The least sample size needed to assure with 90% confidence that the sample mean will not differ from the population mean by more than 5 minutes will be 416.16.
What is normal distribution?A normal distribution is a data set design in which the majority of values cluster around the middle of the range and the remainder taper off symmetrically toward either end. Data in a normal distribution are symmetrically distributed and have no skew. The majority of values cluster around a central location, with values decreasing as one moves out from the center. In a normal distribution, the measures of central tendency (mean, mode, and median) are all the same. The normal distribution, like any other probability distribution, defines how the values of a variable are distributed. Because it properly captures the distribution of values for many natural occurrences, it is the most important probability distribution in statistics.
Here,
The z value at the 90 percent confidence interval is 1.645.
t ≥ z*s/√n
5≥1.645*62/√n
√n≥20.398
√n≥20.4
n≥416.16
The smallest sample size required to ensure that the sample mean does not deviate from the population mean by more than 5 minutes with 90% confidence is 416.16.
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Solve the system of equations.
Answer:
(7,5)
Step-by-step explanation:
[tex]-3y+4x=13 \implies -15y+20x=65 \\ \\ -5y-6x=-67 \implies 15y+18x=201 \\ \\ \therefore 38x=266 \implies x=7 \\ \\ \implies -3y+4(7)=13 \implies y=5 \\ \\ \therefore (7,5)[/tex]
The table shows a set of values for x and y
y is inversely proportional to the square x.
a) Find an equation for y in terms of x. (2)
b) Find the positive value of x when y = 25 (2)
Answer:
see explanation
Step-by-step explanation:
(a)
given y is inversely proportional to x² then the equation relating them is
y = [tex]\frac{k}{x^2}[/tex] ← k is the constant of variation
to find k use any ordered pair from the table
using (2, 4 ) , then
4 = [tex]\frac{k}{2^2}[/tex] = [tex]\frac{k}{4}[/tex] ( multiply both sides by 4 )
16 = k
y = [tex]\frac{16}{x^2}[/tex] ← equation of variation
(b)
when y = 25 , that is
25 = [tex]\frac{16}{x^2}[/tex] ( multiply both sides by x² )
25x² = 16 ( divide both sides by 25 )
x² = [tex]\frac{16}{25}[/tex] ( take square root of both sides )
x = ± [tex]\sqrt{\frac{16}{25} }[/tex] = ± [tex]\frac{4}{5}[/tex]
the positive value of x is then [tex]\frac{4}{5}[/tex]
Solve for x:
[tex]\sqrt{x-3} =\sqrt{x} +3[/tex]
A. -2
B. 2
C. no solution
D. 4
Answer: The answer is C: No solution
Step-by-step explanation:
By squaring the other side (to therefor remove the square off X) you get [tex]x-3=x+6\sqrt{x} +9[/tex]
You then cancel out the equal terms, in this case x, to reach the equation:
[tex]-3=6\sqrt{x} +9[/tex]
This equation, has no solution, as the left side is always negative, and the right side will always be positive, making any statement for x false.
What is the slope of a line that is perpendicular to y=4/5x+15 and passes through point (−3, 4)?
Answer:
Step-by-step explanation:
The slope of the line y = -5x-4 is -5 or -5/1 so the slope of the perpendicular line is +1/5 eg…
y = x/5 + c
To find c we substitute x=15, y=-2
-2 = 15/5 + c
-2 = 3 + c
C = -5
So the equation is
Y = x/5 - 5
passes through A (2, "-5)" parallel to BC with (1, 3) and ( 4, 5) PLS HURRRY!!!!!
The equation for the linear equation parallel to BC is:
y = (2/3)*x - 19/3
How to get the linear equation?
A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If the line passes through two points (x1, y1) and (x2, y2), then the slope is:
slope = (y2 - y1)/(x2 - x1)
And two lines are parallel if both lines have the same slope and different y-intercept.
So if we want to et a line parallel to BC whose endpoints are (1, 3) and ( 4, 5), the slope should be:
slope = (5 - 3)/(4 - 1) = 2/3
So our line is like:
y = (2/3)*x + b
And this must pass through (2, -5)
Replacing these values we get:
-5 = (2/3)*2 + b
-5 - 4/3 = b
-15/3 - 4/3 = b
-19/3 =b
Then the linear equation is:
y = (2/3)*x - 19/3
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max and orlena bought 23 acres of land for $110,400. they bought some of the acres at $4000 per acre and some at $6300 per acre. how many acres did they buy at each price?
They bought 15 acres at $ 4000 per acre and 8 acres at $6300 per acre
Let,
They bought x acres at $ 4000
and ( 23-x ) acres at $ 6300
From information,
By using algebra,
4000x + 6300(23-x) = 110,400
4000x - 6300x+ 144900 = 110,400
-2300x = 110,400-144900
- 2300x = - 34500
x =34500 /2300
x = 15
x = 15
They bought 15 acres at $ 4000 per acre
(23 - 15 ) = 8 acres at $6300 per acre
Hence, they purchased 8 acres for $6300 per acre and 15 acres for $4,000 each.
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HELPP!!!1 i'm rushing like i need to summit that ASAP!!
The missing expression in step 2 should be [(6² + 2)/0.5] - 14.8 ÷ 8.
The missing expression in step 6 should be 76 - 1.85.
How to evaluate and solve the given expression?In order to evaluate this expression, we would apply the PEMDAS rule, where mathematical operations within the parenthesis are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the expression to the right. Lastly, the mathematical operations of addition or subtraction would be performed from left to right.
For step 1, we have the following:
[(6² + 2)/|-0.5|] - 14.8 ÷ 8.
In step 2, we would take the absolute value of -0.5:
[(6² + 2)/0.5] - 14.8 ÷ 8.
Therefore, we would have the quantity of the sum of six squared (6²) plus two (2) divided by 0.25, minus 14.8 ÷ 8
In step 3, we would take the exponent of 6:
[(36 + 2)/0.5] - 14.8 ÷ 8.
In step 4, we would add 36 and 2 together:
[(38)/0.5] - 14.8 ÷ 8.
In step 5, we would divide 38 by 0.5:
76 - 14.8 ÷ 8.
In step 6, we would divide 14.8 by 0.5:
76 - 1.85
In step 7, we would subtract 1.85 from 76 as follows:
Solution = 76 - 1.85 = 74.15.
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Lolly wrote a total of 10 pages over 5 hours. How many hours will Lolly have to spend writing this week in order to have written a total of 20 pages?
Answer:
10 hours
Step-by-step explanation:
since she spent 5 hours writing 10 pages. you just have to multiple by 2 to know how long it will take to write 20 pages
Complete the function table. Function: t = 5d − 2
The table for the linear equation is summarized below:
d t
3 13
4 18
5 23
6 28
How to complete a table related to a linear function
In this problem we have a two-column table associated to a linear function, the first column of the table represent a set of values of the domain (d) of the function and the second column of the table is for the set of values of the range (t) of the same. We need to fill the second column of the table with the values associated with the range:
d = 3
t = 5 · 3 - 2
t = 15 - 2
t = 13
d = 4
t = 5 · 4 - 2
t = 20 - 2
t = 18
d = 5
t = 5 · 5 - 2
t = 25 - 2
t = 23
d = 6
t = 5 · 6 - 2
t = 30 - 2
t = 28
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Rewrite in simplest terms: 6(8v-7)-10v
Step-by-step explanation:
[tex]6(8v - 7) - 10 \\ 48v - 42 - 10 \\ 48v - 52[/tex]
Which of the expressions below would help you to calculate the percent
increase from Value 1 to Value 2?
Answer:
D. (Value 2 - Value 1) ÷ Value 1Step-by-step explanation:
Percent increase is the percent of the increased value over the initial value.
In our case the increase is represented by the difference of values and the initial value is Value 1.
So the matching choice is D.
=====================================
Answer choices in the comment:
A. Value 2 ÷ Value 1B. Value 1 ÷ Value 2C. (Value 2 - Value 1) ÷ Value 2D. (Value 2 - Value 1) ÷ Value 1ERROR ANALYSIS Describe and correct the error. QRS=VWX by the ASA Congruence Theorem
Answer:
The error made is that the ASA theorem cannot be used here because the congruent side is not directly in between the two congruent angles in either triangle. Really, the information we are given is Angle-Side-Side, not Angle-Side-Angle, and this is not a congruence theorem unless the triangles given are right triangles.
Use the properties of operations to multiply (8-2x) (-0.25x)
_x + _x^2
the _ is the blanks im supposed to fill in
The blanks are -2 and 0.5 respectively, by solving the expression (8 - 2x) *(-0.25x)
What does the term Algebraic Expression means?
In mathematics, an algebraic expression is an expression composed of variables and constants as well as algebraic operations (addition, subtraction, etc.). Terms combine to form expressions.
Solution:
Given the expression, we need to solve it by using the properties of basic multiplication.
= (8 - 2x)*(-0.25x)
= (8*(-0.25x)) + (-2x * (-0.25x))
= -2x + 0.5[tex]x^{2}[/tex]
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Which answer is correct?
(A)4x + y = 6
−2x + y = −5
(B)x + y = 8
2x − 9y = 4
(C)x − 4y = −6
−2x − y = 5
(D) −x + y = 9
9x + 2y = 4
The system of equations best represented by the graph are 4x + y = 6 and −2x + y = −5
How to determine the system of equations represented by the graph?The solution of the equations plotted in the graph can be found by checking the point of intersection of the lines
By examining the given graph we can guess the x and y values of the point of intersection. We need to guess because we do not have a means of getting the exact value from the graph. I guess x = 1.9 and y = -1.4
In order to find the system of equations represented by the graph, we need to solve the equations given in the option and check which one gives us x and y values close to what we guessed from the graph
By Solving 4x + y = 6 and −2x + y = −5:
4x + y = 6 (1)
−2x + y = −5 (2)
Using elimination, subtract (2) from (1), this gives:
6x = 11
x = 11/6 = 1.83
Put x = 11/6 into (1):
4(11/6) + y = 6
y = 6 - 4(11/6)
y = 6 -44/6 = -4/3 = -1.33
Since these calculated values are very close to the guessed values
Therefore, 4x + y = 6 and −2x + y = −5 are the system of equations best
represented by the graph. So option A is the answer
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you roll a six-sided die 20 times. what is the probability of having exactly 8 rolls land on a number greater than 4?
The probability of getting a number greater than 4 when the dice is rolled 20 times is 7.
The number on dice greater than 4 is 2 (that is 5 and 6 on dice) thus the probability of getting a number greater than 4 is
P = 2/6
P = 1/3
This is the probability if the dice were rolled once but if the dice were rolled 20 times thus the probability, in this case, needs to be multiplied by 20
P = 1/3*20
P = 6.66
equivalents to 7
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assume the state of arkansas placed a tax on playing cards of 6 cents per pack. if the state generated $48600 in revenue, how many packs of cards were sold?
The number of pack of cards sold at the state of Arkansas is 8100.
Describe the term division?Multiplication is the complete reverse of division. If participants of 4 add up to 12, then 12 divided into three classes of equally sized results in 4 in each group.For the values given in question.
The tax on playing card in state of Arkansas = 6 cents per pack.
Total revenue generated = $48600.
Divide total revenue by one pack price to get the number of packs.
Number of pack = Total revenue/price of each pack
Number of pack = $48600/6
$48600.Number of pack = 8100
Thus, the number of pack of cards sold at the state of Arkansas is 8100.
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A group of 4 people go to a restaurant and the bill without tax comes to $105.73. Tax is 6%. Remember to round to the nearest hundredth because this is money. After tax is added, you want to leave a 20% tip on the new total. The group of 4 people decides to split the total cost equally. How much will each person pay?
i need the answer fasttttt
Each person need to pay $ 80.88345.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Bill without tax = 105.73
Tax = 6%
So, bill amount after tax = 105. 73 + 105. 73 x 6/100
= 105.73 + 6.3438
= $112.0738
Addition of 20% tip = 112.0738 + 211.46 = $323.5338.
If the amount is divided among 4 people, each will pay
= 323.5338/4
= $ 80.88345
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A model of a car is 1 feet wide and 3 feet long. If the actual car is 15 feet long, what is the width of the actual car?
A. 3 feet
B. 5 feet
C. 15 feet
D. 45 feet
Answer:
5 feet.
Step-by-step explanation:
if we see that 3 feet is the model and 15 feet is the actual, we find the ratio is 3:15 or 1:5. since the width is 1 foot, then we see the actual is 5 feet long.
13.ERROR ANALYSIS Describe and correct the error in
the student's reasoning.
Answer:
Step-by-step explanation:
3. Functions f and g are shown below. Which
best represents
function g?
a. g(x) = f(x) - 3
b. g(x) = -f(x)
c. g(x) = f(x)
d. g(x) = f(x - 2)
Answer:
i think it might be c
Step-by-step explanation:
express (3) - (2tan^2 x) in terms of cos x
The expression of [tex]3-2tan^2x\\[/tex] in terms of [tex]cosx[/tex] is [tex]3-2(\frac{1-cos^2x}{cos^2x})[/tex]. Similarly, any tirigonometric equation can be convereted into other forms of trigonometric functions.
What is trigonometric functions?
Denoting the relation between a right-angled triangle's angle and sides are trigonometric functions, which are periodic functions.
Consider the given expression.
[tex]3-2tan^2x\\[/tex]
Now, substitute [tex]\frac{sinx}{cosx}[/tex] for [tex]tanx[/tex] as follows:
[tex]3-2tan^2x=3-2(\frac{sinx}{cosx})^2\\=3-2(\frac{sin^2x}{cos^2x})[/tex]
Now, all the terms are converted into cos x except the sin x terms in the numerator. Hence, using the relation between sin x and cos x. Substitute [tex]1-cos^2x[/tex] for [tex]sin^2x[/tex].
[tex]3-2tan^2x=3-2(\frac{1-cos^2x}{cos^2x})[/tex]
Now, all the terms are in cos x. Hence, the expression of [tex]3-2tan^2x\\[/tex] in terms of [tex]cosx[/tex] is [tex]3-2(\frac{1-cos^2x}{cos^2x})[/tex]. In the similar way any function can be conveted into other trigonometric functions.
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Decide whether each equation is true for all, one, or no values of x.
Answer:
Theres nothing to see?
Step-by-step explanation:
Answer:
First is one value of x
Second is no values of x
Third is all values of x
Step-by-step explanation:
Please give brainliest!
Which step contains a mistake in solving for the system of equations?
x + 2y = 5
y = 3x - 8
1. x + 2(3x) - 8 = 5
2. x + 6x - 8 = 5
3. 7x = 13
4. x = 13/7
5. 7x 8 5
Answer:
First step, correct answer is (3,1)
Step-by-step explanation:
1.it should be x+2(3x-8)=5
2. x+6x-16=5
3.7x=21
4. 7x/7=21/7
5. x=3
then you can eitheir take x+2y=5 or y=3x-8 i suggets taking second option as it is easier, just input values for x in
) 3x-8=y
6. 3(3)-8= 1
7. x=3, y=1
You are a prep cook in a restaurant. A particular
recipe uses 4 cups sugar. You only need to
make 1/3 of the normal amount. How many cups of sugar should you measure?
Quadrilateral PONY is rotated 180° about the origin.
Draw the image of the rotation
The given quadrilateral PONY is rotated to 180° as P'O'N'Y' and its coordinates are:
P': (2, -7)O': (2, -3)N': (6, -3)Y': (5, -6)What is rotation?A transformation in geometry is an action that moves, flips, or modifies a shape to produce a new shape. A rotation is an example of a transformation where a figure is rotated a set number of degrees around a fixed point (referred to as the center of rotation).The circular motion of an item around a center or axis is the definition of rotation in mathematics. The rotation of the earth on its axis is one of the best examples of rotation in nature.So, rotate the given quadrilateral at 180° as follows:
Given quadrilateral: PONY
P: (7, -2)O: (3, -2)N: (3, -6)Y: (6, -5)Rotate to 180° and plot as follows:
Quadrilateral after rotation: P'O'N'Y'
P': (2, -7)O': (2, -3)N': (6, -3)Y': (5, -6)(Refer to the graph attached below)
Therefore, the given quadrilateral PONY is rotated to 180° as P'O'N'Y', and its coordinates are:
P': (2, -7)O': (2, -3)N': (6, -3)Y': (5, -6)Know more about rotation here:
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Answer:
P': (2, -7)
O': (2, -3)
N': (6, -3)
Y': (5, -6)
Step-by-step explanation:
Give the numerical coefficient of the term.
−7x
The numerical coefficient is _____.
The numerical coefficient is -7
How to determine the numerical coefficient?From the question, the expression is given as
-7x
Considering an expression given as
Ax
The numerical coefficient of the above expression is A
When compared to the expression -7x, we have
The numerical coefficient is -7
So, we can conclude that the numerical coefficient of -7x is -7
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Answer:
-7
Step-by-step explanation:
The numerical coefficient is -7
If f(x)=4x^3+5, then what is the remainder when f(x) is divided by x−3?
Using Remainder theorem
Answer:
113
Step-by-step explanation:
Finding a remainder seems like you should be dividing. Remember everything is a shortcut for something else in math. So first you learn Long Division, but that's too much writing, so then you learn Synthetic Division, but there's an even shorter shortcut. It is called Remainder Theorem. If you just substitute 3 (because x-3 in the question) into the function, and you calculate it, you get the remainder.
f(x) = 4x^3 + 5
f(3) = 4(3)^3 + 5
f(3) = 4(27) + 5
= 108 + 5
= 113
See image.
3. Martin finishes a swim race in 78.934 seconds. His teammate, Abby finishes the race in 83.978 seconds and their last teammate finishes the race in 84.765 seconds.
CHALLENGE: How many minutes in total did they spend completing the race?
Help me pkleasee :((
The number of minutes in total that the three swimmers spent in completing the race is; 4.12795 minutes
How to carry out units conversion?We are given;
Time taken by Martin to finish swimming = 78.934 seconds
Time taken by Abby to finish swimming = 83.978 seconds
Time taken by the last teammate to finish the race = 84.765 seconds
Thus;
Total time taken by the three swimmers to finish the race = 78.934 + 83.978 + 84.765 = 247.677 seconds
Now, we want to know the total time they spent in minutes and we know that the unit of conversion is;
60 seconds = 1 minute
Thus;
247.677 seconds = (247.677 * 1)/60 = 4.12795 minutes
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an isosceles triangle has a base that measures x 2 with legs that measure 4x - 3 and 2x 5. what is the value of x? an isosceles triangle has a base that measures x 2 with legs that measure 4x - 3 and 2x 5. what is the value of x?
The value of x is 4 for the isosceles triangle has a base that measures x+2 with legs that measure 4x-3 and 2x+5.
What is an isosceles triangle?Therefore, an isosceles triangle has two equal sides as well as two equal angles. An equilateral triangle is one in which all of its sides are equal, and a scalene triangle is one in which none of its sides are equal. The characteristics of an isosceles triangle are as follows: There is agreement between two sides. The base of an isosceles triangle refers to the third side of the triangle, which is unequal to the other two sides. The two angles that are opposite the equal sides line up perfectly.
Here,
Since the adjacent sides of isosceles triangles are equal,
4x-3=2x+5
4x-2x=5+3
2x=8
x=4
The isosceles triangle has a base that measures x+2 and legs that measure 4x-3 and 2x+5, so x is equal to 4.
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1. A typical Chinese restaurant will often feature a Special Dinner, in which the customer has the choice of ordering one appetizer and one entree.
a. If there are 8 appetizers and 11 entrees, how many different Special Dinners
are there?
b. If there are 12 appetizers and 7 entrees, how many different Special Dinners
are there?
a) 88 unique special dinners are there if there are 8 appetizers and 11 entrees.
b) 84 unique special dinners are there if there are 12 appetizers and 7 entrees.
Given that,
In a typical Chinese restaurant, the Special Dinner is frequently offered, allowing the customer to select one appetizer and one entrée.
We have to find
a) How many unique special dinners are there if there are 8 appetizers and 11 entrees.
b) How many unique special dinners are there if there are 12 appetizers and 7 entrees.
We solve
a) We just multiply
8×11=88
b) 12×7=84
Therefore, a) 88 unique special dinners are there if there are 8 appetizers and 11 entrees.
b) 84 unique special dinners are there if there are 12 appetizers and 7 entrees.
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