 69
-x = 69 - 34
-x = -35
x = -35
Answer:
x = 73
x = -35
what is the inverse of the following function? 50 points
The inverse of the given function [tex]f(x)=\sqrt[5]{x^3}[/tex] is [tex]f^{-1}(x)=x^{\frac{5}{3}}[/tex]
Inverse of a functionThe given function is:
[tex]f(x)=\sqrt[5]{x^3}[/tex]
This function can be written in exponent form as:
[tex]f(x)=x^\frac{3}{5}[/tex]
Make x the subject of the formula:
[tex]x=[f(x)]^\frac{5}{3}[/tex]
Let x be replaced by [tex]f^{-1}(x)[/tex] and f(x) be replaced by x
The inverse function therefore becomes:
[tex]f^{-1}(x)=x^{\frac{5}{3}}\\\\ f^{-1}(x)=\sqrt[3]{5}[/tex]
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find the slope of this line
Which expression is it equivalent too help a brother out
The expression which is equivalent to the given expression in the task content is; 1/x²⁴.
Which expression is equivalent to the given expression?It follows from the task content that the given expression is; ((x)^-6/x²)³.
Hence, it follows from the laws of indices that the expression can be evaluated as follows;
= (x^-8)³
= x^-²⁴
= (1/x²⁴).
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Find function then simplify tje answer
Answer:
a)(x+h+2)²=x²+2xh+h²+4x+4h+2
b)(x+h+2)²–(x+2)²=2xh+h²+4h
c)2x+4+h
Step-by-step explanation:
f(x)=x²+4x+2
Aight so for part a you have to replace x with x+h
a)f(x+h)=(x+h)²+4(x+h)+2=x²+2xh+h²+4x+4h+2
and then for part b you need to subtract f(x) from part a:
b)f(x+h)–f(x)=x²+2xh+h²+4x+4h+2–x²–4x–2===>
2xh+h²+4h
and for part c divide the answer by h:
c)
[tex] \frac{f(x + h) - f(x)}{h} = = = > \\ \frac{2xh + 4h + {h}^{2} }{h} = = = > \\ 2x + 4 + h[/tex]
and if you limit h by 0 you'll get the derivative of f(x)
If $4,000 is invested in an account for 25 years. Calculate the total interest earned at the end of 25 years if the interest is: (a) 7% simple interest: $ (b) 7% compounded annually: $ (c) 7% compounded quarterly: $ (d) 7% compounded monthly: $ Round your answers to the nearest cent.
The interest is a) $7000
b) $17709.73
c) $18672.62
d) $18901.67
What is the formula for simple and compound interest?
Simple interest = (P× r× t)
Compound interest = P(1+r/n)^nt - P
We will find the interest as shown below:
P=$4,000
t=25 years
a) r=7%=0.07
Simple interest = (P× r× t)
= (4000×0.07×25)
= $7000
b) r=7%=0.07
Compound interest = P(1+r)^t - P
= 4000(1+0.07)^25-4000
= $17709.73056
rounding to nearest cents
= $17709.73
c) r=7%=0.07
n=4
Compound interest = P(1+r/n)^nt - P
= 4000(1+0.07/4)^(25*4)-4000
= $18672.62375
rounding to nearest cent
= $18672.62
d) r=7%=0.07
n=12
Compound interest = P(1+r/n)^nt - P
= 4000(1+0.07/12)^(25*12)-4000
= $18901.6728
rounding to nearest cent
= $18901.67
Hence, the interest is a) $7000
b) $17709.73
c) $18672.62
d) $18901.67
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An American roulette wheel contains 38 slots. Eighteen of the slots are colored red and eighteen are colored
black. The remaining two slots are colored green. A ball is spun on the wheel and comes to rest in one of the
38 slots. If you bet $1 on the the number 32 and win, the house pays you $36.
What is the expected value of betting on 32?
$1
O-$1
4
O-$5.30
O-$0.053
The expected value of betting 32 is -$0.053, making the 4th option the right choice.
In the question, we are asked for the expected value of betting on 32, given that if we bet $1 on the number 32 and win, the house pays $36, and there are 38 slots.
The probability distribution can be shown as:
x $35 -$1
p(x) 1/38 37/38
as, if we get 32, which has the probability of 1/38, the winning number, we gain $35, and for the rest, having a probability of 37/38, the losing number, we lose -$1.
Thus, the expected value can be calculated as E(x) = ∑x.p(x).
Thus, the expected value = $35(1/38) + (-$1)(37/38) = -$2/38 = -$0.05263 ≈ -40.053.
Hence, the expected value of betting 32 is -$0.053, making the 4th option the right choice.
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ayuda, no le entiendo :)
Trabajando 10 horas por día, en 6 días se producen 3000 ruedas.
¿Cuántos dias tardarán en fabricar 3000 ruedas si trabajan 10 horas diarias?Sabemos que trabajando 8 horas, en 5 dias producen 2000 ruedas.
El número total de horas que trabajan en esos 5 dias es:
(8 horas)*5 = 40 horas
Entonces se producen 2000 ruedas en 40 horas, es decir, la razon de trabajo es:
(2000 ruedas)/(40 horas) = 50 ruedas por hora.
Ahora, sí en la fabrica trabajan 10 horas al día, entonces van a producir:
10h*(50 ruedas por hora) = 500 ruedas por día.
El número x de días que deben trabajar para producir 3000 ruedas es:
x*(500 ruedas por dia) = 3000 ruedas
x = (3000 ruedas)/(500 ruedas por dia) = 6 dias.
Trabajando 10 horas por día, en 6 días se producen 3000 ruedas.
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Which of the following rational functions is graphed below?
Answer: D
Step-by-step explanation:
There are vertical asymptotes at x=7 and x=-3, so the denominator should have factors of (x-7) and (x+3).
This eliminates everything except for D.
The following data show the scores of some students in a competition:
13 points
24 points
31 points
24 points
27 points
23 points
11 points
Which box plot represents the data?
A box plot titled "Scores of Participants" and labeled "Score" uses a number line from 10 to 35 with primary markings and labels at 10, 15, 20, 25, 30, and 35. The box extends from 23 to 27 on the number line. A line in the box is at 24. The whiskers end at 11 and 31.
A box plot titled "Scores of Participants" and labeled "Score" uses a number line from 10 to 35 with primary markings and labels at 10, 15, 20, 25, 30, and 35. The box extends from 13 to 27 on the number line. A line in the box is at 24. The whiskers end at 11 and 31.
A box plot titled "Scores of Participants" and labeled "Score" uses a number line from 10 to 35 with primary markings and labels at 10, 15, 20, 25, 30, and 35. The box extends from 13 to 27 on the number line. A line in the box is at 23. The whiskers end at 11 and 31.
A box plot titled "Scores of Participants" and labeled "Score" uses a number line from 10 to 35 with primary markings and labels at 10, 15, 20, 25, 30, and 35. The box extends from 13 to 27 on the number line. A line in the box is at 24. The whiskers end at 10 and 35.
The box plot that represents the data is a box plot titled "Scores of Participants" and labeled "Score" uses a number line from 10 to 35 with primary markings and labels at 10, 15, 20, 25, 30, and 35. The box extends from 13 to 27 on the number line. A line in the box is at 24. The whiskers end at 11 and 31.(second option)
Which box plot represents the data?A box plot is used to study the distribution and level of a set of scores. The whiskers represent the minimum and maximum values.
On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile. 75% of the scores represents the upper quartile.
The data arranged in ascending order : 11, 13, 23, 24, 24, 27, 31
Median = 24
First quartile = 1/4 x (7 + 1) = 2nd term =13
Third quartile = 3/4 x (7 + 1) = 6th term = 27
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which of the following regression equation best fits the data graphed below?
Answer:
D
Step-by-step explanation:
Which of the following estimates at 895% confidence level most likely comes from a small sample?
A. 67% (+-7%)
B. 59 % (+-21%)
C. 53 % (+-3%)
D. 48 % (+-5%)
Option B. The estimate that would most likey come from the small sample is going to be B. 59 % (+-21%).
How to find the sample
The sample space can be gotten rom the margin of error. A smaller sample space would be gotten by dividing with a larger number.
This would give a margin of error that is large. In the second option, we can see that the largest margin of error is ± 21%.
Hence this is the answer to the question.
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2. State two (2) values of θ (theta) to the nearest degree for
sin θ = − 0. 966
Using equivalent angles, the solutions to the equation are given as follows:
[tex]\theta = 255^\circ, \theta = 285^\circ[/tex]
What are equivalent angles?Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.
In this problem, the equation is:
[tex]\sin{\theta} = -0.966[/tex]
Applying the inverse relation:
[tex]\theta = \arcsin{-0.966} = 255^\circ[/tex]
Which is on the third quadrant. The equivalent angle on the fourth quadrant is given as follows:
[tex]270^\circ + (270^\circ - 255^\circ) = 285^\circ[/tex]
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You should rotate tires on a car at regular intervals. In how many ways can four tires be arranged on a car?
The tires can be arranged in 24 ways. Computed using permutation.
The permutation is a way of selecting a smaller set from a larger set when the order of selection is not of concern.
For selecting r number of items, from n number of items, with the order of selection not being a concern, we can calculate the number of ways using permutation:
nPr = n!/(n - r)!.
In the question, we are asked the number of ways in which the four tires can be arranged on a car.
As we need to select 4 tires, from 4 tires, with any order, we will use permutation.
Thus, the number of ways can be calculated as 4P4, which can be calculated using the formula, nPr = n!/(n - r)!.
Thus, 4P4 = 4!/(4 - 4)! = 4!/0! = 24/1 = 24.
Thus, the tires can be arranged in 24 ways. Computed using permutation.
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For a function f(x), the difference quotient is x + one-half h + 15. Which statement explains how to determine the average rate of change of f(x) from x = 5 to x = 8? Substitute 5 for x and 3 for h in the expression x + one-half h + 15. Substitute 5 for x and 8 for h in the expression x + one-half h + 15. Substitute 8 for x and 5 for h in the expression x + one-half h + 15. Substitute 8 for x and 3 for h in the expression x + one-half h + 15.
The average rate of change of f(x) from x = 5 to x = 8 would be gotten by; B: Substituting 5 for x and 8 for h in the expression x + one-half h + 15
How to used difference quotient to find average rate of change?The difference quotient is defined as a measure of the average rate of change of a function over an interval.
The limit of the difference quotient which is the derivative is the instantaneous rate of change.
This differential quotient in calculus is usually expressed as;
[f(x + h) - f(x)]/h
We are given the differential quotient as;
f(x) = x + ¹/₂h + 15
Thus, the average rate of change of f(x) from x = 5 to x = 8 would be gotten by;
Substituting 5 for x and 8 for h in the expression x + one-half h + 15
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The base of the right pyramid is a rectangle with an area of 1326 square cm. If the volume of the pyramid is 21,452 cubic cm, find its approximate height.
The height of the right pyramid is 48.53 cm.
What is the height of the pyramid?A rectangle pyramid is a 3-dimensional shape that is made up of a rectangular base and 4 triangular faces.
Height = ( 3 x Volume of a pyramid) /( area)
Height = (3 x 21452) / 1326 = 48.53 cm
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Question 22: 4 pts
Nine cards are numbered from 1 to 9 and placed in a box. One card is selected at random and not replaced.
Another card is randomly selected. What is the probability of selecting two prime numbers?
2/9
O1/12
1/9
1/6
The probability of selecting two prime numbers is 1/6.
What is the probability?Probability determines the odds that a random event would happen. The odds that the random event would happen lie between 0 and 1.
The probability of selecting two prime numbers = (number of prime numbers between 1 and 9 / total numbers between 1 and 9) x [(number of prime numbers between 1 and 9 / total numbers between 1 and 9) - 1]
Prime numbers between 1 and 9 = 2, 3, 5, 7
4/9 x 3/8 = 1/6
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Complete the statements. If both expressions have the same value after substituting and simplifying two different values for the variable, then they are . The value of both expressions when k = 3 is and when k = 5 is 45, so the expressions are .
When both expressions have the same value, then they are equal to each other.
What is an equivalent expression?The equivalent is the expressions that are in different forms but are equal to the same value.
Consider the expressions 5 + 8k and 8k + 5.
Using k = 3
5 + 8k = 8k + 5
5 + 8(3) = 8(3) + 5
5 + 24 = 24 + 5
29 = 29
Using k = 5
5 + 8k = 8k + 5
5 + 8(5)= 8(5) + 5
5 + 40 = 40 + 5
45 = 45
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Complete question:
Consider the expressions 5 + 8k and 8k + 5. Determine why the expressions are equivalent.
Using k = 3 5 + 8k 8k + 5 5 + 8(3) 8(3) + 5 5 + 24 = 29 24 + 5 = 29
Using k = 5 5 + 8k 8k + 5 5 + 8(5) 8(5) + 5 5 + 40 = 45 40 + 5 = 45
Complete the statements.
If both expressions have the same value after substituting and simplifying two different values for the variable, then they are.
The value of both expressions when k = 3 is and when k = 5 is 45, so the expressions are.
Write the expression as a polynomial:
(a-2)(4a³-3a²)
Answer:
[tex]4a^{4} -11a^{3} + 6a^{2}[/tex]
decreased by 0% is 800 what number?
Answer:
800
Step-by-step explanation:
zero percent is just no percent...
800 - (0% × 800) =
800 - (0 ÷ 100 × 800) =
800 - (0 × 800) =
800 - 0 =
800
lol
The 0% of 800 is 800
What is percentage?Percentage is a fraction or a ratio in which the value of whole is always 100. For example, if Sam scored 30% marks in his math test, it means that he scored 30 marks out of 100. It is written as 30/100 in the fraction form and 30:100 in terms of ratio.
Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Calculation of PercentageCalculating percentage means to find the share of a whole, in terms of 100. There are two ways to find a percentage:
By using the unitary method.By changing the denominator of the fraction to 100.Given:
800 - (0% × 800)
=800 - (0 ÷ 100 × 800)
=800 - (0 × 800)
=800 - 0 =800
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Give the name (monomial, binomial,
trinomial, etc.) and the degree of the
polynomial.
2x - 4
Name? [?]
Degree? [ ]
Binomial
First Degree
Step-by-step explanation:Naming and giving the degree of a polynomial can help people understand the different properties of an expression.
Naming Polynomials
Polynomials are named based on the number of terms in the expression.
Terms are the different coefficients and variables that are added or subtracted together.For example, the expression above has 2 terms. The first being 2x and the second being 4. There are 2 separate terms being subtracted.
There are 3 main types of polynomials
Monomials have 1 termBinomials have 2 termsTrinomials have 3 termsMost polynomials above that are just called polynomials.This specific expression is a binomial.
Degree
The degree of a polynomial is the highest exponent in the expression. For example, if the largest exponent is a 6, then the degree is also 6.
In the binomial above, there is no written exponent; however, it can be assumed that the variable "x" has an exponent of 1. Thus, this binomial is of the first degree.
Additionally, when writing a polynomial in standard form, the terms should be written in descending order of exponents.
The transformation from parallelogram LMNO to parallelogram L'M'N'O' was carried out as shown in the coordinate plane below.
The transformation from parallelogram LMNO to parallelogram L'M'N'O' is a reflection across the x-axis
How to determine the transformation?The complete question is added as an attachment
From the graph, we have the following highlights:
Parallelogram LMNO and parallelogram L'M'N'O' are on either sides of the x-axisThey are equidistant from the x and y axesThey have equal dimensionsThis means that parallelogram LMNO is reflected across the x-axis to get parallelogram L'M'N'O'
Hence, the transformation from parallelogram LMNO to parallelogram L'M'N'O' is a reflection across the x-axis
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In which data set is the mean greater than the median?
how do I find the value of x?
Answer: x = 15
Step-by-step explanation:
The formula for calculating the sum of the interior angles of a regular polygon is: (n - 2) × 180°. Where n is number of sides.
sum of angles = (n - 2) × 180
sum of angles = (7 - 2) × 180
sum of angles = 5 × 180
sum of angles = 900°
Now to find the value of x, we have to set each of the interior angles, added up, equal to 900°:
7x + 1 + 10x + 6x + 7 + 10x - 9 + 9x + 4 + 8x + 10 + 9x + 2 = 900
Combine like terms:
(7x + 10x + 6x + 10x + 9x + 8x + 9x) + (1 + 7 - 9 + 4 + 10 + 2) = 900
59x + 15 = 900
59x + 15 - 15 = 900 - 15 subtract 15 from both sides
59x = 885
59x/59 = 885/59 divide by 59 on both sides
x = 15
Consider the probability that fewer than 26 out of 107 cell phone calls will not be disconnected. Assume the probability that a given cell phone call will not be disconnected is 25%.
Specify whether the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.
Yes or no
please explain in detail how to do these
Since both np > 5 and n(1 - p) > 5, the normal curve can be used as an approximation to the binomial distribution.
What is the binomial probability distribution?It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The normal approximation can be used if:
np > 5.n(1 - p) > 5.In this problem, the parameters are:
n = 107, p = 0.25.
Hence:
np = 107 x 0.25 = 26.75.n(1 - p) = 107 x 0.75 = 80.25.More can be learned about the binomial distribution at https://brainly.com/question/24863377
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